Chs 4016 2010 Prelim III p1

CHS/4016 2010/ PRELIM III/P 1

Page 1 of 14

1 It is given that 89.512.34 14.19

x =+

.

(i) Without the use of a calculator, estimate the value of x, showing your steps clearly.

(ii) With your calculator, find the value of x to 1 decimal place.

Answer (i) [2]

(ii) [1]

2. (a) Express 1072 + xx in the form 2( )b x a + .

(b) Hence solve the equation 01072 =+ xx , giving your answers correct to two decimal places.

Answer : (a)......................................[2]

(b) .................................... [2]


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3. Given that ( ) ( )3 23 9 qm m pm = , find the value of p and q.

Answer p = [1]

q = [1]

4. In a marathon, Fique ran 42.195 km in 2 hours 20 minutes and 24 seconds.

(i) Express 2 hours 20 minutes and 24 seconds in hours.

(ii) Find Fiques speed in km/h.

Answer (i) ..h [1]

(ii) .. km/h [1]

5. Mr Le withdrew $300 and $150 worth of $5 and $2 new notes respectively from the bank. He intends to distribute the notes equally into red packets so that there would be the same number of $5 and of $2 notes in each red packet. Find

(i) the greatest number of red packets he could obtain as a result, and

(ii) the amount of money in each red packet.

Answer (i) [2]

(ii)$ [1]


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6. Write down the equation of the graph shown below.

Answer [2]

7. The radius of a water molecule is about 0.2 nanometres while a piece of paper is approximately 100 micrometres thick. Calculate the number of water molecules needed to be lined up in a straight line down the thickness of the paper. Leave your answer in standard form.

Answer [2]

8. Given that p is a perfect square, find the smallest possible value of p for which

pp +


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9. A teacher asked a group of students to check the number of children there were in each of their households. The pie chart below represented the data gathered from these children with 90o being 6 households. Use the answer space provided to illustrate the information.

[2]

Calculate the mean number of children per household.

Answer . [2]

10. It is given that

=

z

yxM

3223

and

=

2218

32

M .

(a) Show that x + y = 3.

(b) Find the value of z.

(b) z =... [2]

1 child

2 child

ren

3 child

ren

1 child

2 child

ren

3 child

ren


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11. Given that

= {2, 4, 6, 8, 10, 12, 14, 16, 18} A = {x : x is a multiple of 4}

B = {x : 15 < 3x < 30}

((((a) Illustrate the above information on the Venn diagram below. [2]

(b) Find ( )'BAn .

(c) Find an element x such that BxAx and ' .

Answer (b) . [1]

(c).. [1]

CHS/4016 2010/ PRELIM III/P

12. Given that AD AE cm EB cm and CE cm= = = =(a) Prove that

(b) State the length of

(a)


5 , 7 13 ,AD AE cm EB cm and CE cm= = = =BAC

and CAE are congruent. State your reasons clearly.

State the length of CD.

Answers (b) ...................................

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5 , 7 13 ,AD AE cm EB cm and CE cm your reasons clearly.

[3]

..............................cm[1]


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13. Given that 8,10, 8,0 and C 0, 6 . Find in the simplest form, the exact value of

(a) sin A C, (b) the area of triangle ABC, and (c) hence, the shortest distance of B from AC.

Answers (a) [2]

(b) units2[1]

(c) units[2]


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14. (i) Sketch the graph of 31 [2] (ii) Hence, state the coordinates of its turning point

Answers (i)refer to graph.[2]

(ii) , [1]

15. The length of time that a group of motorists parked their vehicles in a particular car park was recorded and illustrated in the stem and leaf diagram.

The data was also illustrated on a box and whiskers diagram below. Find the values of a and b as indicated on the diagram.

Answer a = ................................. [1]

b =...................................[1]

0 8 6 1 2 4 3 2 1 8 4 3 3 4 4 0 1 2


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16. The 6-sided polygon ABCDEF in the diagram has 4 angles of x . Given that AF is parallel to BC and CD is perpendicular to DE. Find (a) the value of x, (b) ABC .

Answer : (a) x = ........................................[3]

(b) .......................................... [1]

17. Given that 22 7 11a =

and 3 22 7b =

, find

(i) the LCM of a and b,

(ii) the smallest possible value of c if a b c is a perfect cube.

Answer (i) [1]

(ii) c = [1]

x

xx

x

A B

C

D

E

F


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18. The resistance, R ohms, of a wire of a constant length is inversely proportional to the square of its diameter , d mm. (a) When the diameter of the wire is 2 mm, the resistance is 24 ohms, find

an equation connecting the resistance of the wire, R, to the diameter of the wire, d.

(b) When the diameter of the wire is of a certain length, its resistance is 32 ohms. Write down the resistance when the diameter is doubled.

Answer (a) ................................. [2]

(b) ....................................[1]

19. On a map whose scale is 1 cm to 0.007 km, the distance between two trees A and B is 60 cm and the area of a fish pond is 100 cm 2.

(a) Calculate the actual distance between A and B in metres. (b) On another map whose scale is 1: n, the area of the fish pond, P is

416 cm2.

Find the value of n.

Answer (a) ...m [1]

(b).. [2]


20. A shop sells two sizes of cylindrical containers which are geometrically similar. The ratio of their diameters is 3 : 4.

(a) The surface area of the smaller container is 125 cmlarger container.

(b) The larger container has a capacity of 135 litres. Find the capacity of the smaller container.

21. The diagram is the distance The car started from rest.

(a) Find the speed of the car when (b) Give a short explanation of what could have occurred at (c) The car moved with a constant acceleration for

this acceleration.(d) On the grid in the

journey.


A shop sells two sizes of cylindrical containers which are geometrically similar. The ratio of their diameters is 3 : 4.

The surface area of the smaller container is 125 cm2. Find the surface area of the

The larger container has a capacity of 135 litres. Find the capacity of the smaller

Answer (a)

(b)

. The diagram is the distance-time graph for the first 30 seconds of a cars journey.The car started from rest.

Find the speed of the car when 20.t = Give a short explanation of what could have occurred at The car moved with a constant acceleration for the first 10 seconds. Find this acceleration. On the grid in the answer space, draw the speed-time graph for the same

Page 11 of 14

A shop sells two sizes of cylindrical containers which are geometrically similar.

. Find the surface area of the

The larger container has a capacity of 135 litres. Find the capacity of the smaller

cm2. [2]

litres [2]

conds of a cars journey.

Give a short explanation of what could have occurred at 25t =.

the first 10 seconds. Find

me graph for the same


(b)


Answers (a)

(c)

Page 12 of 14

m/s [1]

[1]

m/s2[2]

[2]


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22. A is the point ( 2, 3), B is the point (9, 6) and O is the origin. P is a point such that 4AP AB=

uuur uuur.

(a) Express each of the following as a column vector, (i) AB

uuur,

(ii) OPuuur

.

(b) It is given that OA =uuur

a and OB =uuur

b. M is a point such that 3BM =

uuuura.

Express each of the following in terms of a and/or b, (i) OP

uuur,

(ii) OMuuuur

.

(c) What can you deduce about points O, P and M ? Explain your deduction clearly.

Answer (a)(i) .................................. [1]

(ii) ................................... [2]

(b)(i) .................................... [2]

(ii) .................................... [1]

(c) [1]

P

O

A

a

b

B


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23. In the answer space below shows the positions of the points A and B. B is due east of A.

(a) C is a point on a bearing of 030 form A and on a bearing of 320 from B. Draw and label the position of the point C. [2]

(b) M is the intersection of the perpendicular bisector of AB and the angle bisector of ABC . By constructing, using compasses and rulers only, the perpendicular bisector and the angle bisector, find and label the position of the point M. [2]

(c) AB and BC are the tangents of a circle with centre M. Draw this circle. [1]

A B

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Chs 4016 2010 Prelim III p1