2014_maths_olevel_mj_paper1

Extracted Content: 2014_maths_olevel_mj_paper1

Page 1

Extracted Text

Surname Forename(s) Centre Number Candidate Number

S —- )
—

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4008/1
PAPER 1

JUNE 2014 SESSION 2 hours 30 minutes

Candidates answer on the question paper.
Additional materials:
Geometrical instruments

Allow candidates 5 minutes to count pages before the examination.

TIME 2 hours 30 minutes

INSTRUCTIONS TO CANDIDATES

Write your name, Centre number and candidate number in the spaces at the top of this page
and your Centre number and Candidate number on the top right corner of every page of this
paper.

Answer all questions.

Check that all the pages are in the booklet and ask the invigilator for a replacement if there are
duplicate or missing pages.

Write your answers in the spaces provided on the question paper using black or blue pens.

If working is needed for any question, it must be shown in the space below that question.
Omission of essential working will result in loss of marks.

Decimal answers which are not exact should be given correct to three significant figures
unless stated otherwise.

Mathematical tables, slide rules and calculators should not be brought into the
examination room.

INFORMATION FOR CANDIDATES FOR EXAMINER’S USE
The number of marks is given in brackets [ ] at the end

of each question or part question.

This question paper consists of 24 printed pages.
Copyright: Zimbabwe School Examinations Council, J2014.

©ZIMSEC 32014 [Turn over

---

Page 2

Extracted Text

Centre Number Candidate’s Number

2

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

1 Express 2046,489 correct to
(a) __ the nearest ten,
(b) 2 decimal places,

(c) 2 significant figures.

Answer: (a) .
(b) EY
(

---

Page 3

Extracted Text

Centre Number Candidate’s Number

Evaluate, giving your answers as common fractions in their lowest terms

3 1
(a) 3°7
5 32
(b) 3% as?
5 1
ate
Answer: (a) {1]
(b) {1]
(c) {1]

annasi ward

---

Page 4

Extracted Text

Centre Number

4

Giving your answer as a decimal, find the exact value of
(a) (0,175 - 0,049,
(b) 0.0144,

(ec) (0,06).

Answer: (a)
(b)
(¢)

Candidate’s Number

[1]

(1)

---

Page 5

Extracted Text

Centre Number

(a) Expand (2a -b)(1+c).

m> —mn m

n? -np “(a= p)

(b) Simplify

Answer: (a)

Candidate’s Number

()

It is given that
& = {30; 31; 32; 33; 34; 35; 36; 37; 38; 39},

A is the set of odd numbers and
B is the set of prime numbers.

(a) _ List the elements of
@ A,
(jij) =

(b) Find n(AMB').

4008/1 J2014

[Turn over

---

Page 6

Extracted Text

Centre Number Candidate’s Number

6
Answer: (a) 7G) { }1Y
fj) { } [1]

() {1

---

Page 7

Extracted Text

Centre Number Candidate’s Number

7
(a) State the special type of a triangle which has one line of symmetry.
(b) — A polygon has n sides. Two of its exterior angles are 55° and 45°.
The remaining (n - 2) exterior angles are each 20°.
Calculate the value of n.
Answer: (a) [1]
(b) ne _ [2]
(a) Express 9 minutes after midnight as time on the 24 hour clock.
(b) In 1998 the population of a village was 2,8 x 10*. In 2004,

the population was 3,5 x 107.

Calculate the percentage increase of the population from 1998 to 2004.

Answer: (a) [1]

(b) [2]

4008/1 J2014

---

Page 8

Extracted Text

8

Centre Number Candidate’s Number

8
Solve the simultaneous equations
=xey,
3 y
2x +y=-7.
Answer: x=
ya [3]

(a) Given that f(x) = (x -1)(x +6) and that f(0) = p, find the value
of p.

(b) If yk = ax — bk, make k the subject of the formula.

Answer: (@ p= {1}

---

Page 9

Extracted Text

Centre Number Candidate’s Number

9

10 (a) Express 3° + 3? +3 as a number in base 3.
(b) Evaluate
(i) 143g + 57s giving your answer in base 8,

(ii) 45 - 23 + ly giving your answer in base 10.

Answer: (a) (1]
® @ oo
Ww

4008/1 J2014

---

Page 10

Extracted Text

Centre Number Candidate’s Number

10

11

In the diagram, ABCD is a circle. Tangents at C and D meet at E and
ED is produced to F such that ADF = 50° and ABC = 116°.

Calculate

(a) ADC,
(b) CDE,
(c) CED.

Answer: (@ (\j

(b) U1]

(c) 1)

---

Page 11

Extracted Text

Centre Number Candidate’s Number

11

12 The cost of making a telephone call on Teneco is 25 cents per minute.
Kuda has p cents and is able to make a call.

Xolani has g cents which is insufficient to make a call. Write down 3 inequalities in
terms of p and/or q, other than p > 0 and g > 0, that satisfy the given conditions.

Answer: @ {ij
WM
(iii) —CéESYJ

13 AB is a line whose equation is 6y = 7x +48.
Find
(a) the gradient of line AB,

(b) the equation of the line parallel to AB which passes through the point
(3; 1), giving your equation in the form ay +bx+c =0.

Answer: (a) {1]

(b) [2]

4008/1 J2014

---

Page 12

Extracted Text

Centre Number Candidate’s Number

12

14 (a) Given that 4m = 7n, find the ratio m:n.
(b) A holiday trip to South Africa cost R333. If the exchange rate was

US$1 to R8, calculate the cost of the trip in US$, giving your answer
to the nearest cent.

Answer: (a) (1

() US$ 2]

15 Factorise completely

3x?y -12xy?.

Answer: [3]

---

Page 13

Extracted Text

Centre Number

Candidate’s Number

13
16 Solve the equation
Ayo
» 4) “16°
Answer: y= or 13]
I
17 (@)_—_ Simplify (32x'°)5.
2 x bk
(b) Given that ——— = 2’, find the value of c.
2
Answer: (a) (2]
(b) c= [2]

---

Page 14

Extracted Text

Centre Number

14

Candidate’s Number

2 1
18 It is given that P = ; ; and Q = 2P — I where I is the identity matrix.

Find
(a) PT,
(b) Q.

Answer:

(a)

(2)

(b)

4008/1 J2014

---

Page 15

Extracted Text

Centre Number Candidate’s Number

15

19

In the diagram, OABCDE is a hexagon.
(a) Express as column vectors

@) OE,

(i) OA+AD.

(b) Describe fully the single transformation which maps side BC onto
side OE.

Answer: (a) G) OE = | fl]
(ii) OR + RB =| | (]

(b)

[2]

4008/1 32014
[Turn over

---

Page 16

Extracted Text

20

Centre Number Candidate’s Number

16

All lengths on a map are a of their actual lengths.

Calculate
(a) the actual length of line represented on the map by a line 7,3 cm,

(b) the area on the map which represents an actual area of 525 m’,
giving your answer in cm”.

Answer: (a) , 1]

(b) em? [3]

---

Page 17

Extracted Text

Centre Number

17

21 Evaluate

log, 64

() log,4’

(b) 1 + logs9.

Answer: (a)

Candidate’s Number

[2]

(0)

22]

4008/1 32014

---

Page 18

Extracted Text

Centre Number Candidate’s Number

18

22 In the answer space below, is a line segment AB which is 7 cm long.
(a) Using ruler and compasses only, construct the locus of points
(i) 3 cm from B,
(ii) above AB, which are 2 cm from line AB.

(b) 3) Mark and label P, and Po, points which are 3 cm from B and
2 em from line AB.

(ii) | Measure the distance P;P2.

a

Answer: (a) i) on diagram {1]
(ii) on diagram (2]
(b) (i) on diagram {J

ji) __ om (1)

---

Page 19

Extracted Text

Centre Number Candidate’s Number

19
23. (a)
Q re)
N ; 237

In the diagram, P and Q are points on level ground. The bearing of P from
Q is 237°. Find the bearing of Q from P.

(b) The diagram shows two semi circles APM and AQB. AM = MB = 3,5 cm.
Taking x to be =, calculate the perimeter of the shaded region.

Answer: (@) {2]

(b) em [3]

4008/1 J2014

---

Page 20

Extracted Text

Centre Number Candidate’s Number

20

24 age in years

pote Ds be te fe

The ages of pupils in a class of 30 are shown in the table.

(a) Two pupils are chosen at random from the class, find the probability
that one is aged 11 years and the other is aged 14.

(b) Calculate the mean age of the pupils.

Answer: (a) {2]

() {3]

---

Page 21

Extracted Text

Centre Number Candidate’s Number

21

25

R

In the diagram, PQ is parallel to RS. PS and QR intersect at X. It is
given that PX = 2 cm, SK =3 cm, QX = (y + 2) cm and RX = (2y - 1) cm

(a) Name the triangle which is similar to triangle PQX.
(b) Using your results in (a), find the value of y.

(c) Write down the length of QR.

Answer: (a) {1]

® ys OBB]
() QRe OY

4008/1 J2014

---

Page 22

Extracted Text

Centre Number Candidate’s Number

22
26
V
(m/s)
0 10 22
u(s)

The diagram is the velocity-time graph of an object which accelerated

uniformly for 10 seconds. During this time the velocity, V m/s, at time t seconds
from the start, was given by V = 6 + 2r. It then decelerated uniformly to rest

in a further 12 seconds.

Calculate

(a) the velocity of the object when t = 0,

(b) __ the deceleration of the object,

(c) the distance covered by the object in the 22 seconds,

(d) the average speed of the object for the whole journey.

4008/1 J2014

---

Page 23

Extracted Text

26

Answer:

Centre Number

Candidate's

23

(a) m/s
(b) m/s*
(©) m
(a) m/s

[1]
[2]

{1]

4008/1 J2014

{Turn over

---

Page 24

Extracted Text

Centre Number Candidate’s Number

24

27

14

In the diagram, ABC is a triangle in which AB =x cm, AC = 2x cm,
BC = 14cm and BAC =120°.

Using as much of the information given below as is necessary, calculate
(a) the value of x, leaving your answer in surd form,

(b) the area of triangle ABC.

[sin60° = 0,87; cos60°=0,5; tan60° = 1,73]

Answer: (a) [4]

@ em

---