M01 - Compilation

M1 (Compilation)

Contents1) MATHEMATICS ( M 1 ) CAAS Exam June 07...........................................................22) CAAS M01 – MATHS EXAM (07 NOV 08).................................................................33) M1-Mathematics.............................................................................................................45) MODULE 1.....................................................................................................................66) M06.1 – Class Test 16 July 08........................................................................................77) Module One...................................................................................................................218) JAR 66 Module 1 Exam Practice Exam Module 1 Mathematics..................................329)........................................................................................................................................58

1) MATHEMATICS ( M 1 ) CAAS Exam June 07

1. The most useful and widely used graph for technical work in the aviation is :

a. Circle graph or pie chart . b. Continuous line graph .c. Bar graph . *

2. The clearest way to show the proportion of time spent on various activities through out the day :

a. Pictograph .b. Circle graph or pie chart . *c. Broken line graph .

3. Cube root of 27 is :a. 3 . *b. 9 .c. 8 .

4. x = ½ [( 3 + 6 ) – ( 4 – 2 )] . Than x = : a. 1.5 . b. 72 . c. 3.5 . *

5. If x = 3a + 4b . Than b = :a. 4 ( x – 3a ) .b. ( x / 3a ) – 4 .c. ( x – 3a ) / 4 . *

6. If A = ‘ pi ‘ x radius square . Than radius r is equal to :

a. Square root of ( A – ‘ pi ‘ ) .b. Square root of ( A / ‘ pi ‘ ) . *c. ( A / ‘ pi ‘ ) square .

7. When simplified the expression ½ ( 10 + 14 ) 6 will equal to :

a. 2 .b. 420 .c. 72 . *

8. The slope or gradient of a velocity – time graph represent the :

a. Acceleration of the body . *b. The mass of the body .

c. The speed of the body .

9. 0.375 as common fraction : a. 375 / 100 .b. 375 / 1000 . *c. 0.375 / 1000 .

10. When using graph , it is most important than an engineer can :

a. Read and interpret a graph . *b. Apporove a graph .c. Draft a graph .

11. 18 / 10 x 5 / 3 = :a. 3 . *b. 5 . c. 8 .

12. 162.6 divided by 1.24 :a. 131.13 . *b. 13.13 .c. 201.62

13. s = u + at , what is u ?a. u = s – at .*b. u = s + at .c. u = at + s .

14. 3xy = 12 , y = 4 , what is x ?a. 1 . *b. 3 .c. 4 .

15. 16.32 X 0.36 :a. 58.32b. 5.832 . *c. 0.5832 .

16. 0.375 as common fraction : -a. 375 / 100 .b. 375 / 1000 . *c. 0.375 / 1000 .

END

2) CAAS M01 – MATHS EXAM (07 NOV 08)

1. If an Aircraft consumed 500 lbs of fuel after 1.5 hrs of flight time, what is the duration if it used up 2000 lbs of fuel.500 lbs = 1.5 hrs2000 lbs = 1.5 x 4= 6 hrs

2. Convert 0.739 to fraction.a. 0.739

1000

b. 739 100

c. 739 ***1000

3. What type of graph to show aircraft monthly flying hours.Bar Graph

4. What type of graph to show maintenance activitiesLine Graph

5. In a rectangular graph, you need to haveFour sides

6. What type of graph is y = x + 3a. Straight Line ***

7. What is the name of the line before intercept with the curve.Gradient / Slope

8. What type of graph is use for activities for the whole day events over a period of time.Line Graph

9. In 3xy = 12, if y = 4, find x3x4 = 1212x = 12x = 12 / 12

= 110. A fuel tank of maximum fuel of 8000 lbs,

60% is occupied. What is the fuel level60 x 8000100

= 4800 lbs

11. What is the equation (x-y)(x+y) equal to= x² + xy – xy - y²= x² - y² ***

12. What is 3 x 7 x 5 x 2a. 210

13. Find b when (6b – 36b) = (-3a – 7a)-30b = - 10a

How Do I Choose Which Type of Graph to Use? When to Use . . .Line graphLine graphs are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be sued to compare changes over the same period of time for more than one group.Pie ChartPie charts are best to use when you are trying to compare parts of a whole. They do not show changes over time.Bar GraphBar graphs are used to compare things between different groups or to track changes over time. However, when trying to measure change over time, bar graphs are best when the changes are larger.Area GraphArea graphs are very similar to line graphs. They can be used to track changes over time for one or more groups. Area graphs are good to use when you are tracking the changes in two or more related groups that make up one whole category (for example public and private groups).X-Y PlotX-Y plots are used to determine relationships between the two different things. The x-axis is used to measure one event (or variable) and the y-axis is used to measure the other. If both variables increase at the same time, they have a positive relationship. If one variable decreases while the other increases, they have a negative relationship. Sometimes the variables don’t follow any pattern and have no relationship.

3) M1-Mathematics

1. The most common use of graphs during aircraft maintenance is for :-A) The performance of aircraft and their associated systems B) Torque loading fastenersC) The preparation of major modifications

2. If X=3a+4b then:- b= ?

3. The product of 7x3x5x2 is :-A) 17B) 210 C) 7352

4. Solve the following equation for A : A=0.5(30+34)5A) 160B) 185C) 217

5. If an 8 000 litres fuel tank was filled to 60% of total capacity, how much fuel are already on board?

A) 4200 litresB) 4800 litresC) 6000 litres

6. If x=1/2(3+6)-(4-2), then __________A) x=3.5B) x=1.5C) x=72

7. If aeroplane uses 24 gallons of fuel to travel 300 miles, how many gallons will it to travel 750 miles?

A) 60 gallonsB) 75 gallonsC) 80 gallons

8. 162.6 divided by 1.24 equals :-A) 131.13B) 13.13C) 201.62

9. The slope or gradient of velocity time graph represents the :-A) Speed of the bodyB) Acceleration of the bodyC) The mass of the body

10. Which of the following function could be graphed on a typical regulator co-ordinate graph?A) The take-off velocity of an aircraft at a given weightB) The total conduced by an engine over a given timeC) The force required to lift an engine from a storage container

11. Graphs are usually based on a rectangular co-ordinate system where the :-A) Vertical axis is the x-axisB) Vertical axis is the y-axisC) Horizontal axis is the y-axis

12. To create a rectangular co-ordinate graph there must be :-A) Only one quantityB) Two 0r more quantityC) At least four quantity

13. What is the parameter of a square with an area of 64 square centimeters :-A) 32B) 16C) 24

14. If 2x+7=11 then x=?

A) x=9B) x=75C) x=2

Sin () = Old/Harry = Opposite/HypotenuseCos () = And/His = Adjacent/HypotenuseTan () = Old/Aunt = Opposite/Adjacent

A

B

C

opposite

hypotenuse

adjacent

4) M01 – CAAS Cat B Maths Exam (06 Mar 09)

1. If an Aircraft consumed 500 lbs of fuel after 1.5 hrs of flight time, what is the duration if it used up 2000 lbs of fuel.500 lbs = 1.5 hrs2000 lbs = 1.5 x 4

= 6 hrs

2. Convert 0.739 to fraction.d. 0.739

1000

e. 739 100

f. 739 ***1000

3. What type of graph to show aircraft monthly flying hours.Bar Graph

4. What type of graph to show maintenance activities

Bar Graph

5. In a rectangular graph, you need to haveFour sides

A rectangular graph is a plane graph where all regions are four-sided and all edges are oriented in either the vertical or the horizontal direction. In addition the graph enclosure must also be rectangular.

6. What type of graph is y = x + 3b. Straight Line ***

7. A fuel tank of maximum fuel of 8000 lbs, 60% is occupied. What is the fuel level60 x 8000100

= 4800 lbs

8. What is the equation (x-y)(x+y) equal to= x² + xy – xy - y²= x² - y² ***

9. What is 3 x 7 x 5 x 2a. 210

10. tan = opposite / adjacent

11. cos = opposite / hypotenuse

12. tan 20°

13. In mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number

14. Binary of 101 to decimala. 5

15. Binary of 10 to decimala. 2

16. Logarithms of 5, 12a. 5 x 2.718, 12 x 2.718

= 13.59, 32.616

5) MODULE 1

Q1) 5/8 of 60 expressed as a DecimalQ2) log 9 - log 3

Q3) Volume of a cone, diameter 10 metres , height 10 metres

Q4) Surface area of a cylinder , diameter 10 metres , height 10 metres

Q5) Obtuse angle (What is it )

Q6) Polygon

Q7) Rhombus

Q8) Octal No. 19, expressed as a Decimal

Q9) -3 + (-3)

Q10) Aircraft travelled 1250 nautical miles in 2 hours 15 minutes.What was it’s speed in knots

Q11) (x-y) (a-b) (c-d) over(b-a) (y-x) (d-c)

a) -1 b) 1 c) 0

Q12) Total of 1800 lbs of fuel , 45% in the No 1 Tank, 33.5% in No 2 Tank, The remainder in the Centre Tank is equal to;

Q13) For the equation a + b x b - c

a) Exponential b) Quadratic c) Linear

Q14) For the equation y = 2x - 6 Gradient a) 1/ 2 - 6 b) 2/1 c) ½

Q15) 4 5/8 - 2 3/5 + ½

6) M06.1 – Class Test 16 July 08 1. What formula is used to find the area of a circle?

Ans: A = 0.7854 x D2 or A = pi x R2

2. What formula is used to find the volume of a cylinder?Ans: V = 0.7854 x D2 x H.

3. What formula is used to find the area of a rectangle?Ans: A = L x W.

4. What formula is used to find the volume of a rectangular solid?Ans: V = L x W x H.

5. What formula is used to find the area of a triangle?Ans: A = (B x H) divided by 2.

6. What is the significance of the constant pi?Ans: Pi is the ratio of the circumference to the diameter of any circle.

7. What is the value of the constant pi?Ans: Pi = 3.1416.

8. What is meant by the root of a number?Ans: The root of a number is one of two or more equal numbers that, when multiplied together, will produce the number.

9. What is the eighth power of 2?Ans: 256.

10. What is the square root of 4,096?Ans: 64.

11. What is meant by a negative number?Ans: A number less than 0, or a number that is preceded by a minus sign.

12. What is meant by a ratio and how is a ratio expressed?

Ans: A fraction that compares one number to another; for example, 6:2 is a ratio.

13. What power of 10 is equal to 1,000,000?Ans: 10 to the sixth power.An easy way to tell the power of 10 to which a number has been raised is to count the number of places the decimal would have to be moved to leave a number between 1 and 10. In this problem, the decimal would have to be moved six places to the left. 1,000,000 is 1 x 10^6

14. What force is exerted on the piston in a hydraulic cylinder if the area of the piston is 1.2 square inches and the fluid pressure is 850 PSI?Ans: 1,020 pounds.The force exerted on a piston by hydraulic fluid is found by multiplying the area of the piston by the amount of pressure acting on each square inch of the piston. In this problem the area is 1.2 square inches and a pressure of 850 pounds acts on each square inch. The force is 1,020 pounds.

15. Find the square root of 3,722.1835.Ans: 61.0097.The square root of a number is the number that, when multiplied by itself, gives the number. By using an electronic calculator, we find that the square root of 3,722.1835 is 61.00970005.

16. A rectangular shaped fuel tank measures 27-1/2 inches in length, 3/4 foot in width, and 8-1/4 inches in depth. How many gallons will the tank contain? (231 cu in = 1 gal)Ans: 8.80.The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together. All dimensions must be in the same units. 3/4 foot = 9 inches.V = L x W x D= 27.5 x 9 x 8.25= 2,041.875 cubic inchesSince there are 231 cubic inches in each gallon, we must divide the total volume of 2,041.875 by 231 to find the capacity of the tank in gallons.Capacity = 2041.875 ÷ 231= 8.83 gallonsThis tank will hold 8.83 gallons of fuel

17. Select the decimal which is most nearly equal to 77/64.Ans: 1.2031.To convert a common fraction into a decimal fraction, divide the numerator by the denominator.77 ÷ 64 = 1.203125

18. What is the speed of a spur gear with 42 teeth driven by a pinion gear with 14 teeth turning 420 RPM?Ans: 140 RPM.The speed ratio is the reciprocal of gear ratio. The spur gear with 42 teeth is driven by a pinion gear with 14 teeth. This is a gear ratio of 3:1. The spur gear will turn at 1/3 the speed of the pinion gear. If the pinion gear turns at a speed of 420 RPM, the spur gear will turn at a speed of 420 ÷ 3 = 140 RPM.

19. What is the ratio of a gasoline fuel load of 200 gallons to one of 1,680 pounds?Ans: 5:07Gasoline has a nominal weight of 6 pounds per gallon. So, 200 gallons of gasoline will weigh 1,200 pounds. The ratio of a load of 1,200-pound load to one of 1,680 pounds is the ratio of:1,200 ÷ 1,680 = 0.7142.The ratio 5:7 is 0.7142.The ratio of 2:3 is 0.6667.The ratio of 5:42 is 0.1190.

20. A four-cylinder aircraft engine has a cylinder bore of 3.78 inches and is 8.5 inches deep. With the piston on bottom center, the top of the piston measures 4.0 inches from the bottom of the cylinder. What is the approximate piston displacement of this engine?Ans: 200 cubic inches.

The piston displacement of one cylinder of a reciprocating engine is found by multiplying the area of the piston head by the length of the stroke. The area of the piston is found by squaring the bore (3.78 inches in this problem) and multiplying this by the constant 0.7854 (one-fourth of pi). When the area of 11.22 square inches is multiplied by the stroke of 4.5 inches (the depth of the cylinder minus the distance from the top of the piston at BDC to the bottom of the cylinder), we find that the displacement of one cylinder is 50.49 cubic inches.This is a four-cylinder engine, so the total displacement is four times that of a single cylinder. The total displacement is 201.96 cubic inches.Area = (pi ÷ 4) x B^2= 0.7854 x 3.78^2= 11.22 square inchesStroke = 8.5 - 4 = 4.5 inchesPD = Area x Stroke x No. cylinders= 11.22 x 4.5 x 4= 201.96 cubic inches

21. How many gallons of fuel will be contained in a rectangular-shaped tank which measures 2 feet in width, 3 feet in length, and 1 foot 8 inches in depth? (7.5 gal = 1 cu ft)Ans: 75The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together.V = L x W x D= 3 x 2 x (20 ÷ 12)= 10 cubic feetSince 1 cubic foot of tank space will hold 7.5 gallons, and there are 10 cubic feet of space in the tank, the tank will hold 10 times 7.5 gallons or 75 gallons of fuel.

22. 1.21875 is equal toAns: 39/32.Divide the decimal fractional part of this mixed number by the decimal equivalent of 1/64.0.21875 ÷ 0.015625 = 14The common fraction equivalent to 1.21875 is 1-14/64. This is the same as 78/64 or 39/32.

23. (Refer to Figure 54.) Compute the area of the trapezoid.

Ans: 52.5 square feet.The area of a trapezoid is found by multiplying its altitude (5 feet in this problem) by the average length of the two bases (the average of 9 feet and 12 feet is 10.5 feet). The area of this trapezoid is 5 x 10.5 = 52.5 square feet.

24. Find the value of 10 raised to the negative sixth power.Ans: 0.000001.

Ten raised to the negative sixth power (10^-6) is equal to 0.000 001. This negative number is the reciprocal of the positive sixth power of ten. It is found by dividing the number 1 by the sixth power of 10 (1,000,000).

25. An engine develops 108 horsepower at 87 percent power. What horsepower would be developed at 65 percent power?Ans: 80

If an engine develops 108 horsepower at 87 percent power, its 100 percent power is 108 ÷ 0.87 = 124.13 horsepower. Its horsepower at 65 percent power is found by multiplying 124.13 by 0.65, or 80.68 horsepower.

26. A rectangular-shaped fuel tank measures 60 inches in length, 30 inches in width, and 12 inches in depth. How many cubic feet are within the tank?Ans: 12.5.The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together.V = L x W x D= (60 ÷ 12) x (30 ÷ 12) x (12 ÷ 12)= 5 x 2.5 x 1= 12.5 cubic feetThe volume is 12.5 cubic feet.

27. Solve the equation.4 - 3[-6(2 + 3) + 4] =Ans: 821. Begin this problem by working the inside parentheses, and then work outward.(2 + 3) = 5(-6 x 5) = -30(-30 + 4) = -262. Next, the multiplication is done.3 x -26 = -783. Now, perform the subtraction.4 - (-78) = 82

28. If the volume of a cylinder with the piston at bottom center is 84 cubic inches and the piston displacement is 70 cubic inches, then the compression ratio isAns: 6 to 1.The volume of a cylinder with the piston at the top of its stroke is found by subtracting the piston displacement of the cylinder from the volume of the cylinder with the piston at the bottom of its stroke. Volume at top = Volume at bottom - displacement = 84 - 70 = 14 cubic inchesThe compression ratio of the cylinder is the ratio of the volume of the cylinder with the piston at the bottom of its stroke to the volume of the cylinder with the piston at the top of its stroke.C.R. = Volume at bottom ÷ volume at top = 84 ÷ 14 = 6This engine has a compression ratio of 6:1.

29. Solve the equation.(32 x 3/8) ÷ 1/6 =Ans: 721. First, work the part of the problem inside the parenthesis:(32 x 3/8) = 12

2. Now divide 12 by 1/6. To divide by a fraction, invert the divisor (1/6) and multiply.12 ÷ 1/6 = 12 x 6 = 72.

30. (Refer to Figure 53.) Solve the equation.

Ans: 0.0419.

The square root of 31 is 5.5677. The square root of 43 is 6.5574. The square of 17 is 289. (5.5677 + 6.5574) ÷ 289 = 0.0419

31. Solve the equation.-6[-9(-8 + 4) - 2(7 + 3)] =Ans: -961. Begin the problem by working the inside parentheses in the first term.(-8 + 4) = -42. Combine the factors in the first term.-9 x -4 = 363. Clear the parenthesis in the second term.(7 + 3) = 104. Multiply this value by 2.10 x 2 = 205. Combine the two terms in the brackets.36 - 20 = 166. Multiply this by -6.-6 x 16 = -96

32. Find the square root of 1,746.Ans: 41.7852.

The square root of a number is the number that, when multiplied by itself, gives the number. By using an electronic calculator, we find that the square root of 1,746 is 41.785165.

33. What is the piston displacement of a master cylinder with a 1.5-inch diameter bore and a piston stroke of 4 inches?Ans: 7.0686 cubic inches.The piston displacement of a master cylinder is found by multiplying the area of the piston head by its stroke. The area of the piston is found by squaring its diameter (1.5 inch in this problem) and multiplying this by the constant 0.7854 (one-fourth of pi). When the area of 1.767 square inches is multiplied by the

stroke of 4.0 inches, we find that the displacement of the master cylinder to be 7.0686 cubic inches.PD = 0.7854 x B^2 x S= 0.7854 x 1.5^2 x 4= 7.0686 cubic inches

34. Sixty-five engines are what percent of 80 engines?Ans: 81 percent.To find the percentage of engines represented by 65 out of 80, we find the ratio of 65 to 80 by dividing 65 by 80.65 ÷ 80 = 0.8125Then we change this decimal fraction into a percentage by multiplying it by 100. Sixty-five engines is 81.25 percent of 80 engines.


Ans: 5To solve this equation, follow these steps: clear all of the parentheses, perform the multiplication, then the addition. Finally take the square root of the number you have just obtained. Any number raised to the zero power is 1.(-4)^0 = 1The fourth root of 1,296 is the same as 1,296 raised to the 1/4 power.1,296^0.25 = 6The square of the square root of 3 = 3

36. Select the fraction which is equal to .020.Ans: 1/50.3/15 is equal to 0.20.1/5 is equal to 0.20. 1/50 is equal to 0.020.

37. A pinion gear with 14 teeth is driving a spur gear with 42 teeth at 140 RPM. Determine the speed of the pinion gear.Ans: 420 RPM.

The speed ratio is the reciprocal of the gear ratio. The spur gear with 42 teeth is driven by a pinion gear of 14 teeth. This is a gear ratio of 3:1. The spur gear will turn at 1/3 the speed of the pinion gear. If the spur gear turns at a speed of 140 RPM, the pinion gear will have to turn at a speed of 420 RPM.

38. (Refer to Figure 55.) Find the area of the triangle shown.

Ans: 6 square inches.

The area of a triangle is one half of the product of its base times its altitude. The base of this triangle is 4 inches and the altitude is 3 inches. The area is (4 x 3) ÷ 2 = 6 square inches.

39. Solve the equation.Ans: (64 x 3/8) ÷ 3/4 = 32First work the part of the problem inside the parenthesis, and then do the division.64 x 3/8 = 2424 ÷ 3/4 = 32

40. The number 3.47 x 10 to the negative fourth power is equal toAns: 0.000347The value of 3.47 x 10^-4 is found by multiplying 3.47 by 1 divided by 10,000 (1 x 10^4).3.47 x 10^-4 = 0.000347

41. Find the cube of 64.Ans: 262,144.00The cube of a number is found by multiplying the number by itself three times.64^3 = 64 x 64 x 64 = 262,144

42. A certain aircraft bolt has an overall length of 1-1/2 inches, with a shank length of 1-3/16 inches, and a threaded portion length of 5/8 inch. What is the grip length?Ans: 0.5625 inch.

The grip length of a bolt is the length of the unthreaded portion of the shank. If the shank is 1-3/16 (1.1875) inches long, and the threaded portion is 5/8 (0.625) inch, the grip length is 1.1875 - 0.625 = 0.5625 inch.

43. Maximum engine life is 900 hours. Recently, 27 engines were removed with an average life of 635.3 hours. What percent of the maximum engine life has been achieved?Ans: 71 percent.

In this problem, 900 hours represents 100 percent of the engine life. The percentage represented by 635.30 hours can be found by dividing 635.30 by 900, and multiplying this answer by 100.635.30 ÷ 900 = 0.70580.7058 x 100 = 70.58 percent

44. What is the ratio of 10 feet to 30 inches?Ans: 4:1

Ten feet is equal to 120 inches. The ratio of 120 ÷ 30 is 4:1.

45. Which decimal is most nearly equal to a bend radius of 31/64?Ans: 0.4844.To convert the common fraction 31/64 into a decimal fraction, divide the numerator, 31, by the denominator, 64.31 ÷ 64 = 0.484375

46. (Refer to Figure 56.) Compute the area of the trapezoid.

Ans: 10 square feet.

The area of a trapezoid is found by multiplying its altitude (2 feet in this problem) by the average length of the two bases (the average of 4 feet and 6 feet is 5 feet). The area of this trapezoid is 10 square feet.


Ans: 14.00.1. First, solve the parts of the problem inside parentheses:(-35 + 25) = (-10)2. Combine the factors (the parts) of the first term (the part of the problem to the left of the plus sign).(-10) x (-7) = 70

3. Clear the parenthesis on the right of the plus sign by raising 16 to its ^-2 power.16^-2 = 1/16^2 = 1/256 = 0.0039064. Multiply the two factors of the second term.(3.1416) x (0.003906) = 0.012275. Add the two terms above the line.70 + 0.0122 = 70.01226. Divide this by the square root of 25, which is 5.70.0122 ÷ 5 = 14.002

48. Find the square root of 1,824.Ans: 0.42708 x 10 to the second power.The square root of 1,824 is 42.708. 42.708 x 10^-2 = 0.42708.42708 x 10^2 = 42.708

49. Which alternative answer is equal to 16,300?Ans: 1.63 x 10 to the fourth power.

1.63 x 10^4 = 16,3001.63 x 10^-3 = 0.00163163 x 10^-2 = 1.63

50. An airplane flying a distance of 875 miles used 70 gallons of gasoline. How many gallons will it need to travel 3,000 miles?Ans: 240

If an airplane uses 70 gallons of gasoline while flying 875 miles, it is getting 875 ÷ 70 = 12.5 miles per gallon of fuel burned. At this rate of fuel consumption, it will require 240 gallons of fuel to fly 3,000 miles. 3,000 ÷ 12.5 = 240


Ans: -5.20.

This problem can be rewritten as 125 ÷ -4, divided by -36 ÷ -6.125 ÷ -4 = -31.25-36 ÷ -6 = 6-31.25 ÷ 6 = -5.208

52. 8,019.0514 x 1/81 is equal to the square root ofAns: 9,801.00Solve this problem in two steps:1. Multiply 8,019.0514 by 1/81. This is the same as dividing it by 81.8,019.0514 x 1/81 =8,019.0514 ÷ 81 = 992. Square 99 to find the number of which 99 is the square root.99^2 = 9,801.

53. A blueprint shows a hole of 0.17187 to be drilled. Which fraction size drill bit is most nearly equal?Ans: 11/64.The hole specified on the blueprint has a diameter of 0.17187 inch. It could be drilled with a 11/64 drill.11/64 is equal to 0.171875.9/32 is equal to 0.28125.11/32 is equal to 0.34375.

54. The result of 7 raised to the third power plus the square root of 39 is equal toAns: 349.24.

7 raised to the 3rd power is 343. The square root of 39 is 6.245. The sum of these two numbers is 349.245.

55. Select the fractional equivalent for a 0.0625 inch thick sheet of aluminum.Ans: 1/16.In order to change this decimal fraction into a common fraction, divide the number by the decimal equivalent of 1/64 (0.015625).0.0625 ÷ 0.015625 = 4/64This is the same as 1/16 inch.

56. How much current does a 30-volt motor, 1/2 horsepower, 85 percent efficient, draw from the bus? (Note: 1 horsepower = 746 watts)Ans: 14.6 amperes.There are 746 watts in one horsepower. The motor produces one-half horsepower (373 watts) at 100 percent efficiency, but it is only 85 percent efficient. 373 ÷ 0.85 = 438.8 watts of power used by the motor. Current drawn by the motor is found by dividing the power by the voltage:I = P ÷ EI = 438.8 ÷ 30I = 14.62 amps

57. What is the square root of 4 raised to the fifth power?Ans: 32

The square root of four is two. Two raised to the fifth power is 32.

58. Select the container size that will be equal in volume to 60 gallons of fuel. (7.5 gal = 1 cu ft)Ans: 8.0 cubic feet.

Since a one-cubic-foot container will hold 7.5 gallons, an 8-cubic-foot container will hold 60 gallons. 60 ÷ 7.5 = 8

59. The radius of a piece of round stock is 7/32. Select the decimal which is most nearly equal to the diameter.Ans: 0.4375.

The diameter of the stock is two times the radius. We need to find the decimal equivalent of 2 x 7/32, or 7/16 inch. By dividing the numerator by the denominator, we find that we will need a piece of round stock with a diameter of 0.4375 inch.

60. An engine of 98 horsepower maximum is running at 75 percent power. What is the horsepower being developed?Ans: 73.50.

Seventy-five percent of 98 horsepower is equal to 98 x 0.75 = 73.50 horsepower.

61. Express 5/8 as a percent.Ans: 62.5 percent.A percentage is a decimal fraction with 100 as its denominator. To convert 5/8 into a percentage, divide five by eight and multiply this by 100.5 ÷ 8 = 0.6250.625 x 100 = 62.5 percent

62. The total piston displacement of a specific engine isAns: the volume displaced by all the pistons during one revolution of the crankshaft.

The piston displacement of an engine is the total volume swept by the pistons in one revolution of the crankshaft. The piston displacement is found by multiplying the area of the piston head by the length of the stroke (this gives the displacement of one cylinder). Multiply the displacement of one cylinder by the number of cylinders in the engine.

63. (Refer to Figure 57.) Determine the area of the triangle formed by points A, B, and C. A to B = 7.5 inches. A to D = 16.8 inches

Ans: 63 square inches.The area of a triangle is equal to one-half the product of its base and its altitude. In this problem, the base is the distance A to D, which is 16.8 inches (this is the same as the distance B to C). The altitude is the distance A to B, which is 7.5 inches. Area = (16.8 x 7.5) ÷ 2= 126 ÷ 2= 63 square inches

64. What is the square root of 16 raised to the fourth power?Ans: 256

The square root of 16 is 4. 4 raised to the 4th power is 256.

65. Solve the equation.(-3 + 2)(-12 - 4) + (-4 + 6) x 2Ans: 201. Begin this problem by clearing the parentheses.(-3 + 2) = -1(-12 - 4) = -16(-4 +6) = 22. Then perform the multiplication.-1 x -16 = 162 x 2 = 43. And finally the addition.16 + 4 = 20

66. What is the speed ratio of a gear with 36 teeth meshed to a gear with 20 teeth?Ans: 5 to 9.

The speed ratio is the reciprocal of the gear ratio. The large gear has 36 teeth and the small gear has 20 teeth. This is a gear ratio of 1.8:1, or a speed ratio of 1:1.8.5 to 12 is a speed ratio of 1:2.4.6.6 to 12 is a speed ratio of 1:1.818.5 to 9 is a speed ratio of 1:1.8.

67. Solve the equation.2/4 (30 + 34) 5 =Ans: 160.

First, solve the part of the problem inside the parenthesis, then multiply by 2/4, and finally multiply by 5.(30 + 34) = 6464 x 2/4 = 32

32 x 5 = 160

68. Find the square root of 124.9924.Ans: 1,118 x 10 to the negative second power.The square root of 124.9924 is 11.18.111.8 x 10^3 = 111,800.1118 x 10^-2 = 0.0011181,118 x 10^-2 = 11.18

69. A six-cylinder engine with a bore of 3.5 inches, a cylinder height of 7 inches and a stroke of 4.5 inches will have a total piston displacement ofAns: 259.77 cubic inches.The piston displacement of one cylinder of a reciprocating engine is found by multiplying the area of the piston head by the length of the stroke. The area of the piston is found by squaring the bore (3.5 inches in this problem) and multiplying this by the constant 0.7854 (one fourth of pi). When the area of 9.621 square inches is multiplied by the stroke of 4.5 inches, we find that the displacement of one cylinder is 43.295 cubic inches.This is a six-cylinder engine, so the total displacement is six times that of a single cylinder. The total displacement is 259.77 cubic inches.Area = (pi ÷ 4) x B^2= 0.7854 x 3.5^2= 9.621 square inchesStroke = 4.5 inchesPD = Area x Stroke x No. cylinders= 9.621 x 4.5 x 6= 259.77 cubic inches

70. The parts department’s profit is 12 percent on a new magneto. How much does the part cost if the selling price is $145.60?Ans: $130.00In this problem, the cost of the magneto is equal to 100 percent. Since a 12 percent profit is specified, the selling price must be 112 percent. If the selling price (112%) is equal to $145.60, the cost (100%) can be found by dividing the selling price by 112% (by 1.12).$145.60 ÷ 1.12 = $130.00


Ans: 11.9.1. Begin this problem by clearing the parentheses.(-5 + 23) = 18(3^-3) = 0.037The square root of 64 = 8

2. Perform the multiplication in the numerator.18 x -2 = -360.037 x 8 = 0.2963. Perform the addition in the numerator.-36 + 0.296 = -35.7044. Perform the division in the denominator.-27 ÷ 9 = -35. Divide the numerator by the denominator.-35.704 ÷ -3 = 11.90

72. Solve the equation.[(4 x -3)+(-9 x 2)] ÷ 2 =Ans: -15In a problem of this type, work from the inside outward:1. First solve the parts of the problem inside the parentheses.4 x -3 = -12-9 x 2 = -182. Now combine the two values just found.-12 + -18 = -303. Divide this answer by 2.-30 ÷ 2 = -15

73. Express 7/8 as a percent.Ans: 87.5 percent.A percentage is a decimal fraction with 100 as its denominator. To convert 7/8 into a percentage, divide seven by eight and multiply this by 100.7 ÷ 8 = 0.8750.875 x 100 = 87.5 percent

74. What size sheet of metal is required to fabricate a cylinder 20 inches long and 8 inches in diameter? (Note: C = pi x D)Ans: 20" x 25-9/64".The sheet metal needed to fabricate a cylinder 20 inches long and 8 inches in diameter is 20 inches long and 25-9/64 inches wide.8 x pi (3.1416) = 25.132825.1328 is slightly less than 9/64

75. A rectangular-shaped fuel tank measures 37-1/2 inches in length, 14 inches in width, and 8-1/4 inches in depth. How many cubic inches are within the tank?Ans: 4,331.25.The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together.V = L x W x D= 37.5 x 14 x 8.25= 4,331.25 cubic inches

76. If an engine is turning 1,965 rpm at 65 percent power, what is its maximum rpm?

Ans: 3,023.00

1,965 rpm is 65% of 3,023 rpm.1,965 ÷ 0.65 = 3,023

7) Module One

1. What is the tangent of 90o? # a) Positive infinity b) Negative infinity c) 0

2. A cuboid has dimensions of 4 cm, 6cm and 12 cm. What is its volume? A) 2.88 m3 B) 0.028 m3# C) 0.000288m3

3. Work out the following sum: 4 {2 (5 – 1) – 3} + 8 a) 37 # b) 28 c) 54

4. 100000 in binary is what number in decimal? a) 16 # b) 32 c) 64

5. D in hexidecimal is what number in decimal? a) 8 # b) 13 c) 17

6. In the following equation what is the y-intercept? 4y = 2x + 8 a) 4 # b) 2 c) 8

7. Two angles of a triangle are 68 o and 32 o. Therefore the third angle must be a) 63o b) 114o # c) 80o

8. Solve the following equation to find x 4x + 8y = 64 2x – 8y = 86 a) 5 # b) 25 c) 125

9. Simplify the following (w + z)(x – y)(y – w) (y – x)(w – y)(w + z)# a) +1 b) -1 c) 0

10. 101012 + 110012 = a) 462 b) 468# c) 4610

11. Which of the following formulae are correct for the triangle shown?

# a) C2 = A2 + B2 b) B2 = C2 + A2

c) A2 = C2 + B2

12. A rectangle 11cm x 120cm. What is its area in m2 a) 1320 b) 13.2 # c) 0.132

13. What is 738 in binary coded decimal? a) 111100010 b) 1011100010 # c) 11100111000

14. If a wheel of radius R revolves ½ a turn, how many radians does it turn through? a) 2p radians # b) p radians c) 2R2 radians

15. If there are two similar angles in a right triangle, these angles are # a) complementary b) supplementary c) subordinate Page 2 - Mod 1

16. The surface area of a cone whose flat is 10 cm and diameter is 8 cm is a) 80 p # b) 40 p c) 120 p

17. (A + B)4 is (A + B)2 # a) (A + B)2 b) A + B c) (A + B)6

18. An equilateral triangle has a) 2 equal sides b) no equal sides # c) 3 equal sides

19. 4 3/8 – 2 1/4 + 1/8 = a) 2 1/8 b) 2 1/2 # c) 2 1/4

20. 11/16 + 5/8 = a) 55/128 # b) 21/16 c) 10/11

21. Given 43 - x = 21, find the value of x # a) 43 - 21 b) 43 + 21 c) 43 / 21

22. ¾ multiplied by 0.82 is equal to a) 1.23 # b) 0.615 c) 2.46

23. 7/6 can be expressed as a) 2.6 b) 1.6 # c) 1.166

24. The ratio of 6:5 can be expressed as a) 20: 25 # b) 24: 20 c) 10: 16

25. 143 can be expressed as a) 14 x 3 # b) 14 x 14 x 14 c) 14 + 14 + 14

26. 0.0000413 can be written as# a) 413 x 10-7 b) 0.413 x 10-7 c) 4.13 x 10-7

27. 5/8 + 3/4 = a) 11/4 # b) 11/8 c) 8/8

28. The LCD for the problem 1/6 + 1/5 + 1/17 + 1/2 is a) 1020 b) 17 # c) 510

29. The formulae for calculating the area of a right angled triangle is a) ½ height + base b) ½ base / height # c) ½ (base x height)

30. The area of a circle whose circumference is given as 12cm is approximately # a) 11.3 sq. cm b) 3.8 sq. cm c) 38 sq. cm

31. Area of a right circular cone is # a) p x r x l b) (p x r x l) + 2 p x r x r c) 2/3 (p x r x l)

32. log 9 - log 3 = # a) log 3 b) log 6 c) log 9

33. The three angles of a triangle summed together equal a) 90° # b) 180° c) 360°

34. In a right-angled triangle the other two angles are both 45°. The length of the opposite side can be calculated by # a) sin 45° x length of the hypotenuse side of the triangle b) cos 45° x length of the adjacent side of the triangle c) sin 45° x length of the adjacent side of the triangle

35. Given that a = X + B, what is y equal to y a) a + X B b) X - B a # c) X +B a

36. Calculate (+ 3) - (- 4) a) -1 # b) +7 c) -7

37. to convert imperial gallons to liters, multiply by # a) 4.5 b) 5.4 c) 4.7

38. Express 9/20 as a percentage # a) 45 % b) 40 % c) 47 %

39. To find the area of a circle, multiply # a) the square of the radius by p b) the square of the circumference by the radius c) twice the radius by p

40. How many centimeters is in an inch? a) 25.4 b) 0.254 # c) 2.54

41. Make L the subject of the formulae 2pfL = x a) L = 2pf b) L = 2pf x # c) L = x 2pf 42. Find the lowest common denominator of 6; 7; 8 a) 84 # b) 168 c) 336

43. The circumference of a circle is found by a) dividing the diameter by 3.142 # b) multiplying the diameter by 3.142 c) multiplying the radius by 3.142

44. What torque loading would you apply to a nut if the force is 50 lbs, exerted 2 feet from its axis? # a) 100 lbs.ft b) 251 lbs.ft c) 600 lbs.ft

45. 67 divided by 127 is equal to a) 1/20 # b) 1/128 c) ½

46. The formula for calculating the torque loading on a nut or bolt is

a) Force used x diameter of the bolt # b) Force used x lever length of the spanner c) Lever length of the spanner Threads per inch 47. Calculate the height of an obtuse triangle whose base is X cm and the area is Y square cm. a) Y x 2 x X B) Y + X 2 # c) Y x 2 X 48. How is the area of a circle calculated? # a) r2 x 3.142 b) d2 x 3.142 c) 2 x 3.142 x r

49. Solve the following 9/4 + 5/12 + 1 3/8 = # a) 4 1/24 b) 2 25/24 c) 4 1/12

50. The specific torque loading for a bolt is 50 lbs.ins but an extension of 2” is needed to reach the bolt in addition to the 8” torque wrench. What will the actual reading? a) 54 lb.ins # b) 40 lb.ins c) 60 lb.ins

51. Express the fraction 7 / 8 as a decimal # a) 0.875 b) 0.785 c) 0.878

52. Solve 0.75 X 0.003 a) 0.225 b) 0.0225 # c) 0.00225

53. Convert 162 knots to mph# a) 186 mph b) 176 mph c) 196 mph

54. To convert inches to millimeters, it is necessary to# a) multiply by 25.4 b) divide by 25.4 c) multiply by 2.54 55. ¾ x 82 = a) 123 # b) 61.5 c) 81.5

56. A circular patch is held together by seven equally spaced rivets, what is their angular relationship? a) 51.50o# b) 51.43o c) 52o

57. Add together; 3/4, 5/16, 7/8 and 0.375

a) 2 1/8 b) 2 ¼ # c) 2 5/16

58. Given that A = X + BY, what is Y equal to? a) A - X minus B b) A - X add B # c) A - X divided by B Page 7 - Mod 1

59. A right-angled triangle has sides of 3 inches and 4 inches, what will the third side be? a) 6 inches # b) 5 inches c) 5.5 inches

60. To convert pounds of fuel into kilograms, it is necessary to a) multiply by 4536 # b) multiply by 0.4536 c) divide by 0.4536

61. If resin to hardener is used in the ratio of 1000:45, how much hardener is used with 60 grams of resin a) 47 grams # b) 2.7 grams c) 145 grams

62. Solve the following 11/16 + 5/8 a) 55/128 # b) 1 5/16 c) 1 1/10 63. 6 mm is equal to a) 0.625” b) 0.375” # c) 0.236” 64. To work out the circumference of a circle# a) D x 3.142 b) D x 0.3142 c) D - 3.142 65. Weight is equal to a) volume x gravity b) mass x acceleration # c) mass x gravity

66. 8 + 4[5 x 2 (5 – 9/3)]# a) Eighty Eight b) Forty Eight c) Twelve 67. To convert gallons to liters a) multiply by 0.568 # b) multiply by 4.55 c) multiply by 0.00455

Page 8 - Mod 1

68. An equilateral triangle has a) two equal side b) no equal sides # c) three equal sides 69. sin ø =

a) C/A# b)A/C c) B/C

70. Cos A = a) 1.2# b) 0.8 c) 0.6

71. 2x – 8y = 14 and 4x + 8y = 16; x = a) –1/2 # b) 5 c) 3

72. 2x – 3 = 4; x = # a) 3.50 b) –3 c) 7

73. If y / x = 4 and y = 5 then x = a) 20 # b) 1 ¼ c) 4 / 5

Page 9 - Mod 1

74. V = (a + b) r2 Find a a) V – r2 – b b) (V – b)/ r2# c) V / r2 – b

75. A quadrilateral with only two parallel sides is a # a) Trapezoid b) Trapezium c) Rhombus

76. 2x2z2 (3x – z2) =# a) 6x3z2 – 2x2z4 b) 6x2z2 – 2x2z2 c) 6x2z2 + 3x – z2

77. A cylinder has a diameter of 20 cm and a length of 20 cm, what is its volume? a) 400cm3 b) 1240cm3 # c) 6200cm3

78. 3 1/8 – 1 1/5 = # a) 1 37/40 b) 1 3/40 c) 2 3/40

79. Make m the subject of the formula y = mx + c # a) y - c x b) y - x c c) y - c x

80. Make x the subject of the formula y = mx + c # a) y - c m b) y - m c

c) y - c m

81. Make c the subject of the formula y = mx + c a) y + mx # b) y - mx c) mx - y

82. What is the formula for calculating the curved area of a cone? a) p x radius2 x height# b) p x radius x height c) 2/3 x p x radius x height

83. A triangle with equal angles is called a) isosceles # b) equilateral c) right angled

84. Two gears are in mesh, one is larger than the other, the smaller gear rotates a) at the same speed b) at a lower speed # c) at a faster speed

85. Calculate 10 x 23 + 10 x 25 a) 32,008,000 b) 520 # c) 400

86. In a right angle triangle, the sine of an angle is # a) opposite divided by hypotenuse b) adjacent divided by hypotenuse c) opposite divided by adjacent

87. In a right angle triangle, the tangent of an angle is a) opposite divided by hypotenuse b) adjacent divided by hypotenuse # c) opposite divided by adjacent

88. In a right angle triangle, the cosine of an angle is a) opposite divided by hypotenuse # b) adjacent divided by hypotenuse c) opposite divided by adjacent

89. Octal is to the base of a) 2 b) 16 # c) 8

90. One radian is equal to # a) 57.5o b) 90o c) 75o

91. The surface area of a cylinder of diameter 10 cm and height 10cm, is # a) 100p b) 50p c) 80p 92. A parallelogram has a base 120cm and height 11 cm. What is the area? a) 1.32 m2# b) 0.132 m2

c) 0.0132 m2 93. The name given to this shape is # a) Parallelogram

b)Trapezoid c) Rhombus 94. The area of this shape is calculated by

# a) Base x Height b) ½ Base x Height c) Perimeter squared

95. The name of this shape is

a) Parallelogram b) Trapezium # c) RhombusPage 12 - Mod 1

96. The area of the shape is calculated by

# a) ½ height x base b) ½ base x ½ height c) ½ height + twice base 97. A triangle with equal sides is a) Isosceles b) Acute # c) Equilateral 98. Two gears are in mesh, one has twice the number of teeth as the other a) the gear with fewer teeth rotates slower than the other # b) the gear with fewer teeth rotates faster than the other c) the two gears rotate at the same speed 99. The area of the curved surface area of a cone is (where r = radius; h = vertical height and l = slant height) a) 1/3pr2h b) pr2h# c) prl 100. What is the area of a cuboid? # a) height x length x width

b) height x ½ base x height c) height x ½ base x length

101. To find the area of a circle, multiply # a) the square of the radius by p b) the square of the circumference by the radius c) twice the radius by p

102. 4 – 6 – 9 - 3 + (- 3) a) 4.5 # b) 3.5 c) 4

103. An aircraft travels 2150 nautical miles in 2 hours 30 minutes What is the average speed of the aircraft? a) 600 knots # b) 860 knots c) 550 knots

104. Locus points plotted equidistant from a central points represent a) diameter b) radius # c) circumference

105. A circle contains a) 4p radians # b) 2p radians c) 2pr radians

106. What is the surface area of a cylinder whose diameter is 20cm and height of 15 cm? a) 942p b) 350p # c) 300p

107. An oblique pyramid is one which has its axis # a) not perpendicular to its base b) perpendicular to its base c) parallel to its base

108. An input gear has 20 teeth and the output gear has 120 teeth. If the input gear rotates 360 degrees, the output gear will rotate a) 90 degrees b) 45 degrees # c) 60 degrees

109. A line from the centre of a circle is called a) its segment b) diameter # c) radius

110. Four percent of 0.01 is a) 0.04 b) 0.004 # c) 0.0004

111. (x - 3)(x + 5) = a) x2 - 15 # b) x2 + 2x - 15 c) x2 + 2x

112. (6+2)2 X 2 – (2 X 45) =# a) 38

b) 218 c) 128 113. V = (a + b) r2 Find a a) V – r2 – b b) (V – b) / r2 # c) V / r2 - b

114. Give the names of a triangle, which has two sides equal in length and two equal angles. a) Equilateral # b) Isosceles c) Obtuse

115. 17 degrees 49 minutes and 10 seconds added to 22 degrees 22 minutes and 59 seconds, equal a) 40 degrees 11 minutes and 69 seconds b) 39 degrees 11 minutes and 9 seconds # c) 40 degrees 12 minutes and 9 seconds 116. the diameter of a cylinder is 200 cm and the height is 20 cm, what is the volume.# a) 628000 cm3 b) 8000 cm3 c) 62800 cm3

117. In an equilateral triangle, all of the angles are equal, to# a) p divided by 3 b) p divided by 2 c) p divided by 4

118. What is an obtuse angle? # a) one greater than 90o, but less than 180o b) one less than 90o c) one greater than 180o 119. What is tan Æ when Æ = 90o # a) + Ve infinity b) 0 c) –Ve infinity

120. 2x2z2 (2x2 - 22)= a) 2x2z2 - 22 b) 4x2z2 - 44x2z2# c) 4x4z2 - 44x2z2

121. in 21 = 43 – X, X is equal to # a) 43 – 21 b) 43 + 21 c) 21 - 43 122. The comparison of the power input to the power output of an inverter is expressed as a # a) ratio b) loss c) gain 123. The ratio of 6 : 4 can also be expressed as a) 64% b) 66%# c) 150% 124. 200 kilo volts can be expressed as a) 2 x 103 volts b) 2 x 10-4 volts# c) 2 x 105 volts

125. What is the surface area of a cone if the base is 8cm diameter and the length is 10cm?# a) 40p b) 80p c) 120p 126. 2x2z2 (3x – z2) =# a) 6x3z2 - 2x2z4 b) 6x2z2 - 2x2z2 c) 6x2z2 + 3x – z2 127. What is the area of a rectangle when its height is 11cm and the width 120cm? a) 1320 m2# b) 0.132 m2 c) 1.32 m2 128. How many times does the X axis get crossed when y = x2 – 3 a) 1# b) 2 c) 3 129. What is an obtuse angle? a) an angle less than 90o# b) an angle between 90o and 180o c) an angle greater than 180o

130. 4 3/8 – 2 ¼ + 1/5 = # a) 2 13/40 b) 3 3/10 c) 2 ¼

131. A congruent triangle has a) same size different shape b) same shape different size # c) same shape and size

132. 4(4 (4 – 1) –1) –1 = a) 15 b) 31 # c) 43

133. Which shape has no parallel sides? a) Rhombus # b) Kite c) Trapezoid

134. On a graph what is the intercept of y when 4y = x + 8 # a) 2 b) 4 c) 8

135. Which number is the lowest common factor of 36, 66 and 126 a) 23 # b) 6 c) 12

136. What is 3% of 0.001 a) 0.3 b) 0.003 # c) 0.00003 137. (a + b)(a – b) = # a) a2 – b2 b) a2 + 2ab – b2

c) a2 + b2

138. 101110 binary is a) 462 b) 468 # c) 4610

139. 11 ¸ 5 = 16 8 a) 10/11 b) 55/128 # c) 11/10

140. an aircraft uses 1680 gallons of fuel, the left tank uses 45%, the right tank uses 32.5%, how much was used by the centre tank? a) 21 gallons b) 210 gallons # c) 378 gallons

141. What is the fraction 1/7 in decimal? a) 0.14295 b) 1.429 # c) 0.14286

142. The supplement of 13 degrees is a) 76 b) 243 # c) 167

143. The properties of a scalene triangle are a) all sides are equal b) acute angle # c) all sides different lengths

144. What is octal 13 in base 10? a) 4 # b) 11 c) 5

145. What is the area of a ring with an outer diameter of 90 inches and an inner diameter of 80 inches? a) p325 # b) 425p c) p435

146. What is the height of an oblique pyramid? # a) The height is perpendicular to the base b) The height is angled to the base c) The height is parallel to the sides

147. What is the area of the shape below in centimeters?

a) 1130 b) 1000

# c) 1225 148. If y/x = 4 and y = 5 x = a) 20 # b) 1 ¼ c) 4/5

149. Calculate x

# a) 9.029 b) 8.971 c) 9.570

150. What is the equation of the line shown?

# a) y = 2 - x # a) y = 2 - x b) y = x - 2 c) y = 2x + 2

151. What is the area of a rectangle with base 160cm and height 12cm? a) 0.00192 m2 b) 0.0192 m2# c) 0.192 m2

152. What is the value of X

a) 30o # b) 35o c) 40o

153. on a right angle triangle, the longest side is 20 cm and the shortest is 12 cm. What is the other side? a) 13 cm # b) 16 cm c) 18 cm

154. How many degrees are there in one the smaller of the segments, where AB is one sixth of AC

a) 14.5o# b) 15o c) 10o

155. Find L in the following expression a) Q2C / R2 b) Q2C2/ R# c) Q2R2C

156. ax2 + bx + c = 0, what type of equation is this?# a) Quadratic equation b) Polynomic equation c) Gradient of the line

157. The graph points (9, 3) and (3, 1) what is the slope? # a) 1/3 b) 3/1 c) 9/5

158. Calculate the area

a) 42.41p# b) 6.75p c) 17.5p

159. What is (X2 x X3)3# a) x15 b) x36 c) x10

160. What is the equation of this line?

# a) x + y = - 2 b) y = 2 - x c) x – y = 2

161. expand (a + b)(a - b) # a) a2 - b2 b) a2 + 2ab - b2 c) a2 + b2

162. Two gear wheels one with 20 teeth and one with 120 teeth meshed together. The small gear turns one revolution. How far does the large gear move? a) 40o # b) 60o c) 90o

163. An aircraft flies 1350nm in 2 hrs 15 minutes. What is the average speed? a) 650kts # b) 600kts c) 850kts

164. The straight line from the center to a circle is known as the a) chord # b) radius c) diameter

165. Hexadecimal is base a) 2 b) 8 # c) 16

166. y = mx + c can also be written a) x = y/m - c # b) x = (y - c)/m c) x = y/(m + c)

167. What is the supplement of 13 degrees 13 minutes 13 seconds? a) 167 degrees 46 minutes 47 seconds # b) 166 degree 46 minutes 47 seconds c) 266 degrees 87 minutes 87 seconds

168. in a right triangle, sin theta = # a) opposite divided by hypotenuse b) adjacent divided by hypotenuse c) opposite divided by adjacent

169. In right-angled triangle the longest side is 20 and the other side is 12. The remaining side is a) 22 # b) 16 c) 10

170. Solve 15.4/2 - 2(6.2 - 15.6) # a) 26.5 b) 4.5 c) 11.1

171. What is angle x

a) 120o# b) 60o c) 30o


a) 12 sq ins # b) 14 sq ins c) 16 sq ins

173. A mound of soil is piled up into a cone of base diameter 1.8m and height 0.6 m. What is the volume of soil? # a) 0.5 m3 b) 1.5 m3 c) 1.0 m3

174. The heat of a resistor is given by the equation h = I2 RT. Find the current I.

a)

# b)

c)

175. What is the area of the shape below?

a) 220 square inches b) 200 square inches # c) 196 square inches

176. Factorise the following: x2 - x - 6 = 0: a) (x + 2) (x - 3)

b) (x - 2) (x + 3)# c) (x + 2) (x - 3)

177. 5/8 ths of 60 is a) 0.01 # b) 37 1/2 c) 96

178. What is the supplement of 13 o 13' 13"? # a) 166o 66' 67" b) 276o 66' 67" c) 76o 66' 67"

179. How many pairs of parallel sides has a trapezium? a) 0 pairs of parallel sides # b) 1 pair of parallel sides c) 2 pairs of parallel sides

180. In a parallelogram, if all the sides are of equal length and 1 angle is 90o, it is a a) rhomboid b) quadrilateral # c) square

181. In a rhombus # a) all sides are equal length with no angles 90o b) adjacent sides are different lengths with no angles 90o c) all sides are different length with no angles 90o

182. What is 1 radian in degrees? # a) 57o b) 270o c) 66o

183. A straight line graph has the equation 3y = 12x - 3 What is the gradient? a) 1/4 b) 3/4 # c) 4/1

184. (52 x 53)2 is a) 512 # b) 510 c) 57

185. (x + y)2 has a base and exponent of (x + y)8 # a) (x + y)-6 b) (x + y)1/4 c) (x + y)10

186. 1/7 in decimal is # a) 0.1428 b) 0.1489 c) 0.1485

187. An isosceles triangle has the following properties: a) Two sides parallel # b) Two sides the same length c) Three sides the same length

188. In an oblique triangle the axis is # a) at a slant to the base

b) parallel to the base c) perpendicular to the base

189. Factorise the following: 4x2 - 6x - 28 = 0 a) (2x + 7) (x - 2) # b) (4x - 14) (x + 2) c) (2x2 +7) (x + 2)

190. Solve for x in the equation 3(x + 2) = 30 + 2(x - 4) a) 15 b) 8 # c) 16

191. Rewrite the following with a positive index: Z-2 and X-3 # a) 1/Z2 and 1/X3 b) (ZX2)2; and (X)3 c) Z/22; and 1/X

192. How far does a wheel of 7m radius travel in one revolution? # a) 44m b) 22m c) 14

193. For an equation 2y = 5x + 3 what is the gradient a) 5x+3 2 b) 3 5x # c) 5 2 194. for a scalene triangle which is true? # a) No 2 sides are equal b) One angle is acute c) 2 sides are equal

195. Evaluate (a+b) (a-b) # a) a2 - b2 b) a + ab + b c) ab

196. Using cosine to find the angle of a triangle, which statement is true? # a) Adj / hyp b) Opp / adj c) Opp / hyp

197. An input gear of 20 teeth drives an output gear of 120 teeth, if the input rotates one revolution, how much does the output turn? # a) 60o b) 30o c) 45o

198. What is 30% of 0.01? a) 0.03 b) 0.0003 # c) 0.003

199. Evaluate 15.4 / 2 – 2(4.6 – 15.7) # a) 29.9 b) 26.5 c) –14.5 Page 27 - Mod 1200. A line to create a segment from the centre of a circle is a

a) chord # b) diameter c) radius

201. How far does a wheel of 7m radius travel in one revolution?# a) 44m b) 22m c) 14m

202. 2x = 4(x - 3) evaluate a) 0.5 b) 2# c) 6

203. A shape with 4 equal sides and one 90° angle is a a) parallelogram b) rhombus# c) square

204. 12x + 14 = 50 When y = 2, solve x 2y a) 14# b) 12 c) 11.6

205. What type of equation is y = x2 + 9x + 14?# a) Quadratic b) Exponential c) Circular

206. How many radians are in 360o?# a) 2pi b) 4pi c) 65

207. 100112 =# a) 1910 b) 292 c) 3510

208. In a right angled triangle the longest side is 20cm long, the shortest side is 12cm. What length is the last side? a) 18cm# b) 16cm c) 13.6cm

209. Complete the following: sin a =# a) opposite side divided by the hypotenuse side b) adjacent side divided by the opposite side c) a squared times b squared

210. The sum of the internal angles of a triangle is a) 360o b) 2pi radians# c) 180o

211. y = 2x + 4, When x = -1, y = # a) 2 b) 4 c) 0.5

212. What is 0111000012 in Octal

a) 324 b) 452# c) 341

213. What is the area of a cylinder diameter 10 cm and 10 cm in height? a) 50pi b) 100pi# c) 150pi

214. What is the highest factor of 153? a) 3 b) 6# c) 9

215. Convert into Decimal fraction 5/8 of 60 a) 40 # b) 37.5 c) 37

216. BCD format of numbering system having base of a) 10 b) 8# c) 2

217. 27y = 3 so y is equal to:# a) 1/9 b) 1/3 c) 9/1

218. An aeroplane has 1800 gallons of fuel on board. 35% in the left wing 42.5% in the right wing how much fuel is in the centre tank?# a) 405 gallons b) 183 gallons c) 545 gallons

219. 2y = 5x + 3 What is the gradient? a) 5/2 + 3# b) 5/2 c) 2/5

220. A triangle has angles 67o and 48o. The third angle is a) 115 b) 75# c) 65

221. 166o, 46', 47" + 13o, 13', 13" =# a) 180o b) 179o 60', 60" c) 179o, 1', 1"

222. What is the slope between the points (3, 1) and (9, 3)?# a) 1/3 b) 3/1 c) 2

223. Determine x in the following: (2x-1) (3x+2) = 0 a) 0.5, 3 b) 1.5, 1# c) -0.67, 0.5

224. The characteristic of Log 0.698 is a) -2# b) -1

c) 1

225. Log 59,000 is equal to a) 5.77452 b) 0.77452# c) 4.7745

226. In the common fraction 2/5 the number 5 is known as# a) the denominator b) the quotient c) the numerator

227. If 42% = 15,000, what does 100% = a) 6,300# b) 35,714 c) 21,300

228. What is 12.75 x 26.1 to two significant figures a) 332.78 b) 332.775# c) 330

229. The fraction 17/11 is classed as# a) an improper fraction b) a mixed fraction c) a proper fraction

230. To convert 1 inch to centimetres a) divide by 25.4# b) multiply by 2.54 c) divide by 2.54

231. 0.000006 volts can be written as a) 60 nanovolts b) 6 millivolts# c) 6 microvolts

232. the median of the values 20, 28, 17, 34, 40, 11, 34, 26 is a) 34.0 b) 26.25# c) 27.0

233. The mode of the following 28, 17, 34, 28, 34, 35, 28,40 is a) 31.0# b) 28.0 c) 30.5

234. 0.004 amperes can be written as a) 4kA# b) 4mA c) 0.4mA

235. A sphere with a radius of 2 cm has a surface area of# a) 16p cm2 b) 64p cm2 c) 8p cm2

236. The sum of the angles of a polygon with 'n' sides is a) 60 x n# b) 180 x (n-2) c) (n/4) x 180 Page 31 - Mod 1

237. The sum of an odd and an even number is# a) always odd b) always even c) sometimes odd, sometimes even

238. A copper pipe has a radius of 7/32 inch. What is this is decimal? a) 0.15625# b) 0.21875 c) 0.28125

239. (x + y + z)(x + y + z) = a) 2(x + y + z)# b) (x + y + z)2 c) 2x + 2y +2z

240. Millibar is the unit of# a) pressure b) density c) temperature

241. A ball rolls down a hill initially at 60 ft/s. It slows down at a rate of 5 ft/s2 for 7 seconds. What will its final speed be?# a) 25 ft/s b) 35 ft/s c) 15 ft/s

242. A piece of wire has a resistance of 160 ohms. Its resistance is increased with a ratio of 5 to 8. What is its new resistance?# a) 100 ohms b) 256 ohms c) 260 ohms

243. If 2x² + kx - 8 = 0 has two equal real roots, then a) k= - 8 b) k= ± 8# c) k is an imaginary number 244. Sector with angle A subtended to the centre point. Area of the sector proportional to: a) Sin A b) Cos A# c) Angle A

245. Suppose the earth to be a real sphere with the radius R. The arc distance from HK (N23) to the North pole is: a) 2.2R# b) 1.2R c) 0.9RPage 32 - Mod 1246. Starting from zero amplitude, the cosine curve repeats itself between a) 0 and 360 degree b) -180 and 180 degree# c) -90 and 270 degree.

247. A dial gauge is calibrated to an accuracy of 0.001 inch, when using the dial gauge, you should# a) round off the answer to calibrated value b) read the true value to 4 decimals c) read five significant figures

248. Given the log of A exceeds that of B by 4, find the correct statement about A and B

a) A is 1000 times the value of B b) A is 4000 times the value of B# c) A is 10000 times the value of B

249. Choose the correct statement: a) Sec²x + tan²x = 1 b) Cos²x - Sin²x = 1# c) Cossec²x - Cot²x = 1

250. What is 11110001 in Octal? a) 684# b) 361 c) 72

251. If x2 - 3 = 6, then x =# a) ± 3 b) ± 2 c) 18

252. in a flight control system, the control cable is allowed an elongation of 3% due to wear. The length from the manufacturer is 78cm, what is its maximum used length? a) 2.34 cm# b) 80.34 cm c) 78.34 cm

253. What is commonly referred to as the law of a straight line? a) The line must pass through the 180 degree datum b) y = x squared plus 180# c) y = mx plus c

254. If x in an equation equals Ly + 7cb, define the formula for finding the subject y# a) x - 7cb L b) x - 7cb L c) x - L 7cb

255. 64y = 64 what does y = a) 0# b) 1 c) 0.5

256. The y intercept of 4y = 4x + 8 is a) 8 b) 4# c) 2

257. You have made 20% profit. Your balance is now £900. What was your pre profit balance? a) £700# b) £750 c) £800

258. A cylinder has a radius of 20cm and a length of 40cm. what is its volume.# a) 50270cm3 b) 800cm3 c) 49600cm3

259. One radian is

a) the angle subtended at the centre of a circle when the arc-length formed between two radial lines is equal to pi# b) the angle subtended at the centre of a circle when the arc-length formed between two radial lines is equal in length to the radius c) 66.67 degrees

260. Find the curved surface area of a cylinder diameter 20cm and length 10cm? a) 400 cm2# b) 1256 cm2

c) 2512 cm2

261. Find (4(4(4-1)-1)-1) a) 28# b) 43 c) 27

Page 34 - Mod 1262. What is Log 9 - Log 3 + Log 4 a) Log 16 b) Log 10# c) Log 12

8) JAR 66 Module 1 Exam Practice Exam Module 1 Mathematics

This is exam number 1. 1. What is the tangent of 90o?a) Positive infinityb)Negative infinityc)0

2.A cuboid has dimensions of 4 cm, 6cm and 12 cm. What is its volume?a) 2.88 m3b)0.028 m3c) 0.000288m3

3.Work out the following sum: 4 {2 (5 – 1) – 3} + 8a) 37b)28c) 54

4.100000 in binary is what number in decimal?a) 16b)32c)64

5. D in hexidecimal is what number in decimal?a) 8b)13c) 17

6. In the following equation what is the y-intercept? 4y = 2x +8a) 4b)2c)8

7.Two angles of a triangle are 68 degree and 32 degree. Therefore the third angle must bea) 63ob)114oc) 80o

8. Solve the following equation to find x4x + 8y = 642x – 8y = 86

a) 5b)25c)125

9. Simplify the following(w + z)(x – y)(y – w)(y – x)(w – y)(w + z)

a) +1

b)-1c) 0

10. 101012 + 110012 =a) 462b) 468c) 4610

Answer1. 2 3 4 5 6 7 8 9 10

a c b b b b c b a c

This is exam number 2. 1. Which of the following formulae are correct for the triangle shown?

a) C2 = A2 + B2b)B2 = C2 + A2c) A2 = C2 + B2

2. A rectangle 11cm x 120cm. What is its area in m2a) 1320b)13.2c) 0.132

3. What is 738 in binary coded decimal?a) 111100010b)1011110010c) 11100111000

4. If a wheel of radius R revolves ½ a turn, how many radians does itturn through?a) 2p radiansb)p radiansc) 2R2 radians

5. If there are two similar angles in a right triangle, these angles are

a) complementaryb)supplementaryc) subordinate

6.The surface area of a cone whose flat is 10 cm and diameter is 8 cmisa) 80 pb) 40 pc) 120 p

7. (A + B)4 is (A + B)2a) (A + B)2b)A + Bc)(A + B)6

8. An equilateral triangle hasa) 2 equal sidesb)no equal sidesc)3 equal sides

9. 4 3/8 – 2 1/4 + 1/8 =a) 2 1/8

b)2 1/2c) 2 1/4

10. 11/16 + 5/8 =a) 55/128b)21/16c)10/11

1. 2 3 4 5 6 7 8 9 10

a c c b a b a c c b

This is exam number 3.

1. Given 43 - x = 21, find the value of xa) 43 - 21b)43 + 21c) 43 / 21

2. ¾ multiplied by 0.82 is equal toA)1.23b) 0.615c) 2.46

3. 7/6 can be expressed asa) 2.6b)1.6c) 1.166

4. The ratio of 6:5 can be expressed asa) 20 : 25b)24 : 20c) 10 : 16

5. 143 can be expressed asa) 14 x 3b)14 x 14 x 14c) 14 + 14 + 14

6. 0.0000413 can be written asa) 413 x 10-7b)0.413 x 10-7c) 4.13 x 10-7

7. 5/8 + 3/4 =a) 11/4b)11/8c) 8/8

8. The LCD for the problem 1/6 + 1/5 + 1/17 + 1/2 isa) 1020b)17c) 510

9. The formulae for calculating the area of a right angled triangle isa) ½ height + baseb)½ base / heightc) ½ (base x height)

10.The area of a circle whose circumference is given as 12cm isapproximatelya) 11.3 sq. cmb)3.8 sq. cmc)38 sq. cm

1. 2 3 4 5 6 7 8 9 10

a b c b b a b c c c


1. Area of a right circular cone isa) p x r x lb)(p x r x l) + 2 px r x rc)2/3 (p x r x l)

2. log 9 - log 3 =a) log 3b)log 6c) log 9

3. The three angles of a triangle summed together equala) 90°b)180°c) 360°

4. In a right-angled triangle the other two angles are both 45°. Thelength of the opposite side can be calculated bya) sin 45° x length of the hypotenuse side of the triangleb)cos 45° x length of the adjacent side of the trianglec) sin 45° x length of the adjacent side of the triangle

5. Given that a = X + B, what is y equal to ya) a + X/Bb)X – B/ac) X +B/a

6. Calculate (+ 3) - (- 4)a) -1b)+7c) -7

7. To convert imperial gallons to litres, multiply bya) 4.5b)5.4c) 4.7

8. Express 9/20 as a percentagea) 45 %b)40 %c) 47 %

9. To find the area of a circle, multiplya) the square of the radius by pb)the square of the circumference by the radiusc) Twice the radius by p

10. How many centimeters are in an inch?a) 25.4b)0.254c) 2.54

1. 2 3 4 5 6 7 8 9 10

a a b a c b a a c a

This is exam number 5..1. Make L the subject of the formulae 2pfL = xa) L = 2pfb)L = 2pf/xc) L = x/2pf

2. Find the lowest common denominator of 6; 7; 8a) 84b)168c) 336

3. The circumference of a circle is found bya)dividing the diameter by 3.142b)multiplying the diameter by 3.142c) multiplying the radius by 3.142

4. What torque loading would you apply to a nut if the force is 50 lbs,exerted 2 feet from its axis?a) 100 lbs.ftb)251 lbs.ftc) 600 lbs.ft

5. 67 divided by 127 is equal toa) 1/20b)1/128c) ½

6. The formula for calculating the torque loading on a nut or bolt isa) Force used x diameter of the boltb)Force used x lever length of the spannerc) Lever length of the spannerThreads per inch

7. Calculate the height of an obtuse triangle whose base is X cm and thearea is Y square cm.a) Y x 2 x Xb) Y + X/2c) Y x 2/X

8. How is the area of a circle calculated?a) R2 x 3.142b) D2 x 3.142c) 2 x 3.142 x r

9. Solve the following9/4 + 5/12 + 1 3/8 =a) 4 1/24b)2 25/24c) 4 1/12

10. The specific torque loading for a bolt is 50 lbs.ins but anExtension of 2” is needed to reach the bolt in addition to the 8” torqueWrench. What will the actual reading?a) 54 lb.insb)40 lb.insc) 60 lb.ins

1. 2 3 4 5 6 7 8 9 10

c b b a b b c a a c

This is exam number 6.1. Express the fraction 7/8 as a decimala) 0.875b)0.785c) 0.878

2. Solve 0.75 X 0.003a) 0.225b)0.0225c) 0.00225

3. Convert 162 knots to mpha) 186 mphb)176 mphc) 196 mph

4. To convert inches to millimetres, it is necessary toa) multiply by 25.4b)divide by 25.4c) multiply by 2.54

5. ¾ x 82 =a) 123b)61.5c) 81.5

6.A circular patch is held together by seven equally spaced rivets,what is their angular relationship?a) 51.50ob)51.43oc) 52o

7. Add together; 3/4, 5/16, 7/8 and 0.375a) 2 1/8b)2 ¼c) 2 5/16

8. Given that A = X + BY, what is Y equal to?a) A - X minus Bb)A - X add Bc) A - X divided by B

9. A right-angled triangle has sides of 3 inches and 4 inches, what willthe third side be?a) 6 inchesb)5 inchesc) 5.5 inches

10. To convert pounds of fuel into kilograms, it is necessary toa) multiply by 4536b)multiply by 0.4536c)divide by 0.4536

1. 2 3 4 5 6 7 8 9 10

a c a a b b c c b b


1. If resin to hardener is used in the ratio of 1000:45, how much hardener is used with 60 grams of resina) 47 gramsb) 2.7 gramsc) 145 grams

2. Solve the following 11/16 + 5/8a) 55/128b) 1 5/16c) 1 1/10

3. 6 mm is equal toa) 0.625”b) 0.375”c) 0.236”

4. To work out the circumference of a circlea) D x 3.142b)D x 0.3142c)D - 3.142

5.Weight is equal toa) volume x gravityb)mass x accelerationc) mass x gravity

6.8 + 4[5 x 2 (5 – 9/3)]a) Eighty Eightb)Forty Eightc) Twelve

7.To convert gallons to litresa) multiply by 0.568b)multiply by 4.55c) multiply by 0.00455

8.An equilateral triangle hasa) two equal sideb)no equal sidesc)three equal sides

9. sin ø =

a) C/Ab)A/Cc) B/C

10. Cos A =

a) 1.2b) 0.8c) 0.6

ANSWERS 1. 2 3 4 5 6 7 8 9 10

B B C A C A B C B B

This is exam number 8.1. 2x – 8y = 14 and 4x + 8y = 16; x =a) –1/2b)5c) 3

2. 2x – 3 = 4; x =a) 3.50b)–3c) 7

3. If y / x = 4 and y = 5 then x =a) 20b)1 ¼c) 4 / 5

4. V = (a + b) r2 Find aa) V – r2 – bb)(V – b )/ r2c) V / r2 – b

5. A quadrilateral with only two parallel sides is aa) Trapezoidb)Trapeziumc) Rhombus

6. 2x2z2 (3x – z2) =a) 6x3z2 – 2x2z4b) 6x2z2 – 2x2z2c) 6x2z2 + 3x – z2

7. A cylinder has a diameter of 20 cm and a length of 20 cm, what is itsvolume?a) 400cm3b)1240cm3c) 6200cm3

8. 3 1/8 – 1 1/5 =a) 1 37/40b)1 3/40c) 2 3/40

9. Make m the subject of the formula y = mx + ca) y - cxb)y - xcc) y - cx

10. Make x the subject of the formula y = mx + ca) y – c/mb)y - m/cc) y - c/m

ANSWERS 1. 2 3 4 5 6 7 8 9 10

B A B C A A C A A A


1. Make c the subject of the formula y = mx + ca) y + mxb)y - mxc) mx - y

2. What is the formula for calculating the curved area of a cone?a) p x radius2 x heightb)p x radius x heightc) 2/3 x p x radius x height

3. A triangle with equal angles is calleda) isoscelesb)equilateralc) right angled

4. Two gears are in mesh, one is larger than the other, the smaller gearrotatesa) at the same speedb)at a lower speedc) at a faster speed

5. Calculate 10 x 23 + 10 x 25a) 32,008,000b)520c) 400

6. In a right angle triangle, the sine of an angle isa) opposite divided by hypotenuseb)adjacent divided by hypotenusec) opposite divided by adjacent

7. In a right angle triangle, the tangent of an angle isa) opposite divided by hypotenuseb)adjacent divided by hypotenusec) opposite divided by adjacent

8. In a right angle triangle, the cosine of an angle isa) opposite divided by hypotenuseb)adjacent divided by hypotenusec) opposite divided by adjacent

9. Octal is to the base ofa) 2b)16c) 8

10. One radian is equal toa) 57.5ob)90oc) 75o

Answer1. 2 3 4 5 6 7 8 9 10

B B B C C A C A A A

This is exam number 10. 1. The surface area of a cylinder of diameter 10 cm and height 10cm, isa) 100pb)50pc) 80p

2. A parallelogram has a base 120cm and height 11 cm. What is the area?a) 1.32 m2b)0.132 m2c) 0.0132 m2

3. The name given to this shape is

a) Parallelogramb)Trapezoidc) Rhombus

4. The area of this shape is calculated by

a) Base x Heightb)½ Base x Heightc) Perimeter squared

5. The name of this shape is

a) Parallelogramb)Trapeziumc) Rhombus

6. The area of the shape is calculated by

a) ½ height x baseb)½ base x ½ heightc) ½ height + twice base

7. A triangle with equal sides isa) Isoscelesb)Acutec) Equilateral

8. Two gears are in mesh, one has twice the number of teeth as the othera) the gear with fewer teeth rotates slower than the otherb)the gear with fewer teeth rotates faster than the otherc) the two gears rotate at the same speed

9. The area of the curved surface area of a cone is(where r = radius; h = vertical height and l = slant height)a) 1/3pr2h

b)pr2hc) prl

10. What is the area of a cuboid?a) height x length x widthb)height x ½ base x heightc) height x ½ base x length

Answer1. 2 3 4 5 6 7 8 9 10

A A A A C A C B C A


1. To find the area of a circle, multiplya) the square of the radius by pb)the square of the circumference by the radiusc) twice the radius by p

2. 4 – 6 – 9- 3 + (- 3)a) 4.5b)3.5c) 4

3. An aircraft travels 2150 nautical miles in 2 hours 30 minutes what is the average speed of the aircraft?a) 600 knotsb) 860 knotsc) 550 knots

4. Locus points plotted equidistant from a central points representa) diameterb) radiusc) circumference

5. A circle containsa) 4p radiansb)2p radiansc) 2pr radians

6. What is the surface area of a cylinder whose diameter is 20cm andheight of 15 cm?a) 942pb)350pc) 300p

7. An oblique pyramid is one which has its axisa) not perpendicular to its baseb)perpendicular to its basec) parallel to its base

8. An input gear has 20 teeth and the output gear has 120 teeth. If theinput gear rotates 360 degrees, the output gear will rotatea) 90 degreesb)45 degreesc) 60 degrees

9. A line from the centre of a circle is calleda) its segmentb)diameterc) radius

10. Four percent of 0.01 isa) 0.04b)0.004c) 0.0004Answer1. 2 3 4 5 6 7 8 9 10

A A C C A A B B B A

This is exam number 12

1. (x - 3)(x + 5) =a) x2 - 15b)x2 + 2x - 15c) x2 + 2x

2. (6+2)2 X 2 – (2 X 45) =a) 38b)218c) 128

3. V = (a + b) r2 Find aa) V – r2 – bb)(V – b) / r2c)V / r2 - b

4. Give the names of a triangle, which has two sides equal in length andtwo equal angles.a) Equilateralb)Isoscelesc) Obtuse

5. 17 degrees 49 minutes and 10 seconds added to 22 degrees 22 minutes and 59 seconds, equala) 40 degrees 11 minutes and 69 secondsb)39 degrees 11 minutes and 9 secondsc) 40 degrees 12 minutes and 9 seconds

6. The diameter of a cylinder is 200 cm and the height is 20 cm, what is the volume.a) 628000 cm3b)8000 cm3c) 62800 cm3

7. In an equilateral triangle, all of the angles are equal, toa) p divided by 3b)p divided by 2c) p divided by 4

8. What is an obtuse angle?

a) one greater than 90o, but less than 180o

b)one less than 90oc)one greater than 180o

9. What is tan Æ when Æ = 90oa) +Ve infinityb)0c) –Ve infinity

10. 2x2z2 (2x2 - 22)=a) 2x2z2 - 22b)4x2z2 - 44x2z2c) 4x4z2 - 44x2z2

Answer1. 2 3 4 5 6 7 8 9 10

B A C B C A A A A C


1. In 21 = 43 – X, X is equal toa) 43 – 21b)43 + 21c) 21 - 43

2. The comparison of the power input to the power output of an inverteris expressed as aa) ratiob)lossc) gain

3. The ratio of 6 : 4 can also be expressed asa) 64%b)66%c) 150%

4. 200 kilo volts can be expressed asa) 2 x 103 voltsb)2 x 10-4 voltsc) 2 x 105 volts

5. What is the surface area of a cone if the base is 8cm diameter andthe length is 10cm?a) 40pb)80pc) 120p

6. 2x2z2(3x – z2) =a) 6x3z2 - 2x2z4b)6x2z2 - 2x2z2c) 6x2z2 + 3x – z2

7. What is the area of a rectangle when its height is 11cm and the width120cm?a) 1320 m2b)0.132 m2c) 1.32 m2

8. How many times does the X axis get crossed when y = x2 – 3a) 1b)2c) 3

9. What is an obtuse angle?a) an angle less than 90ob)an angle between 90o and 180oc) an angle greater than 180o

10. 4 3/8 – 2 ¼ + 1/5 =a) 2 13/40b)3 3/10c) 2 ¼

Answer1. 2 3 4 5 6 7 8 9 10

C C C B B A C B A A


1. A congruent triangle hasa) same size different shapeb)same shape different sizec) same shape and size

2. 4(4 (4 – 1) –1) –1 =a) 15b)31c) 43

3. Which shape has no parallel sides?a) Rhombusb)Kitec) Trapezoid

4. On a graph what is the intercept of y when 4y = x + 8a) 2b)4c) 8

5. Which number is the lowest common factor of 36, 66 and 126a) 23b)6c) 12

6. What is 3% of 0.001a) 0.3b)0.003c) 0.00003

7. (a + b)(a – b) =a) a2 – b2b)a2 + 2ab – b2c) a2 + b2

8. 101110 binary is

a) 462b)468c) 4610

9. 11 ¸ 5 =16 8a) 10/11b)55/128c) 11/10

10. An aircraft uses 1680 gallons of fuel, the left tank uses 45%, theright tank uses 32.5%, how much was used by the centre tank?a) 21 gallonsb)210 gallonsc) 378 gallons

Answer1. 2 3 4 5 6 7 8 9 10

C C B A B C A C C C

This is exam number 15. 1. What is the fraction 1/7 in decimal?a) 0.14295b)1.429c) 0.14286

2. The supplement of 13 degrees isa) 76b)243c) 167

3. The properties of a scalene triangle area) all sides are equalb)acute anglec) all sides different lengths

4. What is octal 13 in base 10?a) 4b)11c) 5

5. What is the area of a ring with an outer diameter of 90 inches and aninner diameter of 80 inches?a) p325b)425pc) p435

6. What is the height of an oblique pyramid?a) The height is perpendicular to the baseb)The height is angled to the basec) The height is parallel to the sides

7. What is the area of the shape below in centimetres?

a) 1130b)1000c) 1225

8. If y/x = 4 and y = 5 x =a) 20b)1 ¼c) 4/5

9. Calculate x

a) 9.029b)8.971c) 9.570

10. What is the equation of the line shown?

a) y = 2 - xb)y = x - 2c) y = 2x + 2

Answer1. 2 3 4 5 6 7 8 9 10

C C C B B A C B A A

This is exam number 16. 1. What is the area of a rectangle with base 160cm and height 12cm?a) 0.00192 m2b)0.0192 m2c) 0.192 m2

2. What is the value of X

a) 30ob)35oc) 40o

3. On a right angle triangle, the longest side is 20 cm and the shortestis 12 cm. What is the other side?a) 13 cmb)16 cmc) 18 cm

4. How many degrees are there in one the smaller of the segments, whereAB is one sixth of AC

a) 14.5ob)15oc) 10o

5. Find L in the following expression

a) Q2C / R2b)Q2C2/ Rc) Q2R2C

6. ax2 + bx + c = 0, what type of equation is this?a) Quadratic equationb)Polynomic equationc) Gradient of the line

7. The graph points (9, 3) and (3, 1) what is the slope?a) 1/3b)3/1c) 9/5


a) 42.41pb)6.75pc) 17.5p

9. What is (X2 x X3)3a) x15b)x36c) x10

10. What is the equation of this line?

a) x + y = - 2b)y = 2 - xc) x – y = 2

Answer1. 2 3 4 5 6 7 8 9 10

C B B B C A A B A A


1. Expand (a + b)(a - b)a) a2 - b2b)a2 + 2ab - b2c) a2 + b2

2. Two gear wheels one with 20 teeth and one with 120 teeth meshedtogether. The small gear turns one revolution. How far does the largegear move?a) 40ob)60oc) 90o

3. An aircraft flies 1350nm in 2 hrs 15 minutes. What is the averagespeed?a) 650ktsb)600ktsc) 850kts

4. The straight line from the center to a circle is known as thea) chordb)radiusc) diameter

5. Hexadecimal is basea) 2b)8c) 16

6. y = mx + c can also be writtena) x = y/m - cb)x = (y - c)/mc) x = y/(m + c)

7. What is the supplement of 13 degrees 13 minutes 13 seconds?a) 167 degrees 46 minutes 47 secondsb)166 degree 46 minutes 47 secondsc) 266 degrees 87 minutes 87 seconds

8. In a right triangle, sin theta =a) opposite divided by hypotenuseb)adjacent divided by hypotenusec) opposite divided by adjacent

9. In right-angled triangle the longest side is 20 and the other side is12. The remaining side isa) 22b)16c) 10

10. Solve 15.4/2 - 2(6.2 - 15.6)a) 26.5b)4.5c) 11.1

Answer1. 2 3 4 5 6 7 8 9 10

A B B B C B B A B A

This is exam number 18. You've been here 1 times.1. What is angle x

a) 120ob)60oc) 30o


a) 12 sq insb)14 sq insc) 16 sq ins

3. A mound of soil is piled up into a cone of base diameter 1.8m andheight 0.6 m. What is the volume of soil?a) 0.5 m3b)1.5 m3c) 1.0 m3

4. The heat of a resistor is given by the equationh = I2 RT. Find thecurrent I.

5. What is the area of the shape below?

a) 220 square inchesb)200 square inchesc) 196 square inches

6. Factorise the following:x2 - x - 6 = 0a) (x - 2)(x - 3)b)(x - 2)(x + 3)c) (x + 2)(x - 3)

7. 5/8 ths of 60 isa) 0.01b)37 1/2c) 96

8. What is the supplement of 13o 13' 13"?a) 166o 66' 67"b)276o 66' 67"c) 76o 66' 67"

9. How many pairs of parallel sides has a trapezium?a) 0 pairs of parallel sidesb)1 pair of parallel sidesc) 2 pairs of parallel sides

10. In a parallelogram, if all the sides are of equal length and 1 angleis 90o, it is aa) rhomboidb)quadrilateralc) square

Answer1. 2 3 4 5 6 7 8 9 10

B B A B C C B A B C


1. In a rhombusa) all sides are equal length with no angles 90ob)adjacent sides are different lengths with no angles 90oc) all sides are different length with no angles 90o

2. What is 1 radian in degrees?a) 57ob)270oc) 66o

3. A straight line graph has the equation3y = 12x - 3What is the gradient?a) 1/4b)3/4c) 4/1

4. (52 x 53)2 isa) 512b)510c) 57

5. (x + y)2 has a base and exponent of (x + y)8a) (x + y)- 6b)(x + y)1/4c) (x + y)10

6. 1/7 in decimal isa) 0.1428b)0.1489c) 0.1485

7. An isosceles triangle has the following properties:a) Two sides parallelb)Two sides the same lengthc) Three sides the same length

8. In an oblique triangle the axis isa) at a slant to the baseb)parallel to the basec) perpendicular to the base

9. Factorise the following: 4x2 - 6x - 28 = 0a) (2x + 7) (x - 2)b)(4x - 14) (x + 2)c) (2x2 +7) (x + 2)

10. Solve for x in the equation 3(x + 2) = 30 + 2(x - 4)a) 15b)8c) 16

Answer1. 2 3 4 5 6 7 8 9 10

A A C B A A B A B C


1. Rewrite the following with a positive index: Z-2 and X-3a) 1/Z2 and 1/X3b)(ZX2)2; and (X)3c) Z/22; and 1/X

2. How far does a wheel of 7m radius travel in one revolution?a) 44mb)22mc) 14

3. For an equation 2y = 5x + 3 what is the gradienta) 5x+32b) 35xc) 52

4. For a scalene triangle which is true?a) No 2 sides are equalb)One angle is acutec) 2 sides are equal

5. Expand (a+b)(a-b)a) a2 - b2b)a + ab + bc) ab

6. Using cosine to find the angle of a triangle, which statement istrue?a) Adj / hypb)Opp / adjc) Opp / hyp

7. An input gear of 20 teeth drives an output gear of 120 teeth, if theinput rotates one revolution, how much does the output turn?a) 60ob)30oc) 45o

8. What is 30% of 0.01a) 0.03b)0.0003c) 0.003

9. Evaluate 15.4 / 2 – 2(4.6 – 15.7)a) 29.9b)26.5c) –14.5

10. A line to create a segment from the centre of a circle is aa) chordb)diameterc) radius

Answer1. 2 3 4 5 6 7 8 9 10

A A C A A A A C A B

This is exam number 21..

1. How far does a wheel of 7m radius travel in one revolution?a) 44mb)22mc) 14m

2. 2x = 4(x - 3) evaluate xa) 0.5b)2c) 6

3. A shape with 4 equal sides and one 90° angle is aa) parallelogramb)rhombusc) square

4. 12x + 14 = 50 When y = 2, solve x2ya) 14b)12c) 11.6

5. What type of equation is y = x2 + 9x + 14?a) Quadraticb)Exponentialc) Circular

6. How many radians are in 360o?a) 2pb)4pc) 65

7. 100112 =a) 1910b)292c) 3510

8. In a right angled triangle the longest side is 20cm long, theshortest side is 12cm. What length is the last side?a) 18cmb)16cmc) 13.6cm

9. Complete the following: sin a =a) opposite side divided by the hypotenuse sideb)adjacent side divided by the opposite sidec) a squared times b squared

10. The sum of the internal angles of a triangle isa) 360ob)2p radiansc) 180o

Answer1. 2 3 4 5 6 7 8 9 10

A C C B A A A B A C


1. y = 2x + 4, When x = -1, y =a) 2b)4c) 0.5

2. What is 0111000012 in Octala) 324b)452c) 341

3. What is the area of a cylinder diameter 10 cm and 10 cm in height?a) 50pb)100pc) 150p

4. What is the highest factor of 153?a) 3b)6c) 9

5. Convert into Decimal fraction 5/8 of 60a) 40b)37.5c) 37

6. BCD format of numbering system having base ofa) 10b)8c) 2

7. 27y = 3 so y is equal to:a) 1/9b)1/3c) 9/1

8. An aeroplane has 1800 gallons of fuel on board. 35% in the left wing42.5% in the right wing how much fuel is in the centre tank?a) 405 gallonsb)183 gallons

c) 545 gallons

9. 2y = 5x + 3 What is the gradient?a) 5/2 + 3b)5/2c) 2/5

10. A triangle has angles 67o and 48o. The third angle isa) 115

b)75c) 65

Answer1. 2 3 4 5 6 7 8 9 10

A C C C B C A A B C

This is exam number 23. You've been here 1 times.

1. 166o, 46', 47" + 13o, 13', 13" =a) 180ob)179o 60', 60"c) 179o, 1', 1"

2. What is the slope between the points (3,1) and (9,3)?a) 1/3b)3/1c) 2

3. Determine x in the following: (2x-1)(3x+2) = 0a) 0.5, 3b)1.5, 1c) -0.67, 0.5

4. The characteristic of Log 0.698 isa) -2b)-1c) 1

5. Log 59,000 is equal toa) 5.77452b)0.77452c) 4.7745

6. In the common fraction 2/5 the number 5 is known asa) the denominatorb)the quotientc) the numerator

7. If 42% = 15,000, what does 100% =a) 6,300b)35,714c) 21,300

8. What is 12.75 x 26.1 to two significant figuresa) 332.78b)332.775c) 330

9. The fraction 17/11 is classed asa) an improper fractionb)a mixed fractionc) a proper fraction

10. To convert 1 inch to centimetres

a) divide by 25.4b)multiply by 2.54c) divide by 2.54

Answer1. 2 3 4 5 6 7 8 9 10

A A C B C A B C A B

This is exam number 24. 1. 0.000006 volts can be written asa) 60 nanovoltsb)6 millivoltsc) 6 microvolts

2. The median of the values 20, 28, 17, 34, 40, 11, 34, 26 isa) 34.0b)26.25c) 27.0

3. The mode of the following 28, 17, 34, 28, 34, 35, 28,40 isa) 31.0b)28.0c) 30.5

4. 0.004 amperes can be written asa) 4kA

b)4mAc) 0.4mA

5. A sphere with a radius of 2 cm has a surface area ofa) 16p cm2b)64p cm2c) 8p cm2

6. The sum of the angles of a polygon with 'n' sides isa) 60 x nb)180 x (n-2)c) (n/4) x 180

7. The sum of an odd and an even number isa) always oddb)always evenc) sometimes odd, sometimes even

8. A copper pipe has a radius of 7/32 inch. What is this is decimal?a) 0.15625b)0.21875c) 0.28125

9. (x + y + z)(x + y + z) =a) 2(x + y + z)b)(x + y + z)2

c) 2x + 2y +2z

10. Millibar is the unit ofa) pressureb)densityc) temperature

Answer1. 2 3 4 5 6 7 8 9 10

C CB B A B B A B B A


1. A ball rolls down a hill initially at 60 ft/s. It slows down at arate of 5 ft/s2 for 7 seconds. What will its final speed be?a) 25 ft/sb)35 ft/sc) 15 ft/s

2. A piece of wire has a resistance of 160 ohms. Its resistance isincreased with a ratio of 5 to 8. What is its new resistance?a) 100 ohmsb)256 ohmsc) 260 ohms

3. If 2x²+kx-8=0 has two equal real roots, then:a) k=-8b)k=±8c) k is an imaginary number

4. Sector with angle A subtended to the centre point. Area of the sectorproportional to:a) Sin Ab)Cos Ac) Angle A

5. Suppose the earth to be a real sphere with the radius R. The arcdistance from HK (N23) to the North pole is:a) 2.2Rb)1.2Rc) 0.9R

6. Starting from zero amplitude, the cosine curve repeats itself betweena) 0 and 360 degreeb)-180 and 180 degreec) -90 and 270 degree.

7. A dial gauge is calibrated to an accuracy of 0.001 inch, when usingthe dial gauge, you shoulda) round off the answer to calibrated valueb)read the true value to 4 decimalsc) read five significant figures

8. Given the log of A exceeds that of B by 4, find the correct statementabout A and B

a) A is 1000 times the value of Bb)A is 4000 times the value of Bc) A is 10000 times the value of B

9. Choose the correct statement:a) Sec²x + tan²x = 1b)Cos²x - Sin²x = 1c) Cossec²x - Cot²x = 1

10. What is 11110001 in Octal?a) 684b)361c) 72

Answer1. 2 3 4 5 6 7 8 9 10

A A C C B C A C C B


1. If x2 - 3 = 6, then x =a) ± 3b)± 2c) 18

2. In a flight control system, the control cable is allowed anelongation of 3% due to wear. The length from the manufacturer is 78cm,what is its maximum used length?a) 2.34 cmb)80.34 cmc) 78.34 cm

3. What is commonly referred to as the law of a straight line?a) The line must pass through the 180 degree datumb)y = x squared plus 180c) y = mx plus c

4. If x in an equation equals Ly + 7cb, define the formula for findingthe subject ya) x - 7cb/Lb)x - 7cb/Lc) x – L/7cb

Answer1. 2 3 4 5 6 7 8 9 10

A B C A

9)

15 div 12 1 5

15 x 51 12

75 12

1 + 3 x 1 - 76 8 2 8

1 + 3 - 7 6 16 8

8 + 9 - 42 48

= 2916 div 9= 324

Vol = πr²h = π (0.05 x0.0 5) h = π x 0.0025 x 10 = 0.025πm³

125ml = 0.125 liter= 750 div 0.125= 6000

60 x 100320

= 18.76%

11.2 0.11+ 8.1 19.41

= 10 + (-4) x 2 + 4 div 2= 10 – 4 x 2 + 4 div 2= 10 – 4 X 2 + 2= 10 – 8 + 2

BIDMAS= 12 – 8= 4Nearest Ans is 8

= (2p² - 4p) – (p² + 2p)= 2p² - 4p - p² - 2p= 2p² - p² - 4p – 2p= p² - 6p or p(p-6)

Vol of Cyclinder = Area x height= π r² x h= π (2 x 2) x 10= π 4 x 10

= 40πm³

(10 , 20)( x , y ).y = 5x + C20 = 5x10 + C20 – 50 = C

C = 20 – 50C = - 30

51.01. x 0.31 15.5131

1 x 51 = 513 x 17 = 5117 x 3 = 51Therefore prime factor of 51 are 1, 3 and 17

90 x 100450

= 20%

1863- 7871076

10.32 10.40+ 10.10 30.82

= 30.82 div 3= 10.27

300 packs = $300 (buy)1 pack = 300 div 3001 pack = $1.00

1 pack = $2.00 (sell)300 packs = 2 x 300 = $600

Profit = $600 - $300 = $300 = 300 x 100 300 = 100%Nearest Ans is 60.00%

= 2 x 150 3

= 2 x 50= 100 tonnes

EXAM QUESTION

1 gallon = 4.5 litres5 gallons = 4.5 x 5 = 22.5 litres

Vol of Cyclinder = Area x height= π r² x h= π (0.5 x 0.5) x 10= π 0.25 x 10= π 2.5= 2.5πm³

10.325 0.821+ 6.510 17.656

56.32x 0.62 34.918

74100

3750

21 24+ 27 72

= 72 div 3= 24

1 x 20 = 202 x 10 = 204 x 5 = 205 x 4 = 20

10 x 2 = 2020 x 1 = 20Therefore prime factor of 20 are 1, 2 , 4. 5 , and 10

30 x 450100

= 3 x 45

= 135

Length : Width 5 : 2 ? : 6

5 x 62

30 2

= 15

2.2kg = 1 lb? kg = 15 lb

=2.2 x 15= 33 kg

1 bar = 14.5 psi5 bar = 14.5 x 5 = 72.5 bar

= 5 – ( - 3) x 2 + 4 div 2= 5 + 3 x 2 + 2= 5 + 6 + 2= 13

( - 5 x -5 x -5 ) + 5 x 5 5

-125 + 25 5

-1005

= - 20

⁴ 16 + (6 x 6) – (3 x 3) 2 x 2 x 2 x 2

2 x 2 x 2 x 2 + 36 - 9 16

2 + 36 – 9 16

2916

= - 2x + (2 ( 2x – 1 ) – 5)= - 2x + 4x – 2 – 5= 2x -7

= 180 – 56 – 32= 92°

Area of Big circle= πr²= π 7cm x 7cm= 49πcm³

Area of Shaded area= πr²= π 3.5cm x 3.5cm= 12.25πcm³

Area of Unshaded area= 49πcm³ – 12.25πcm³= 36.75 cm³

But the nearest Ans is12.75πm³

Δy = 12 – 2 Δx 5 – 1

= 10 4

= 2.5

3 x 2 x 54 3 8

516

.( +, + ).( -, + )

.( -, - ) .( +, - )

.x

.y

.( x, y ) .( x, y )

625 div 51000 div 5

125 div 5200 div 5

25 div 540 div 5

5 8

35 56

= 56 -35= 21 (can div by 7)

35 div 756 div 7

5 8

7 - 5 8 6

42 - 40 48

2 48

1 24

2 8 , 6 2 4 , 3 2 2 , 3 2 1 , 3 3 1 , 1

= 2 x 2 x 2 x 2 x 3= 48

³ 216

6 x 6 x 6= 6

15 x 0.48100

7.2100

= 0.072

4(2x – 12) = 128x – 48 = 128x = 12 + 488x = 60X = 60 div by 8 = 7.5

32 = 40 x ? 1 100

? = 32 x 100 40

? = 320 4

? = 80 km/h

25 raised to the third power

= 5³= 5 x 5 x 5= 125

45 div 560 div 5

9 div 312 div 3

3 x 1004

75= 13.75

10 feet = 120 inches

= 120 : 30= 4 : 1

3965

= 65 – 39= 26 (can be div by 13)

39 div 1365 div 13

35

24.936

a² - b²a² - b²

= 1 EXAM QUESTION

34

43

44

EXAM QUESTION

IMPORTANT IMFORMATION

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