ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
**PAPER 1**
4008/1, 4028/1
2 hours 30 minutes
Candidates answer on the question paper.
Additional materials: Geometrical instruments
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. 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 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 23 printed pages and 1 blank page.**
Copyright: Zimbabwe School Examinations Council, J2011.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
Simplify \(\frac{\frac{2}{3}+\frac{3}{4}}{1 \frac{1}{6}}\).
Answer:
Question 2
(a)
Express the ratio 20 minutes : \(1 \frac{1}{3}\) hours, in its simplest form.
(b)
Two partners, A and B, shared their profits from a business in the ratio 5:3.
If B received \(\$ 4800000\), calculate A's share.
Answer:
$$ \text { (a) } \$ \text {, } $$
[1]
[2]
Question 3
In the diagram, PQRS is a parallelogram. \(\mathrm{PS} \mathrm{Q}=85^{\circ}, \mathrm{SRQ}=60^{\circ}\) and SQT is a straight line. Find
(a)
PQ R ,
(b)
\(\quad R \hat{S} Q\),
(c)
\(\mathrm{R} \hat{\mathrm{Q}} \mathrm{T}\).
Answer: (a) \(\quad P \hat{Q} R=\)
(b) \(R \hat{S} Q=\)
(c) \(R \hat{Q} T=\)
Question 4
The bearing of village \(P\) from village \(Q\) is \(109^{\circ}\). Find
(a)
the three figure bearing of Q from P ,
(b)
the compass bearing of Q from P .
Answer:
(a) \(\_\_\_\_\)
(b) \(\_\_\_\_\)
Question 5
(a)
Solve \(x-3 \leq 3 x+10\).
(b)
Given that \(x\) is an integer, write down the least value of \(x\) for which \(x-3 \leq 3 x+10\).
Answer:
(a)
[2]
(b) \(x=\) \(\_\_\_\_\)
Question 6
Make \(u\) the subject of the formula \(T=\frac{m u^{2}}{K}-5 m g\).
Answer: \(\quad u=\) \(\_\_\_\_\)
Question 7
Express \(5^{2}+3 \times 5+4\) as a number in
(a)
base 5 ,
(b)
base 8 .
Answer:
(a) \(\_\_\_\_\)
(b) \(\_\_\_\_\)
[2]
Question 8
(a)
State the order of rotational symmetry of a parallelogram.
(b)
The triangle \(X Y Z\) has \(X Y=5 \mathrm{~cm}\) and \(Y Z=6 \mathrm{~cm}\).
Given that the triangle XYZ has only one line of symmetry, write down the two possible lengths of XZ .
Answer:
(a)
[1]
(b) \(\_\_\_\_\) cm or \(\_\_\_\_\) cm [2]
Question 9
A rectangle measures \(10,2 \mathrm{~cm}\) by \(7,1 \mathrm{~cm}\), correct to one decimal place.
Find the minimum possible perimeter of the rectangle.
\(\_\_\_\_\) cm
Question 10
(a)
A car uses \(l\) litres of petrol for every \(d\) kilometres travelled.
State the type of variation between \(l\) and \(d\).
(b)
Given that the car uses 5 litres to cover 60 kilometres, find the equation connecting \(l\) and \(d\).
Answer:
(a)
[1]
(b) \(\_\_\_\_\)
Question 11
Evaluate
(a)
\(3 \mathrm{~m}^{-5} \times 2 \mathrm{~m}^{5}\),
(b)
\(\left(\frac{4}{9}\right)^{-\frac{1}{2}}\).
Answer:
(a) \(\_\_\_\_\) [1]
(b) \(\_\_\_\_\) [2]
Question 12
In the diagram, \(A B C D\) and \(P B C Q\) are intersecting circles. \(D C Q\) and \(A B P\) are straight lines.
(a)
Given that \(\mathrm{A} \hat{\mathrm{DC}}=95^{\circ}\), calculate
#### (i)
ABC ,
#### (ii)
PQ C .
(b)
Given also that \(\mathrm{DAB}=x^{\circ}\), find an expression for BPQ in terms of \(x\).
Answer: (a) (i) \(A \hat{B} C=\ldots\)... [1]
(ii) \(P \hat{Q} C=\) [1]
(b) \(B \hat{P} Q=\) [1]
Question 13
In the Venn diagram, \(\mathrm{R}, \mathrm{S}, \mathrm{T}\) and \(\xi\) are sets with their elements as shown.
Use the Venn diagram to find
(a)
\(\mathrm{R}^{\prime} \cap \mathrm{S}\),
(b)
\(\quad(R \cap S) \cup(R \cap T)\),
(c)
\(\quad n(R \cup S \cup T)^{\prime}\).
Answer:
(a)
(b)
(c) \(\_\_\_\_\)
Question 14
Express \(\log _{10} x+2 \log _{10} y=1\) as an equation in index form.
Answer:
Question 15
It is given that \(\mathbf{p}=\binom{6}{-8}, \quad \mathbf{q}=\binom{3}{5}\) and \(\mathbf{r}=\binom{m}{n}\).
(a)
Express \(\mathbf{p}-3 \mathbf{q}\) as a column vector.
(b)
Given that \(\mathbf{p}+\mathbf{q}=3 \mathbf{r}\), find the value of \(m\) and the value of \(n\).
Answer:
(a)
(b) \(m=\) \(\_\_\_\_\)
\(n=\) \(\_\_\_\_\)
Question 16
(a)
Convert
#### (i)
the fraction \(\frac{3}{8}\) to a percentage,
#### (ii)
\(9 \%\) to a decimal fraction.
(b)
Simplify the expression \(\sqrt{3}+\sqrt{12}\).
Answer：
(a)
#### (i)
\(\_\_\_\_\)
\%
#### (ii)
[1]
(b)
\(\_\_\_\_\) [2]
Question 17
In the diagram, \(\mathrm{O}, \mathrm{A}, \mathrm{B}\) and C are four points on the velocity-time graph of an object.
(a)
Describe the motion of the object as illustrated on the section of the graph.
#### (i)
O to A ,
#### (ii)
A to B .
(b)
Calculate the distance covered by the object during the 20 seconds.
Answer:
(a)
#### (i)
\(\_\_\_\_\)