Pre-Algebra Name: Review Worksheet Final Exam Mr. Cierech Date: Chapter 1: Number Patterns 1) Find the next three numbers in the sequence: a) 4, 9, 14, 19, 24. . . b) 16, 8, 4, 2, 1,… 2) If an athletic conference has 12 teams and each of the teams plays each of the other teams, how many games will there be? 3) Write an algebraic expression for that represents each verbal expression: a) The cost of movie ticket $8.50 increased by the cost of a soda s b) The number of hours in d days c) The decibel level of a rock concert 120 decreased by ear plugs with an efficiency rating of p decibels.

4) Julia rents surfboards at the beach for $5 plus $1.50 per hour. Write an equation for the cost, using the variable h and c.

5) Find the value of d when c is the indicated value. a) c = 5.6d, c = 67.2 b) c = 3.6d + 24, c is 88.8 6) A can of sot drink contains 355 ml of liquid. If 5 people split 2 cans evenly, how many milliliters will each get? 7) How many $5 raffle tickets must you sell to raise $32? 8) Determine whether each number is prime, composite or neither: a) 47 b) 1 c) 0 d) 372 e) 57

Number of hours: h Process Cost: c

9) Given the following numbers state whether they are divisible by 2, 3, 5, 6, 9, or 10: a) 1728 b) 3570 c) 730 d) 108 e) 6234 10) Make a list of the factors of 72. Circle all the prime factors. 11) Use exponents to rewrite the expression: a) 5 5 5 5 b) 3 3 3x x x 12) Evaluate each power: a) 52 b) 23 c) 4.5 13) Write the prime factorization of each number: a) 54 b) 399 14) Simplify using the correct order of operations:

a) 187 34 17 b) 97 1728 59

15) Evaluate each expression: a) 2 5 4 9 b) 27 6 2 9

16) Given a is 5, b is 3, and c is 4 evaluate each expression: 1) (a + b) – c 2) 2a b c 17) Name the property illustrated: a) 27 98 73 27 98 73

b) 6 3 5 6 5 3 5

c) ( 17) 18 18 ( 17)

Pre-Algebra Name: Review Worksheet Final Exam Mr. Cierech Date: Chapter 2: Patterns with Integers 1) Find the opposites of the following numbers:

a) -5 b) 34

c) 0 d) 78

2) Find the absolute value of the following numbers:

a) | -2 | b) | .897| c) 25

3 d) | 0 |

3) Circle the following integers:

1, -5, 1

2 , 0, -6, 6.3

4) Find the following sums: a) -28 + 50 b) -43 + 82 + | -19 | c) 14 + ( -29) + ( -12) d) -15 + | -45 + 13 | 5) Show the set of integers on the number line and then list them in order from least to greatest: -2, -2.5, 4, -3.5, 3 , 0, 1.5 6) Find the distance between the pair of points on a number line. a) -6 and 15 b) -8 and -20 c) 12 and 34 7) Evaluate:

a) ( 12) ( 4) 3 b) 15 3 6 2 c) ( 90) ( 15) ( 1) (3)

8) Write a linear equation to describe the set of data:

Time ( in hours) 0 1 2 3 Cost ( in dollars) 12 16 20 24 9) Find the first and second differences for the sequence 20, 27, 36, 47, 60 10) Suppose a rocket takes 36 minutes after its launch to reach the ground. How many minutes of flight did it take to reach its maximum height? 11) Make a table of values for y = -2x + 5 using integer values of x from -3 to 3. Then graph the equation.

x Process: -2x + 5 y

12) Find each difference: a) 13 – ( -13) b) 12 – 15 – ( - 15 ) c) - 18 - | -18| - ( -18) 13) Use < or > to indicate the relationship between the following numbers: a) -3 0 b) -18 -15 c) -6.5 -6.006 14) Find the value of the expression 15h -23 when h = -4. 15) Simplify: 22(3 4) 2 3 (4) 6 1 Date:

Chapter 3: Rational Numbers and Probability

1) Is 710

closer to ½ , 0 or 1?

2) Compare the fractions using the symbols < , > or =:

a) 2 53 6

and b) 4 305 40

and c) 36 1245 9

and

3) Reduce each fraction to lowest terms:

a) 5614

b) 4872

c) 150600

4) Find the LCD of the following fractions then use the symbols <, >, or = to compare them

a) 2532

58

b) 2 5 3 16

c) 32 8 88 22

5) Write the list of fractions from least to greatest: 1 2 4 1 7 2, , , , ,3 5 5 2 1 0 3

a n d

6) Order the decimals from the least to the greatest: 6.091, 6.01, 6.009, -6.9, and 6.19

7) Order the numbers from least to greatest 2 3 10.6, , 0.74, , .05,3 5 3

8) Write each number as a mixed number or a fraction in lowest terms and as a decimal: a) five hundred five and twenty-five thousandths b) six hundred sixty-seven thousandths c) three hundred two and seventy-five ten-thousandths 9) Write a mixed number or fraction in lowest terms for each decimal: a) 3.2 b) -0.0001 c) 47.032 10) Add or subtract :

a) 2 16 33 4 b) 1 7 21

2 8 3

c) 7 78

10 8

11) Find the reciprocals of the following numbers:

a) 13

b) 325

c) 2.3

12) Find the area of the rectangle with sides 235

and 57

inches.

13) Find the product:

a) 1 535 7

b) 5 12 58 4 c) 1 23 6

2 3

14) Find the following quotients

a) 2 59 35 6 b) 1 24 2

2 3 c) 210 1

3

15) Complete each proportion:

a) ? 754 9

b) 20 ?30 3

c) 75 15? 16

16) The ratio of apple trees to peach trees in Mr. Green’s orchard are 7 : 4. How many peach trees are planted if Mr. Green has 56 apple trees in his orchard? 17) Change each decimal to a percent: a) 3.59 b) .045 c) 12.56 d) 0.002

18) Change each fraction to a percent:

a) 3138

b) 7210

c) 45

d) 912

19) Last year 48% of the crimes committed in a certain state were robberies or burglaries. If there are 263 crimes this year, how many can be expected to be robberies or burglaries? 20) An investment is expected to yield a profit of 9.8% per year. If the investment is $4050, what is the approximate yield for the year? 21) A bag contains 12 marbles: 4 red ( R), 6 green ( G) and 2 white (W) if the marbles are randomly drawn from each bag find the following : a) P ( G) b) P ( R) c) P (not W) d) P ( R or W) 22) What is the theoretical probability that you would roll a number that is greater than 3 in two rolls of a 6 sided number cube?

23) Trial 1 2 3 4 5 Coin 1

H T T T H

Coin 2

T T H H T

Use the data in the table above to find the experimental probability of: a) At least one coin is heads b) Both coins are tales c) Both coins are heads

Chapter 4 Use your calculator to compute the actual values: 1) 5 2) 170 3) 40 4) 132 Find the squares of the following numbers:

5) 23 6) 21.25 7) 212 8) 2

132

9) State the Pythagorean Theorem: 10) Find the length of the missing side of the given right triangle: 11) Is the triangle that has sides that measure: 1, 1.5, and 2 yards a right triangle? 12) The cable company buries a line diagonally across a lot. The lot measures 105 feet by 60 feet. How long is the line?

10

8

a

13) Katrina’s height is 1.6 meters. Her shadow measures 1.1m. How big is the shadow of a tree that measures 13 m. 14) Find the areas of the given polygons: a) Square with sides 2” b) Rectangle with sides 2’ and 3.5’ c) Triangle with alt. 4 m, and base of 6m. d) Trapezoid with 1b = 3ft, 2b =8 ft, h = 5.5 ft.

e) Parallelogram with base of 5.7 cm, and a height of 2.1 cm. Simplify: 15) (2a + 3b + 5c) + (7a - 3b + 5c) 16) ( x + y + z ) = ( 2w + 3y + 5)

17) 1 13 2x x

Chapter 5 Find the sum:

1) 3 2 4 6x x 2) 3 7a b a b

3) Find the a simplified expression for the perimeter of the triangle: A picture is surrounded by a frame that is 2 inches wide. If the picture by itself is b inches wide and h inches high, find the following dimensions of the picture and frame combined. 4) The total height: 5) The total width: 6) The total perimeter: Find the opposite of each expression: 7) 5 x 8) 3 4z q

Find the difference:

9) 8 3 2 4y z y z 10) 3 1 6 5x x

Solve each equation. Show all steps for problem solving:

2x + 5 3x + 2

4x -1

11) 3 1a 12) 4 1z 13) 4 3b

14) 4.3 3.7P 15) 2 15 2

x 16) 1 21

2 33b

17) Write an equation to show that the perimeter of this rectangle is 52. Then solve for x. Show your work. Equation: x = 18) Solve the following for y: x y z Simplify each polynomial by combining like terms. Show all work:

19) 2 23 3 2 5a a a a 20) 6 2 7 2y x y x Simplify each binomial subtraction expression. Show all work:

21) 22 7 7 3x x 22) 2 24 3 2 6 3x x x x

12

x

Chapter 6 Evaluate 2x y for each value of x and y

1) x = 3 and y = -2 2) x = 12

and y = 13

Multiply or divide. Simplify when possible.

3) 33 3x 4) 2 7 2t

5) 30 363

y

6) 229 8 4 3x x

Solve each equation. Show all steps for problem solving:

7) 17 85x 8) 0.58

w

9) 2.2 33h 10) 2.4

10y

Use the Distributive Property to find each product.

11) 5 4h 12) 24 7t t 13) 212 11b b b

Write each polynomial in factored form.

14) 26 8x 15) 35 25c c 16) 4 25z z

Solve each equation. Show all steps.

17) 4 47

x 18) 1 2.59

w 19) 316 4y

Solve each proportion. Show all steps.

20) 126 9n 21) 13 39

27n 22) 11.4 45.6

8 x

Find each answer. Show all work.

23) What is 55% of 60? 24) What percent of 15 is 3? 25) 28 is 70% of what number? 26) What is 150% of 28?

Chapter 7 Solve each equation. Show all steps.

1) 2 5 8x 2) 2 533 8

x 3) 3 4 8x

4) 3 1 6 5w w 5) 4 5 7 2x x

Solve each word problem. Show all steps.

6) Find three consecutive integers whose sum is 141.

7) Lynn has scores of 95, 91, and 88 on three tests. Write and solve an equation to find a fourth score that will produce an average of 90 for the four tests.

8) Jackson is the manager of the men’s department store. His base salary is $500 per

week plus a commission of 1.2% of the weekly sales in the department. What must the total of the weekly sales be if he wants to earn a weekly income of $1000?

9) Ted has 16 mL of a solution that is 2% acid. How many mL of a 5% solution does he need to add to get a solution that is 3% acid?

10) The perimeter of a rectangle is 56 feet. The length is 3 feet more than the width.

What are the dimensions of the rectangle?

11) The area of a trapezoid is 192 square inches. If the height is 16 inches and one base is 10 inches, find the length of the second base.

12) The measure of the large of two complementary angles is 4 times more measure of the smaller angle. Find the measure of both angles.

13) One number is 7 more than another. Twice the larger is 22 less than 4 times the smaller. Find the numbers.

Solve each inequality:

23) 1 4x 24) 3 12p 25) 4 2 2 3x x Solve the Following Absolute-Value Equations:

26) 2 10x 27) 2 9 15x 28) 3 2 4 11x

Find the values of x that solve each absolute value inequality. Graph each answer on the number line. Chapter 8 1-5.) Label the 4 quadrants and the origin. Name the letter that corresponds to the following points, and give its quadrant: 6.) (-9, -6):

7.) (0, 8) :

Name the coordinates of the following points:

8.) F

9.) H

x

y

x

y

A

B

C

N

H

V

SD

E

F

O

Graph each list of ordered pairs. State whether they lie on a straight line.

10.) (-2, 1), (0, -2), (2, -5) 11.) (-3, -4), (0, 0), (3, 3) 6

4

2

-2

-4

-6

y

-5 5x

6

4

2

-2

-4

-6

y

-5 5x

12.) Find the values for y by substituting -2, -1, 0, 1, and 2 in for x. Make a table and graph your results.

y = 3x – 2

6

4

2

-2

-4

-6

y

-5 5x

13.) A photography studio charges $10 per sitting and an additional $5 for each print

ordered. Represent the number of prints ordered by p and the cost of the prints by c. Write a function to express the cost of the prints in terms of p. Graph the function for orders of 5 to 25 prints.

Prints Cost Ordered Pair

Equation:

Graph the function for orders of 5 to 25 prints:

What is the independent variable? What is the dependent variable? What is the domain? What is the range?

14. Find the slope of the line with a rise of -3 and a run of -9 15. What is the slope of the line that passes through the points (-2, 1) and (-6, 0) Write an equation in slope-intercept form for each line:

16.) The slope is 12

and the y-intercept is 4.

17.) The slope is 3and the line passes through point (-2, 5) Write an equation in slope-intercept form for each line passing through the following points: Show all work 18.) (2, -10) and (1, -5) 19.) State the general equation of the Standard Form of the Line. 20.) Find the slope of a line given two points (1,-4) (5, -3). 21.) Give the slope of the line containing the origin and the point (-4, 16). 22.) What is the equation of the line? 23.) Given the equation y = 3x; The y- intercept is: The slope is:

24.) Given the equation: 3

72

y x

The y- intercept is: The slope is:

25.) Find the slope of the line passing through the pair of points: (0,-7), ( -4, 0) 26.) Write the equation of the line in slope-intercept form: passes through (0, 6) and with slope of -4. 27.) The equation 2 4 8x y is written in: (Circle the correct answer)

a) Standard Form b) Slope-Intercept Form c) Point Slope Form 28.) Describe the graph of the line 3 5y x . 29.) Graph the following equation using the x- and y-intercepts.

4 3 12x y 29.) Write the equation of a vertical line that passes through the point ( 8, 0) 30.) What is the slope of the line y = -2.5 ? 31.) Find the equation of the line that contains point ( 3,-1) and is

a) parallel to the line 2 3y x b) perpendicular to the line - 2 3y x

x

y

32.) Graph the inequality: 2 3y x 33.) Graph the inequality : y > -2 34.) Write the equation of the inequality that is graphed below:

x

y

x

y

x

y