Download and practise with this ZIMSEC O-Level Mathematics Paper 2 November 2008 question paper. Useful for exam revision, past paper practice, and preparation in Zimbabwe.
A free account is needed to download. Sign in or create one
This is the ZIMSEC O-Level Mathematics question paper for Paper 2 from November 2008. Use it for exam practice under timed conditions. The paper code is 4008/2. Time allowed: 2 hours 30 minutes.
# ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
**4008/2**
**PAPER 2**
**NOVEMBER 2008 SESSION**
**2 hours 30 minutes**
Additional materials:
Answer paper
Geometrical instruments
Graph paper (3 sheets)
Mathematical tables
Plain paper (1 sheet)
TIME 2 hours 30 minutes
### INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the answer paper/answer booklet.
Answer all questions in Section **A** and any three questions from Section **B**.
Write your answers on the separate answer paper provided.
If you use more than one sheet of paper, fasten the sheets together.
**Electronic calculators must not be used.**
All working must be clearly shown. It should be done on the same sheet as the rest of the answer.
Omission of essential working will result in loss of marks.
If the degree of accuracy is not specified in the question and if the answer is not exact, the answer should be given to three significant figures. Answers in degrees should be given to one decimal place.
### INFORMATION FOR CANDIDATES
The number of marks is given in brackets [] at the end of each question or part question. Mathematical tables may be used to evaluate explicit numerical expressions.
**This question paper consists of 11 printed pages and 1 blank page.**
Copyright: Zimbabwe School Examinations Council, N2008.
**Section A [64 marks]**
Answer all the questions in this section.
## Question 1
### (a)
Express \(3 \frac{2}{5}-2 \frac{13}{20}\) as a single fraction in its lowest terms.
### (b)
Remove the brackets and simplify
$$
3(a+2 c)-4(2 a-c)
$$
### (c)
Solve the equation
$$
\frac{4 x-5}{7}=1 \frac{3}{4}
$$
### (d)
Find the number of circular rings each of diameter \(6,3 \mathrm{~cm}\) which can be made from a wire \(19,8 \mathrm{~m}\) long.
( Use \(\pi=\frac{22}{7}\) ).
## Question 2
### (a)
Factorise completely
#### (i)
\(2 x^{2}+a x-2 b x-a b\),
#### (ii)
\(3-12 y^{2}\).
### (b)
It is given that \(\mathrm{P}(4 ; 8)\) and \(\mathrm{R}(-4 ;-2)\) are points on the Cartesian plane. Find
#### (i)
\(\overrightarrow{\mathrm{PR}}\) as a column vector,
#### (ii)
\(|\overrightarrow{\mathrm{PR}}|\).
### (c)
Two cyclists, Alice and John, started a journey at the same time from two villages which are 27 km apart. Alice cycled at \(x \mathrm{~km} / \mathrm{h}\) and John cycled at \(2 x \mathrm{~km} / \mathrm{h}\). They travelled towards each other and met after \(\frac{3}{4}\) hour.
#### (i)
Write down, in terms of \(x\), the distance that Alice travelled in \(\frac{3}{4}\) hour.
#### (ii)
Form an equation in \(x\) and solve it.
#### (iii)
Hence write down the numerical value of John's speed.
## Question 3
In the diagram, the Sun, Earth and Mars are in a straight line. It is given that the Earth is \(1,496 \times 10^{8} \mathrm{~km}\) from the Sun and Mars is \(2,279 \times 10^{8} \mathrm{~km}\) from the Sun.
#### (i)
Write down \(1,496 \times 10^{8}\) in ordinary form.
#### (ii)
Find, in standard form, the distance of Mars from the Earth.
### (b)
In a certain year, a paint manufacturer mixed 27 litres of white paint with 9 litres of red paint to produce 36 litres of pink paint. If one litre of the white paint cost \($ 36800\) and the average cost of the pink paint was \($ 33575\) per litre, calculate the cost of one litre of the red paint then.
### (c)
#### (i)
Solve the simultaneous inequalities
$$
2 x-6<5 x+3 \leq 3 x+11
$$
giving your answer in the form \(a<x \leq b\) where \(a\) and \(b\) are integers.
#### (ii)
Write down the least possible value of \(x\).
## Question 4
### (a)
In the diagram, ABCD is a quadrilateral in which AD is parallel to BC and AC and BD intersect at X such that the ratio \(\mathrm{BX}: \mathrm{XD}=3: 2\). Given that \(\Delta \mathrm{ABX}=9 \mathrm{~cm}^{2}\) in area,
#### (i)
calculate the area of \(\triangle \mathrm{ADX}\),
#### (ii)
name, in correct order, the triangle which is similar to \(\triangle \mathrm{BCX}\),
#### (iii)
hence calculate the area of \(\triangle \mathrm{BCX}\).
### (b)
In the diagram, AP and AQ are tangents to the circles ABQ and ABPC respectively. Given that \(\mathrm{A} \hat{\mathrm{PB}}=30^{\circ}\) and \(\mathrm{A} \hat{\mathrm{Q} B}=50^{\circ}\), calculate
#### (i)
\(\mathrm{BAP}\),
#### (ii)
\(B \hat{A} Q\),
#### (iii)
reflex \(\mathrm{P} \hat{\mathrm{B}} \mathrm{Q}\),
#### (iv)
\(\mathrm{A} \hat{\mathrm{C}} \mathrm{P}\).
## Question 5
### (a)
Express as a single fraction in its simplest form
$$
n+\frac{2 n}{6 n+5}
$$
### (b)
Make \(m\) the subject of the formula
$$
a=\frac{m-5}{3 m-2}
$$
### (c)
Given that \(\mathbf{A}=\left(\begin{array}{cc}3 | 5 -2 | 7\end{array}\right)\) and \(\mathbf{B}=\left(\begin{array}{ll}5 | y y | 3\end{array}\right)\) find
#### (i)
\(\mathrm{A}^{2}\),
#### (ii)
the two possible values of \(y\) given that the determinant of the matrix \(\mathbf{B}\) is \(5 y+1\).
## Question 6
Answer the whole of this question on a sheet of plane paper.
Use ruler and compasses only for all construction and show clearly all construction lines and arcs.
### (a)
On a single diagram, construct
#### (i)
a line OP, 9 cm long,
#### (ii)
a circle centre O and radius 3.5 cm ,
#### (iii)
the locus of points which are equidistant from O and P ,
#### (iv)
the circle whose diameter is OP to cut the circle centre O at R and Q ,
#### (v)
the two tangents to the circle centre O from the point P .
### (b)
OP represents a certain locus. Describe this locus fully.
### (c)
A point T lies inside the quadrilateral PQOR and is such …