Candidate Centre Number Number

TIME 2 hours

INSTRUCTIONS TO CANDIDATES

Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. If working is needed for any question it must be shown below that question. Omission of essential working will result in loss of marks. NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

FOR EXAMINERS USE

This question paper consists of 15 printed pages and 1 blank page. MFK (0454) QF72012 63 UCLES 1997 [Turn over

For Exirtiioier

U.se 2

NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE USED IN THIS PAPER.

1 (a) Arrange the following three numbers in order, starting with the smallest. 1 - 0.22, 0.033. 5 '

(b) On a particular day the temperature varied by 28 "C. The highest temperature recorded was 22 "C. What was the lowest temperature recorded on that day?

Answer (a) [I1

( b ) "C PI

...............................................................

..........................................................

2 The mirror image of the words FIRE RESCUE is painted on the front of some fire engines. Drivers of vehicles in front can then read the words when looking in their mirrors. Complete the mirror image shown in the answer space.

Answer

Actual words I Mirror image I I I

FIRE RESCUEhU I - - - - - - 23FI 3FIl ---- I I I 1

1 [21 ~ ~ _ _ ~

3 Given that matrix A =

(a) calculate the value of the determinant of A, (b) write down A-'.

PI Answer (a ) ...............................................................

(b ) A-' = ( ) [l]

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Use 3

4 The exterior angle of a regular polygon is 15".

How many sides does it have?

...................................................................... Answer 121

5 Evaluate

(a) 3-2,

P I Answer (a) ...............................................................

............................................................... ( b ) P I

6 The mass of the earth is 5.9763 x l O Z 7 grams.

Expressing your answers in standard form, correct to 3 significant figures, write this mass

(a) ingrams,

(b) in kilograms.

Answer (a) ............................................................ g P I

(b ) kg PI ..........................................................

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4

7 In June 1995,l dollar = 3.56 Pula.

(a) On the axes in the answer space, draw a graph which you can use to convert from one currency to the other.

(b) Use your graph to estimate the cost in dollars of a T-shirt priced at 65.20 Pula.

Answer (a)

Pula

10 20 Dollars

[I1 Answer ( b ) $ ............................................................

4 K W 1 , 4024111397

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5

8 Solve the equations

3 (a) -=4 ,

X

(b) 5y - 3(y - 1) = 23.

......................................................... Answer (a) x = P I (b ) y = PI .........................................................

9 When it is 07 00 in New York, the time in London is 12 00.

(a) What is the time in London when it is 22 00 in New York?

(b) A flight from London departs at 4.30 p.m. The flying time is 6 hours.

What is the time in New York when it arrives?

................................................................ Answer (a) P I (b) PI ................................................................

10 Given that 87 x 132 = 11484,

(a) complete the statement

88 x 132 = 11484 + .......

(b) write down the exact value of

(i) 0.087 x 13200,

(ii) 0.11484 i 0.0087.

............................. Answer (a) 88 x 132 = 11484 + PI (6 ) (i) 111

(ii) P I

..........................................................

.........................................................

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11 Solve the simultaneous equations

7~ - 5y = 17,

3~ - 2y = 7.

Answer x = ...............................................................

............................................................... [31 y =

12 Evaluate

(a) 16-2 x 3,

(b) f x21, 7 1 (c) 8 + fi.

................................................................ P I Answer ( a )

............................................................... P I ( b )

................................................................ U1 ( c )

For Examinrr '

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7

13 In a shop, a bicycle is priced at $451. The price inciudes Government Tax at 10%.

How much is the tax?

................................................................... Answer $ [31

14 (a) Write down all the integer values of n for which

- 3 < n ~ 1 .

(b) Solve the inequality

3 - 5 x z - 18.

Answer ( a ) ............................................................... [I1

............................................................... ( h ) PI I__ - - .____

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15 The sequence of numbers

1, 5 , 11, 19. 29, ..........

can also be expressed in the form

l 2 + 0 , 2 2 + 1 , 3 2 + 2 , 4 2 + 3 , ...........

(a) Express the 5th term in the same form.

(b) Write down, in terms of n, a formula for the nth term.

(c) Calculate the value of the 100th term of the sequence.

............................................................... Answer (a ) P I ( b ) PI ( c ) E11

...............................................................

................................................................

16 Given that y is directly proportional to the cube root of x, and that y = 18 when x = 27,

(a) express y in terms of x,

(b) calculate the value of y when x = 125.

PI Answer ( a ) ...............................................................

( h ) PI ...............................................................

9

17 Miss Jones asked thechildren in her class, 'What is your favourite colour?' Her results are shown on the bar chart.

Frequency

10

8

6

4

2

n

(a) (i) How many children are in her class?

(ii) What is the mode of the distribution?

......................................................... Answer (a) (i) P I (ii) [11 .........................................................

(b) The information is also to be represented in a pie chart.

Calculate the angle of the sector representing Yellow.

................................................................ Answer ( b ) PI

18 Factorise completely

(a) 5-45t2 ,

(b) 6 p 2 - p - 2 .

............................................................... Answer (a) PI ( b ) PI ...............................................................

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10

19 The diagram in the answer space shows the triangles A and R.

(a) Triangle A is mapped onto triangle C by the translation (-;)- On the diagram, draw and label triangle C.

Answer ( a )

y4

(b) Describe fully the single transformation which maps triangle A onto triangle B .

ilnswcr ( h ) .............................................................................

.............................................................................

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11

20 The cumulative frequency curve shows the age distribution of the population of the United States of America in 1950.

Cumulative Frequency (millions)

150

100

50

U 20 80 100

Use the curve to estimate

(a) the median age of the distribution,

(b) the upper quartile of the distribution,

(c) the probability that an American chosen at random would be more than 60 years old.

............................................. [I1

( b ) Upper Quartile = P I ( c ) 121

Answer (a ) Median =

................................

................................................................

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21

12

(a) Given that

3 t - 2 '

s=-

express t in terms of s.

.......................................................... [*I Answer (a) t = (b) Express as a single fraction

4 3 2 x - 1 5 x + 6 ' ---

............................................................... P I Answer (b )

For .ruminer

Use

13

22 OACBisa quadrilateral. F

OB is parallel to AC.

D is the point on BC such that B D = ~ B C .

The lines OB and AD produced meet at F. A

0

(a) (i) Explain why triangles ACD and FBD are similar.

Answer (a)(i) ...........................................................................................................

........................................................................................................... E21 (ii) Show that FB = f AC.

Answer (a)(ii) ..........................................................................................................

.......................................................................................................... 111

4

(b) Given also that A C - = (- E) , calculate the value of I B F I . ............................................................... Answer ( b ) E11

+ (c) Given also that OB = AC, and , express FC as a column vector

................................................................ Answer (c) E21

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Use 14

23

The diagram is the plan of an area of level ground which Jill is surveying. It is drawn to a scale of 1 cm to 5 m.

From a point A she walks 40 m along a straight path to B. A line to represent A B is already drawn on the plan.

(a) At B, she turns clockwise through 150" and walks along another straight path. Draw a line on the plan to represent this path. P I

(b) She stops at a point Cwhich is 40 m from A. Mark the point Con the diagram and find, in metres, the actual distance between B and C.

m I21 Answer ( b ) BC = .................................................

(c) By making appropriate constructions on your diagram, shade the region representing those points which are less than 10 m from BC and less than 15 m from A . [31

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!4

15

In this question F, stands for the set of factors of the number p .

For example, F, , = { 1, 2, 3, 4, 6, 12}, and the number of elements in F , 2 is n(F,,) = 6.

(a) List the elements of F18.

Answer (a) F,, = { .......................................... .......

(b) Show that n(F3& = 8.

Answer (b ) ...............................................................

............................................................... Cl1

(c) Given that n(F,) = 2, what kind of number is p?

................................................................ 111 Answer (c)

In the remaining parts of the question there are many possible answers but you only need to give one for each.

(d) Find a value of p such that F, C F12.

......................................................... Answer ( d ) p = PI (e) Find a value of p such that n(F,) = 3.

......................................................... 121 Answer (e ) p =

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