Download and practise with this ZIMSEC O-Level Mathematics Paper 2 June 2007 question paper. Useful for exam revision, past paper practice, and preparation in Zimbabwe.
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This is the ZIMSEC O-Level Mathematics question paper for Paper 2 from June 2007. 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**
PAPER 2
JUNE 2007 SESSION
Additional materials:
Answer paper
Geometrical instruments
Graph paper (3 sheets)
Mathematical tables
Plain paper (1 sheet)
4008/2
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 13 printed pages and 3 blank pages.
Copyright: Zimbabwe School Examinations Council, J2007.
**Section A [64 marks]**
Answer all the questions in this section.
## Question 1
### (a)
Find the value of \(4-2 \frac{2}{3} \times 1 \frac{1}{5}\).
### (b)
P, Q and R are subsets of \(\xi\) where
\(n(\mathrm{P} \cap \mathrm{Q})=0\),
\(\mathrm{R} \subset \mathrm{Q}\),
\(\mathrm{P} \cap \mathrm{R}=\phi\).
Draw and label the Venn diagram that represents these sets.
### (c)
Factorise completely
#### (i)
\(3 d f-d^{2}-3 e f+d e\),
#### (ii)
\(3 m^{3}-27 m\).
## Question 2
### (a)
Given that
\(\mathbf{A}=\left(\begin{array}{ll}3 | -2 4 | -5\end{array}\right), \quad \mathbf{B}=\binom{2}{3}\) and \(\mathbf{C}=\left(\begin{array}{cc}-1 | 5 3 | 0\end{array}\right) \quad\).
Find
#### (i)
\(2 \mathrm{~A}+\mathrm{C}\),
#### (ii)
AB,
#### (iii)
\(\mathrm{A}^{-1}\).
### (b)
Given that \(V=\sqrt{\frac{l+b}{l-b}}\),
#### (i)
make \(l\) the subject of the formula,
#### (ii)
find \(l\) when \(b=16\) and \(V=\frac{1}{3}\).
## Question 3
### (a)
#### (i)
Solve the inequalities
$$
y-4<3 y+2 \leq 6,
$$
leaving your answer in the form \(a<y \leq b\).
#### (ii)
Illustrate your answer on a number line.
### (b)
Solve the equation
$$
\frac{4}{x-3}=\frac{2}{x}+1
$$
### (c)
A tourist exchanged 4200 South African Rands (R) for 157500 Zimbabwean dollars (Z$).
Calculate
#### (i)
the equivalent of R1 in Z$,
#### (ii)
the amount in Z$ he would get if he exchanged R250,
#### (iii)
the equivalent cost, in Rands, of a gift marked Z$ 46200.
## Question 4
### (a)
In the diagram, OACB is a sector of a circle of radius 15 cm.
\(A \hat{D} O=90^{\circ}\) and \(O D=12 \mathrm{~cm}\).
Calculate
#### (i)
the size of \(A \hat{O} B\) to the nearest degree,
#### (ii)
the maximum number of such sectors which can be drawn in the circle without overlapping,
#### (iii)
the angle of the sector which remains.
### (b)
In the diagram, A, B, C and D are points on the circumference of a circle centre O. AT and CT are tangents to the circle.
\(\hat{\mathrm{BAT}}=30^{\circ}\) and \(\hat{\mathrm{AOC}}=100^{\circ}\).
Find
#### (i)
\(\mathrm{OAB}\),
#### (ii)
\(\mathrm{A} \hat{\mathrm{D}} \mathrm{B}\),
#### (iii)
\(\mathrm{A} \hat{\mathrm{T}} \mathrm{C}\),
#### (iv)
\(B \hat{D} C\).
## Question 5
### (a)
The distances of three planets from the sun are as follows.
| Planet | Distance \(/ \mathrm{km}\) |
| :--- | :--- |
| B | \(5,97 \times 10^{7}\) |
| C | \(7,78 \times 10^{8}\) |
| D | \(2,87 \times 10^{9}\) |
#### (i)
Find the ratio of the distance of planet D from the sun to the distance of planet B from the sun, in the form \(k: 1\), giving \(k\) to the nearest whole number.
#### (ii)
Light travels at a speed of \(3 \times 10^{8}\) metres per second. Calculate the time, correct to the nearest minute, that light takes to travel from the sun to planet C.
### (b)
A packet contains 60 identical sweets of which 40 are red and the rest are yellow.
#### (i)
If one sweet is picked at random from the packet, find the probability that it is red.
#### (ii)
Two sweets are picked from the packet without replacement. Draw a probability tree diagram to illustrate all the possible outcomes.
#### (iii)
Hence or otherwise find the probability that the two sweets picked are of the same colour.
## Question 6
Answer the whole of this question on a sheet of plain paper.
**Use ruler and compasses only and show all construction lines and arcs.**
### (a)
Construct, on a single diagram,
#### (i)
a quadrilateral ABCD in which \(\mathrm{AB}=10 \mathrm{~cm}, \mathrm{AD}=6 \mathrm{~cm}\). \(B C=13 \mathrm{~cm}, A \hat{B} C=30^{\circ}\) and \(\hat{D A B}=120^{\circ}\),
#### (ii)
the locus of points equidistant from AB and AD,
#### (iii)
the locus of points 5 cm from A,
#### (iv)
the locus of points 3 cm from AD and on the same side of AD as B.
### (b)
Measure and write down the size of \(B \hat{C} D\).
**Section B [36 marks]**
Answer any three questions in this section.
## Question 7
### (a)
The cash price of an electric stove is $3400000. The stove may be bought on hire purchase by paying a deposit of \(35 \%\) of the cash price and 12 equal monthly instalment of $300000 each.
Calculate
#### (i)
the deposit,
#### (ii)
the total amount to be paid if the stove is bought by hire purchase,
#### (iii)
the difference between the cash price and the hire purchase price.
### (b)
A bus was …