ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS <br> PAPER 1**
4008/1, 4028/1
2 hours 30 minutes
**NOVEMBER 2008 SESSION**
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.
This question paper consists of 26 printed pages and 6 blank pages.
Copyright: Zimbabwe School Examinations Council, N2008.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
(a)
Simplify
#### (i)
\(6,3 \times 1,1\), giving your answer as a decimal,
#### (ii)
\(\frac{2}{3}-\frac{3}{4}\), giving your answer as a common fraction.
(b)
Find 5% of 130 metres.
Answer ..... [1]
(a) (i)
(ii)[1]
(b) m[2]
Question 2
(a)
Evaluate \(54_{6}+305_{6}\), giving your answer in base 6.
(b)
Convert \(10011_{2}\) to a number in base 3.
Answer
(a)
\(\_\_\_\_\) ..... [1]
(b)
\(\_\_\_\_\)
Question 3
Given that \(94 \times 152=14288\),
(a)
find the value of N if \(95 \times 152=14288+\mathrm{N}\).
(b)
Write down the exact value of
#### (i)
\(0,094 \times 1520\),
#### (ii)
\(0,14288 \div 0,0094\).
Answer (a) ..... [1]
(b) (i) ..... [1](ii)[1]
Question 4
(a)
Simplify \((0,2)^{3} \times(0,2)^{2}\), giving your answer as a decimal.
(b)
Solve the equation
$$ 5 x-2(x+3)=9 . $$
(a)
(b) \(x=\) \(\_\_\_\_\)
Question 5
(a)
Write 0019 in 12-hour notation.
(b)
Tapiwa and Netsai share some money in the ratio 2:5. Given that Tapiwa's share is \(\$620000\), calculate Netsai's share.
Answer (a) ..... [1]
(b) \(\$\) ..... [2]
Question 6
In the diagram, BCD is a straight line and AB is parallel to ED. Given that \(\mathrm{BC}=\mathrm{AC}, \mathrm{A} \hat{\mathrm{DB}}=20^{\circ}\) and \(\mathrm{A} \hat{\mathrm{C} B}=50^{\circ}\), calculate
(a)
\(B \hat{A} \mathrm{~A}\),
(b)
\(\mathrm{D} \hat{\mathrm{A}} \mathrm{C}\),
(c)
\(\mathrm{A} \hat{\mathrm{D}} \mathrm{E}\).
Answer
(a) \(\hat{\mathrm{BAC}}=\) \(\_\_\_\_\)
(b) \(\mathrm{DA} \mathrm{A} \mathrm{C}=\) \(\_\_\_\_\)
(c) \(\mathrm{A} \hat{\mathrm{D}} \mathrm{E}=\) \(\_\_\_\_\)
Question 7
Given that \(m=4 \times 10^{6}\) and \(n=2,4 \times 10^{-3}\) giving each answer in standard form, calculate
(a)
\(m n\),
(b)
\(\frac{n}{m}\).
Answer (a) ..... [1]
(b) ..... [2]
Question 8
WXYZ is a cyclic quadrilateral. The diagonals XZ and YW intersect at P and YX is produced to \(\mathrm{S}. \mathrm{Y} \hat{\mathrm{W}} \mathrm{X}=70^{\circ}, \mathrm{X} \hat{\mathrm{Y}} \mathrm{P}=25^{\circ}\) and \(\mathrm{Y} \hat{\mathrm{P}} \mathrm{Z}=43^{\circ}\).
Calculate
(a)
\(X Z \cap\),
(b)
\(\mathrm{Y} \hat{\mathrm{X}} \mathrm{Z}\),
(c)
\(s \hat{x} w\).
Question 9
(a)
The bearing of town B from town A is \(141^{\circ}\). Find the bearing of town A from town B.
(b)
The interior angle of a regular polygon is \(162^{\circ}\). Find the number of sides of the polygon.
Question 10
(a)
In the diagram, the shaded sector AOB is \(\frac{7}{15}\) of the circle centre O. Calculate AÔB.
(b)
Calculate the radius of a circle whose area is \(154 \mathrm{~cm}^{2}\).
[Take \(\pi\) to be \(\frac{22}{7}\)]
Question 11
Taurai is \(x\) years old. Zvikomborero, her brother is 9 years older than her. Their father is 3 times as old as Taurai. Their mother is twice as old as Zvikomborero.
(a)
Write down and simplify, in terms of \(x\), an expression for the total age of the four members of the family.
(b)
Given that the sum of the ages of the four members is 139 years, find the value of \(x\).
(a)
[1]
(b) \(x=\)
[2]
Question 12
The scale of a map is \(1:1000000\).
Find
(a)
the length, in cm, of a line on the map, which represents a road 160 km long,
(b)
the actual area of a piece of land which is represented by \(2,64 \mathrm{~cm}^{2}\) on the map, giving your answer in \(\mathrm{km}^{2}\).
(a) \(\_\_\_\_\) cm
(b) \(\_\_\_\_\)
Question 13
If \(f(x)=x^{2}-7 x+5\), find
(a)
\(f(-1)\),
(b)
the values of \(x\) for which \(f(x)=-7\).
Answer
(a)
(b) \(x=\) \(\_\_\_\_\) or \(\_\_\_\_\) [2]
Question 14
A bag contains red, blue and green counters all of which are identical except for colour.
A counter is picked at random from the bag. Its colour is noted and then it is replaced. The probability that it is red is 0,2 and the probability that it is blue is 0,5.
(a)
Calculate the probability that the counter picked is either blue or green.
(b)
Two counters are picked at random one after the other, with replacement. Calculate the probability that one is red and the other is blue.
Answer
(a)
(b)
Question 15
(a)
Factorise \(x^{2}-y^{2}\).
(b)
Given that \(x-y=4\) and \(x^{2}-y^{2}=20\), find the value of \(x\) and the value of \(y\).
Answer (a) ..... [1]
(b) \(x=\) ..... [1] ..... [3]
Question 16
The diagram shows an isosceles triangle ABC with \(\mathrm{AB}=\mathrm{AC}, \mathrm{BC}=24 \mathrm{~cm}\) and AD is perpendicular to BC.
Given that the area of the triangle is \(108 \mathrm{~cm}^{2}\), find
(a)
AD,
(b)
AC.
Answer
(a) \(\mathrm{AD}=\) \(\_\_\_\_\) cm
(b) \(\mathrm{AC}=\) \(\_\_\_\_\) cm [2]
Question 17
The diagram shows a cross-section of a swimming pool which is 25 m long, 1 m deep at the shallow end and 2 m deep at the deep end.
(a)
Calculate the area of the cross-section in \(\mathrm{m}^{2}\).
(b)
Given that the swimming pool is 10 m wide, calculate the volume of the pool in \(\mathrm{m}^{3}\).
Answer