ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary Level
**MATHEMATICS**
**PAPER 1**
**JUNE 2014 SESSION**
Candidates answer on the question paper.
Additional materials:
Geometrical instruments
Allow candidates 5 minutes to count pages before the examination.
**4008/1**
2 hours 30 minutes
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.
FOR EXAMINER'S USE
**This question paper consists of 24 printed pages.**
Copyright: Zimbabwe School Examinations Council, J2014.
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**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
Express 2046,489 correct to
(a) the nearest ten,
(b) 2 decimal places,
(c) 2 significant figures.
Answer:
(a)
(b)
(c)
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 2
Evaluate, giving your answers as common fractions in their lowest terms
(a) \(\frac{3}{5}+\frac{1}{7}\),
(b) \(\quad \frac{5}{8} \times \frac{32}{45}\),
(c) \(\frac{5}{24} \div \frac{1}{3}\).
(a) ..... [1]
(b) ..... [1]
(c) ..... [1]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 3
Giving your answer as a decimal, find the exact value of
(a) 0,175-0,049,
(b) \(\sqrt{0,0144}\),
(c) \(\quad(0,06)^{2}\).
| Centre Number | Candidate's Number | | :--- | :--- | | | |
5
Question 4
(a)
Expand \((2 a-b)(1+c)\).
(b)
Simplify \(\quad \frac{m^{2}-m n}{n^{2}-n p} \div \frac{m}{(n-p)}\).
Answer:
(a)
[2]
(b)
[1]
Question 5
It is given that
$$ \xi=\{30 ; 31 ; 32 ; 33 ; 34 ; 35 ; 36 ; 37 ; 38 ; 39\} $$
A is the set of odd numbers and
\(B\) is the set of prime numbers.
(a)
List the elements of
(i) A ,
(ii) \(\quad \mathrm{B}^{1}\).
(b)
Find \(n\left(A \cap B^{1}\right)\).
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Answer:
(a)
(i) \(\_\_\_\_\) \} [1]
(ii) \{ \(\_\_\_\_\) \} [1]
(b)
[1]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 6
(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 \(55^{\circ}\) and \(45^{\circ}\). The remaining ( \(n-2\) ) exterior angles are each \(20^{\circ}\).
Calculate the value of \(n\).
Answer:
(a) \(\_\_\_\_\) [1]
(b) \(n=\) \(\_\_\_\_\)
Question 7
(a)
Express 9 minutes after midnight as time on the 24 hour clock.
(b)
In 1998 the population of a village was \(2,8 \times 10^{2}\). In 2004, the population was \(3,5 \times 10^{2}\).
Calculate the percentage increase of the population from 1998 to 2004.
Answer:
(a) \(\_\_\_\_\)
(b) \(\_\_\_\_\)
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 8
Solve the simultaneous equations
$$ \begin{aligned} & \frac{1}{3} x=y, \\ & 2 x+y=-7 . \end{aligned} $$
Answer:
$$ \begin{aligned} & x= \\ & y= \end{aligned} $$
Question 9
(a)
Given that \(f(x)=(x-1)(x+6)\) and that \(f(0)=p\), find the value of \(p\).
(b)
If \(y k=a x-b k\), make \(k\) the subject of the formula.
Answer:
(a) \(p=\) \(\_\_\_\_\)
(b) \(k=\) \(\_\_\_\_\)
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 10
(a)
Express \(3^{4}+3^{2}+3\) as a number in base 3 .
(b)
Evaluate
(i) \(143_{8}+57_{8}\) giving your answer in base 8,
(ii) \(\quad 4_{5}-2_{3}+1_{2}\) giving your answer in base 10 .
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Question 11
In the diagram, ABCD is a circle. Tangents at C and D meet at E and ED is produced to F such that \(\mathrm{A} \hat{\mathrm{D} F}=50^{\circ}\) and \(\mathrm{A} \hat{\mathrm{B} C}=116^{\circ}\).
Calculate
(a) \(\quad \mathrm{A} \hat{\mathrm{D}} \mathrm{C}\),
(b) \(\quad \mathrm{CDE}\),
(c) \(\quad \mathrm{CED}\).
Answer:
(a) \(\_\_\_\_\)
(b)
(c)
[1]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 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 \(q\) cents which is insufficient to make a call. Write down 3 inequalities in terms of \(p\) and/or \(q\), other than \(p>0\) and \(q>0\), that satisfy the given conditions.
Answer:
(i) \(\_\_\_\_\) [1]
(ii) \(\_\_\_\_\) [1]
(iii) \(\_\_\_\_\)
Question 13
AB is a line whose equation is \(6 y=7 x+48\).
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 \(a y+b x+c=0\).
Answer:
(a) \(\_\_\_\_\)
(b) \(\_\_\_\_\)
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 14
(a)
Given that \(4 m=7 n\), 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]
(b) US\$ \(\_\_\_\_\) [2]
Question 15
Factorise completely
$$ 3 x^{3} y-12 x y^{3} $$
| Centre Number | Candidate's Number | | :--- | :--- | | | |