4004q1 specimen

Extracted Content: 4004q1 specimen

Page 1

Extracted Text

C )

ZIMBABWE SC HOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4004/1
PAPER 1
SPECIMEN PAPER 2 hours 30 minutes

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

L Allow candidates 5 minutes to 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 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
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, Specimen Paper.

©ZIMSEC Specimen Paper [Turn over

---

Page 2

Extracted Text

. 8
1 (a) _ Find the value of 004"

(b) Simplify 1

Ne

x , 4 giving the answer as a fraction in its simplest form.

4004/1 Specimen Paper

---

Page 3

Extracted Text

@ 244,
6) p’g-r.

4004/1 Specimen Paper
[Turnover

---

Page 4

Extracted Text

(a) Calculate the difference in the distances they run giving the answer in
standard form.

(b) A lap is 400 m long.

Find the number of laps in the 5 000 m race.

Answer (a) [2]

(b) [1]

4004/1 Specimen Paper

---

Page 5

Extracted Text

It is given that OP = ) and 0a = (*%) where O is the origin.

(a) Express PO as a column vector.
(b) =‘ Find
@ [09],

(¢1)) the co-ordinates of M, the midpoint of PQ.

ce
Answer (a) ¢
e

6) a
a) ( 3 )

4004/1 Specimen Paper

[Turnover

---

Page 6

Extracted Text

6

Express 1 x 33+ 2 x 33 +1 x 3! as a number in base 3.
Convert 10119 to a number in base 9.

Evaluate 203, - 154, giving the answer in base 7.

4004/1 Specimen Paper

---

Page 7

Extracted Text

Solve the simultaneous equations:

2x +3y =28
x +5y =35

Answer x

4004/1 Specimen Paper

[Turnover

---

Page 8

Extracted Text

Solve the equation:

2y +5 _9
3y-2 4

4004/1 Specimen Paper

---

Page 9

Extracted Text

Make a the subject of the formula i “ =3.
a

4004/1 Specimen Paper
[Turnover

---

Page 10

Extracted Text

When baking scones, a baker mixes six cups of flour, one cup of sugar, two
cups of water and half a cup of milk, together with other ingredients.

(a) Express the quantities of flour, sugar, water and milk as a ratio in its
simplest form.

(b) Calculate the number of cups of water needed if the baker uses four
cups of flour.

4004/1 Specimen Paper

---

Page 11

Extracted Text

11

The probability that Sihle will bring a calculator is 2 while that for Yemurai

is 3

Giving the answer as a fraction in its simplest form, find the probability that,

(a) Sihle will not bring a calculator for the lesson,

(b) only one of them will bring a calculator for the lesson.

(b) [2]

4004/1 Specimen Paper

[Turnover

---

Page 12

Extracted Text

12

Write down the special name given to a polygon with five sides.

State, for a regular five sided polygon, the
@ number of lines of symmetry,

di order of rotational symmetry.

4004/1 Specimen Paper

---

Page 13

Extracted Text

12 Solve the inequality 2- x £2x-1<11, giving the answer in the form a £ x <b,
where a and b are integers.

Answer Ex< [3]

4004/1 Specimen Paper
[Turnover

---

Page 14

Extracted Text

>Z

A
In the diagram, A, B and C are positions of 3 boreholes where BA =BC. The
borehole at C has a bearing of 116° from the borehole at B.

Calculate

(a) = ACB,

(b) the bearing of the borehole at A from the borehole at C.

4004/1 Specimen Paper

---

Page 15

Extracted Text

(b)

15

If log,,7 =0,8451, evaluate

10gjo 0,07,

109,49.

al 6
Evaluate jog 5 Sag

Answer(a) @ 2 [1]
G@) [1]
(b) [2]

4004/1 Specimen Paper
[Turn over

---

Page 16

Extracted Text

16

The table shows part of Ms Dube’s payslip for a particular month.

(a)

(b)

Earnings $ Deductions $
transport allowance 100,00 pension contribution 6,00
housing allowance 129,00 union subscription 10,00

medical aid 8,00
Insurance 17,50
basic salary 275,00 totaldeductions =
netsalary
Calculate the

@ total deductions,

di net salary.

Express the pension contribution as a percentage of her basic salary.

Answer (a) (@)

4004/1 Specimen Paper

---

Page 17

Extracted Text

(b) Find xif 9*1 “ 3°"? =3,
Answer @ [2]
() x= [2]

4004/1 Specimen Paper
[Turn over

---

Page 18

Extracted Text

18

Given that yis inversely proportional to (x - 1)’and that y = 2 when x =7,

(a) express y in terms of x,

(b) calculate the values of x when y = 8.

) x= or

4004/1 Specimen Paper

---

Page 19

Extracted Text

18 A luxury coach leaves Bulawayo for Harare every morning at 7.30 am and
arrives in Harare at 1.00 pm.

(a) Express the departure time as a time in the 24 hour notation.
(b) Calculate the total time taken to travel from Bulawayo to Harare.

(c)_ Calculate the average speed of the bus to the nearest whole number if
the distance from Bulawayo to Harare is 439 km.

Answer @ [1]
Ob [1]
(c) km/h [2]

4004/1 Specimen Paper
[Turn over

---

Page 20

Extracted Text

Factorise completely
(a) cg- dg- ch+dh,

(b) 5d’- d- 4.

20

4004/1 Specimen Paper

---

Page 21

Extracted Text

20

The pie chart shows the distribution of an athlete’s daily exercise programme.
(a) —_ Calculate the value of x
(b) If the athlete spent 18 minutes jogging, calculate the

(i) time she spent on weight lifting,

(i) _ total time spent exercising.

Answer (a) x= [1]
b @ [1]
(ii) [2]

4004/1 Specimen Paper
[Turn over

---

Page 22

Extracted Text

21

a5) Q

In the diagram, PQR is an isosceles triangle such that PQ =PR =7 cm and
PRQ =35°.

Using as much of the information given below as is necessary, calculate

(a) QR,
(b) the area of triangle POR.

sin35° = 0,57 cos35° = 0,82 tan35° = 0,70

sin70° = 0,94 cos70° = 0,34 tan70° = 2,75
Answer @ cm [2]
(b) cm? [2]

4004/1 Specimen Paper

---

Page 23

Extracted Text

xX ={r 31 £ <37 andx is an integer}
P ={x:x is a multiple of 3},
Q ={x x is a factor of 99} and

R ={x:x is a prime number}.

(a) List all the elements of R.
(b) Write down n(P E R)¢

(© List all elements of (PE Q ER)

Answer (a) [1]
® [1]
(c) [2]

4004/1 Specimen Paper
[Turn over

---

Page 24

Extracted Text

23 A map is drawn to a scale of 1: 75 000.

(a) Calculate in km the actual distance between two towns which are
40 cm apart on the map.

(b) — An airport has an actual area of 22,5 km?.

Calculate in cm? the area of the airport on the map.

4004/1Specimen Paper

---

Page 25

Extracted Text

speed (m/s)
30

4 10
time (s)
In the diagram, a moving object decelerates from a speed of 30 m/s to a
speed of 18 m/s in 4 seconds and further decelerates from a speed of
18 m/s to rest after a further 6 seconds.
Calculate the
(a) speed of the object after the first 2 seconds,

(b) total distance covered by the object in the 10 seconds.

4004/1 Specimen Paper
[Turn over

---

Page 26

Extracted Text

26

The diagram shows three shapes A, B and C on a Cartesian plane.

(a) Describe completely the single transformation which maps
shape A onto shape B.

(b) Shape B is mapped onto shape C by a transformation P.
Describe fully the transformation P.

Answer (a)

(b)

4004/1 Specimen Paper

---

Page 27

Extracted Text

27

In the diagram, O is the centre of the circle. TAS is a tangent to the circle at A,
BAS = 40° and OBC = 54°.

Calculate,
(a) OAB,
(b) AGB,
@ ADC,

(d)_ reflex AOC.

Answer (a)

(b)

(c)

(@)

4004/1 Specimen Paper

[Turn over

---

Page 28

Extracted Text

fay 6 ze 6 6
IfF=¢ 3 x +G=¢° -2 + and H=c / =“

e-4 -6g é2 -1g alg
find

(a) F-+3G in terms of x,
(b) _ the value of x if the determinant of F is -14,

(c) GH.

Answer (a)

(b)

()

4004/1 Specimen Paper

---