2018_maths_olevel_mj_paper1

Extracted Content: 2018_maths_olevel_mj_paper1

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Candidate Name Centre Number Candidate Number

Hy mr
Vor Purformaes Meantreintes

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4030/1.

PAPER 1
JUNE 2018 SESSION 2 hours 30 minutes

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

Allow candidates 5 minutes te count pages before the examination.
This booklet should not be punched or stapled and pages should not be removed.

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 r~ .nber on the top right corner of every page of this paper.

Answer ail 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 biue 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. Answers in degrees should be given correct to one decimal place

unless stated otherwise.

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

INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.

This question paper consists of 28 printed pages.

Copyright: Zimbabwe School Examinations Council, 32018.
©ZIMSECI2018 [Turn over

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Centre Number Cangicsic Mumber

2

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

1 (a) Express 3598
0) as a number in standard form,

(ii) —_ correct to 2 significant figures.

(b) ‘Find the approximate value of ¥3598.

Answer: (@ {1}
GD {lt}
(b) fl]

FT P2008

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2 (a) Find the exact value of wd 7,03 - 2,145,

(iil) = 4,32 x 0,11.

(b) Simplify 1 z +2 * giving the answer as a mixed number.

Answer (@ (G)

(ii)

(b)

(1)
(1)
[1]

4030/1 32018

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Centre Number Candidate Number 4 (a) Express the time 00 25 in 12 hour notation. (b) A goods train left Johannesburg at 20 30 on a Wednesday and arrived in Beitbridge after travelling for 27 hours 45 minutes. @ State the day on which the train arrived at Beitbridge. (ii) Find the time at which the train arrived at Beitbridge. Answer (a) . ___ {1} (b) (i) a fl (ii) ee 6 8 ae

4030; f 32018

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Evaluate

(a)

0,027 ,

wy (2%,

{c)

3°x3-2,

Answer

(a)
(b)

(ce)

Centre Number

4036/1 J2018

Candidate Number

{I}
[1

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ha

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Centre Number Candidate Number

6

(a) State the number of lines of symmetry of a regular nonagon.
(b) The sum of interior angles of a regular polygon is 3 960°.

Find the number of sides of the regular polygon.

Answer (a {i}

OM I

ANIO/ 013

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{a) {b)

Centre Number Candidate Number

7

Simplify 1044, — 175g, giving the answer in base 8.

Convert 10111, to a number in base 6.

Answer

(a) (1)
(b} [2}

4030 E 2048
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Centre Number Candidate Number

In the diagram W, X, Y and Z are points on the circumference of a circle centre O,
WX = XY and X2W = 42°,

Calculate
(a) WYX,
(by) YW%Z,
(ec) WRY.

Answer (a) fj

(0) {1}

(c) (1]

AO30'1 J2013

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Centre Number Candidate Number

9
8 Solve the equations:
(a) dx-1=
(by) 47-3 =8
Answer (a xe {i}
n= [2]
4030} J2018

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Centre Number Candidate Number

10

(a) Three sets A, B and C are such that A C Band c A. In the
answer space, draw the Venn diagram to show the relationship
between sets A, B and C.

(b)

In the diagram, three sets P, Q and R are intersecting. Use set
notation to describe the shaded region.

Answer (a) [2]

by (1)

AGIOr1 $2018

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Centre Number

11

10 It is given that y varies directly as the square of (x — 3).
{a} Express y in terms of x and a constant &.

(b) Given that y= 16 when x = 1, find y when x = 10.

Answer (a)

(b)

Candidate Number

(1)
(2)

4030/1 J2048

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Centre Number

12

el Solve the simultaneous equations:

Nir

xty = 5

Nope

x-ay = 2

Answer x

4030/1 J2018

Candidate Number

{3]

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Centre Number Candidate Number

13

12 It is given that 3x + 2y = 12 is an equation of a straight line.
(a) Find the gradient of the straight line.

(b) Find the coordinates of the point where the straight line crosses the y-axis.

Answer (a) (13

OW

a tt RI I A,
4030/1 $2018

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14
13 Simplify

3x% x
x2—5x x? - 25°

Answer {3}

4030/1 12018

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14

Centre Number Candidate Number

15

The formula for converting a temperature in degrees centigrade (°C) to a temperature
in degrees Fahrenheit (*F) is F = 32 +.

(a) Find F when C = 30°,

(b) Make C the subject of the formula.

Answer (a) Fe

4030/5 J2018

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16

15 (a) Expand and simplify,
—3( — 7) + (2 — 4x).

(b) The length of a side of a regular hexagon is 3,4 cm correct to one decimal
place.

Find the least possible perimeter of the regular hexagon.

Answer (a) {2]

(b) (2}

eee

403071 12018

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Centre Number Candidate Number

7

16 (a) Factorise completely
@) e—x,
( x? +2x4+1,

(b} —_ Hence or otherwise find the Highest Common Factor (HCF) of
x3 —xandx? +2x+1,

Answer (a) jp {2]
(i). i
(b) NY
4030/1 $2018
{Turnever

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18

7 It is given that vector p = (4) and vector q = (-”).
{a) Calculate p — q in terms of x.
(b) Find the value of
i) |pj, the magnitude of vector p.

tii) = xsuchthat2p = —3q.

Answer fa) p-q = ae © 6 |
6) W |pl [1]
() x = [2]

4024 12014

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18

Centre Number Candidate Number

19
The marks of 6 of the students who wrote a mathematics test are as
follows:
15; 14, 9 12; 11; 15.
{a) Find the median mark for the 6 students.
(b) A seventh student got x marks from the same test and the mean

mark for the seven students was 13.

Find x, the mark of the seventh student.

Answer (a) {1]

() 3) |

40501 12018
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Centre Number Candidate Nurmber

20

19 It is given that set

p ={-14; -2; 0; 1; 2 3; Vit; 9; 17 21}

{a} A number is chosen at random from set P.

Find the probability that the number is either a negative number or a
prime number.

(b) | Two numbers are chosen at random from set P one after the other,
without replacement.

Find the probability that one is a perfect square and the other is a
factor of 21.

Answer (a)

(b) {2]

4OF0/E J2018

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20

(a)

(i)

Centre Number Candidate Number

21

Solve the inequality
2x -—3) <7.

Write down the largest perfect square that satisfies the
inequality 2(x — 3) <7.

(b) =‘ Two similar bottles have heights 8 cm and 12 cm. The mass of
the bottle of height 8 cm is 40 g.

Find the mass of the similar bottle that has a height of 12 cm.

Answer fa) Oa _ . (2]
(ii) Uj
(b) ee ce _— 12}

4040/1 J2ULB

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Centre Number Candidate Number.

a

22

c A
ABC is a triangle with AB = 9 cm, BC = 4.cm and ABC = 120°.

Use as much of the information given below as is necessary.

[tan 60° = 1,73; Sin 60°= 0,87; Cos 60° = 0,5]

Find the
(a) area of triangle ABC,

(b) _—_ length of AC leaving the answer in surd form.

Answer (a) em? [2]

(b) cm [3]

4030/1 J2G18

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30

Speed
m/s

t
0 4 9 T

Time (sec)
The diagram is the speed -time graph of an object whose initial
speed is 12 m/s. The object accelerates uniformly for 4 seconds
until it reaches a speed of 30 m/s. It then travels at this speed for
5 seconds and then decelerates at 6 m/s” until it comes to rest.
Calculate the
(a) acceleration fromt=0 to #f =4,

(b) distance travelled from ?=0 to ¢=9,

(c} value of T, the total time taken for the whole journey.

Answer (a) [Y
(b) [2]
(c) ne £4

4030/1 32088

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23

In the diagram, ABCDEF is a solid triangular prism. AB = 6 cm,
BC = 20 cm, AF = 8 cm, FB = x cm and BAF = 90°,

(a) =‘ Find x.

(b) Calculate the total surface area of the prism.

Answer

(a)
(b)

:

20

Centre Number Candidate Number
24

[2]
(3)

wae . .
+e et taining tcue piper spar serena nga gpm REREH Ia SRDPEPEORRTEEOEN Sapo tokens ina ePC mes RANA a +

4030/1 2018

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Centre Number Candidate Number

25

(a) — Evaluate

(i) logs 45 — log, 5,

ve log 0,2
(ii) log 5”

(b) Express as a logarithm of a single number,

3log2 + = log 81.

Answer (yd @& [2]
(ti) (2]
(b) _ 2

4030/1 EB

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26

It is given that

a 1
3(f n)-G a) = iC? ia)

Find the value of
@ P,
tii) 4,
; Gi} or.
Answer (i) <strong></strong>—s-—*(F2J
(i) oY
(ii) —— £2)

43011 J2018

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26
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T : er? : im 7
az 4 rE yeaxis C
f th a HH Sorry. : i ri Hott LH
t T Ct 8 SETI
+ { 4 7 -| Cc a {.
65 t 7
t 4 5
A 2 A B oy
J rCy Fj i‘
76 EEE = a CEEEEH | EEE 2 (r4 4 8 £0 x-axis
ne Cy O4a mn
tH HH EHH H Hie PE H co
C, pepper Ant > HE ;
rH im t tr TH
ff i a 1A sWswaseedeun
B, oe EEA: HB 4
4 H ceEeeGEeeanee
~6 +
The diagram shows three triangles ABC, Ai BiC; and A2B:C,
(a) Triangle ABC is mapped onto triangle A,B,C, by a single transformation.
Describe fully this trans formation.
Answer (a) _
ce - [3}

4030/1 I2018

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26 (b) Triangle ABC is mapped onto triangle A2B2Cz by a reflection.

Find the
(i) equation of the axis of reflection,

(ii) —_—s matrix that represents this reflection.

® MY

ae |

4030/1 J2018

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