ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS** **PAPER 1**
4008/1, 4028/1
**JUNE 2008 SESSION** **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 24 printed pages.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER**
Question 1
(a)
Express 0,0000526 in standard form.
(b)
Estimate by first rounding off each number to one significant figure, the value of \(\frac{3,04 \times 1,98-9,48}{2,91}\).
\_\_\_\_\_
(b) \_\_\_\_\_
Question 2
Express
(a)
\(5,3 \mathrm{~km}^{2}\) in hectares,
(b)
20 litres in cubic centimetres,
(c)
408 hours in weeks and days.
Answer
(a) \_\_\_\_\_ ha [1]
(b) \_\_\_\_\_
(c) \_\_\_\_\_ weeks \_\_\_\_\_ days [1]
Question 3
(a)
Find the value of the base \(y\) such that \(6703_{y}-725_{y}=5756_{y}\).
(b)
Convert \(134_{5}\) to a number in base two.
Answer
(a)
[1]
(b) \_\_\_\_\_
Question 4
In a shop one loaf of bread cost \(\$ 65000\).
(a)
Find
#### (i)
the cost of a dozen loaves of bread,
#### (ii)
the number of loaves of bread that could be bought for \(\$ 4550000\).
(b)
Write down the type of variation which connects the cost of bread and the number of loaves of bread bought.
Answer
(a)
(i) \$ \_\_\_\_\_ [1]
(ii) \_\_\_\_\_ [1]
(b) \_\_\_\_\_ variation [1]
Question 5
(a)
Write down one capital letter of the alphabet which has rotational symmetry of order 2 but no line of symmetry.
(b)
The mean of \(m, p, q\) and \(r\) is 8,25.
The mean of \(m, n, p, q\) and \(r\) is 4,6.
Find the value of \(n\).
Answer
(a) [1]
(b) [2]
Question 6
The radius, \(r \mathrm{~cm}\), of a circle is given as 9 cm, correct to the nearest whole number.
(a)
Write down the limits between which \(r\) must lie.
(b)
Calculate the least possible circumference of the circle, giving your answer in terms of \(\pi\).
Answer
(a)
[1]
(b) \_\_\_\_\_ cm
[2]
Question 7
The diagram shows a pattern which is made up of identical semi-circular arcs. The shortest distance between the ends A and B is 98 cm.
Calculate
(a)
the diameter of each semi-circle,
(b)
the distance from A to B along the curves.
\[ \left(\text { Take } \pi=\frac{22}{7}\right) \]
Answer
(a) \_\_\_\_\_ cm [1]
(b) \_\_\_\_\_ cm [2]
Question 8
The Venn diagram shows the universal set, \(\xi\) and the sets \(\mathrm{P}, \mathrm{Q}\) and R with their members.
(a)
From the Venn diagram, list the members of
#### (i)
\(\mathrm{P} \cap \mathrm{Q}\),
#### (ii)
\(\mathrm{P}^{\prime} \cap \mathrm{Q}^{\prime}\):
(b)
Find \(n(P)\).
Answer
(a)
(i) \(\mathrm{P} \cap \mathrm{Q}=\) \_\_\_\_\_
(ii) \(\mathrm{P}^{\prime} \cap Q^{\prime}=\) \_\_\_\_\_ [1]
(b) \(\mathrm{n}(\mathrm{P})=\) \_\_\_\_\_ [1]
Question 9
The diagram is the distance-time graph of a cyclist who goes out shopping and returns home.
Calculate
(a)
the time spent at the shopping centre,
(b)
the average speed for the whole journey.
Answer
(a) \_\_\_\_\_
\_\_\_\_\_ hours
(b) \_\_\_\_\_
\_\_\_\_\_ \(\mathrm{km} / \mathrm{h}\)
Question 10
A bag contains 60 identical marbles, except for colour. In the bag 36 are green, \(x\) are red and the rest are blue.
(a)
If the probability of selecting a red marble at random is \(\frac{1}{3}\), find \(x\).
(b)
Two marbles are drawn, one after the other, with replacement. Find the probability that neither marble is green, giving your answer as a common fraction in its lowest terms.
Answer
(a) \(x=\) \_\_\_\_\_ [1]
(b) \_\_\_\_\_ [2]
Question 11
In the diagram ABCD is a circle centre O. Arc \(\mathrm{AD}=\operatorname{arc} \mathrm{DC}, \mathrm{DAO}=55^{\circ}\) and AOB is a straight line.
Calculate
(a)
\(B \hat{C} D\),
(b)
\(\mathrm{A} \hat{\mathrm{C}} \mathrm{B}\),
(c)
\(\mathrm{D} \hat{\mathrm{A} C}\).
Answer
(a) \(\mathrm{B} \hat{\mathrm{CD}}=\) \_\_\_\_\_
(b)
\(\mathrm{A} \hat{\mathrm{C}} \mathrm{B}=\) \_\_\_\_\_
\_\_\_\_\_
Question 12
Evaluate
(a)
\((-32)^{\frac{3}{2}}\),
(b)
\(\frac{1}{5^{-3}}\).
Answer
(a)
[2]
(b) \_\_\_\_\_ [2]
Question 13
Factorise completely
(a)
\(15 m+18-10 m n-12 n\),
(b)
\(27 x^{2}-12 y^{2}\).
Answer
(a) ..... [2]
(b)[2]
Question 14
The following is an extract of Mr Dube's telephone bill for the month of January 2002 whereby \(x\) is the number of units used and \(y\) is the Value Added Tax (VAT).
| DATE | ACCOUNT DETAILS | AMOUNT | | :--- | :--- | :--- | | 31 Jan 2002 | Rental from 01/02/02 to 28/02/02 | 140,00 | | | Metered units 0278101685 (x units) | 2192,00 | | | Sub Total | 2332,00 | | | VAT @ 15,0\% | \(y\) | | | Amount Due | |
(a)
Find,
#### (i)
the units used, \(x\)
#### (ii)
the cost per unit.
(b)
Calculate the Value Added Tax, \(y\).
Answer
(a) (b)
(i)
[1]
(ii) \$ \_\_\_\_\_ [2]