Download and practise with this ZIMSEC O-Level Mathematics Paper 2 June 2006 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 2006. Use it for exam practice under timed conditions. The paper code is 4008/2. Time allowed: 2 hours 30 minutes.
# ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary Level
**MATHEMATICS**
4008/2
PAPER 2
JUNE 2006 SESSION
2 hours 30 minutes
Additional materials:
Answer paper
Geometrical instruments
Graph paper (3 sheets)
Mathematical tables
Plain paper (1 sheet)
ME 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 12 printed pages.
Copyright: Zimbabwe School Examinations Council, 2006.
**Section A [64 marks]**
Answer all the questions in this section.
## Question 1
### (a)
Express as a fraction in its simplest form \(\frac{3}{2}+\frac{4 x-1}{3}\).
### (b)
Given the formula \(\mathrm{S}=\frac{1}{2} n(r+l)\),
#### (i)
calculate the value of S when \(n=13, r=7\) and \(l=11\),
#### (ii)
make \(r\) the subject of the formula.
### (c)
Calculate the principal that earns \($ 18450\) simple interest at \(6\%\) per annum in \(1 \frac{1}{2}\) years.
### (d)
Solve the equation \(5(y+3)-7=3(4-y)\).
## Question 2
Harare
| 141 | Kadoma | | |
| :---: | :---: | :---: | :--- |
| 275 | 134 | Gweru | |
| 439 | \(x\) | 164 | Bulawayo |
| 879 | 738 | 604 | 440 |
| | | Victoria Falls | |
The figure above shows a distance chart for five towns. The distances are in kilometres. From the chart the distance between Gweru and Victoria Falls is 604 kilometres.
### (a)
#### (i)
Write down the distance between Harare and Victoria Falls correct to the nearest 10 kilometres.
#### (ii)
Calculate \(x\), the distance between Kadoma and Bulawayo.
### (b)
A motorist travels from Bulawayo to Victoria Falls at an average speed of \(80 \mathrm{~km} / \mathrm{h}\).
Calculate
#### (i)
the time the motorist takes to complete the journey,
#### (ii)
the fuel the motorist needs if the car uses 6,5 litres for every 100 kilometres travelled.
## Question 4
Answer the whole of this question on a sheet of plain paper.
Use ruler and compasses only for all constructions and show clearly all the construction lines and arcs.
### (a)
Construct on a single diagram
#### (i)
a pentagon PQRST in which \(\mathrm{PQ}=6 \mathrm{~cm}, \mathrm{QR}=7 \mathrm{~cm}, \mathrm{RS}=\mathrm{ST}=8 \mathrm{~cm}\), \(\mathrm{PT}=4 \mathrm{~cm}, \hat{\mathrm{PQR}}=120^{\circ}\) and \(\hat{\mathrm{QPT}}=135^{\circ}\),
#### (ii)
the locus of points equidistant from ST and SR,
#### (iii)
a line through \(R\) parallel to \(P Q\) to cut \(S T\) at \(X\).
### (b)
State the reason why triangles \(P R Q\) and \(P X Q\) are equal in area.
## Question 5
### (a)
In a group of 25 students, 15 study Mathematics, 12 Physics and 18 Chemistry. It is given that
8 study Mathematics and Physics, 5 study Physics and Chemistry, 10 study Chemistry and Mathematics and \(x\) study all the three subjects.
Each student studies at least one of these subjects.
#### (i)
Copy and complete the Venn diagram to show the number of elements in each subset in terms of \(x\).
#### (ii)
Form an equation in \(x\) and solve it. Hence or otherwise find the number of students who study Mathematics and Chemistry only.
### (b)
Two fair-sided coins are tossed at the same time and the results noted.
#### (i)
Using the symbols H for Heads and T for Tails, list all the four possible outcomes.
#### (ii)
Write down the probability of getting two Heads or two Tails.
### (c)
Solve the equation
$$
2^{2 n-1}=64
$$
**Section B [36 marks]**
Answer three questions in this section.
## Question 7
The diagram shows three villages \(P, Q\) and \(R\). The bearing of \(Q\) from \(P\) is \(328^{\circ}\) and the bearing of R from Q is \(191^{\circ}\). \(\mathrm{PQ}=3 \mathrm{~km}\) and \(\mathrm{QR}=6 \mathrm{~km}\).
### (a)
Calculate
#### (i)
\(\mathrm{PQR}\),
#### (ii)
the distance Q is north of P,
#### (iii)
PR.
### (b)
Find the bearing of R from P, giving your answer correct to the nearest degree.
## Question 8
Answer the whole of this question on a sheet of graph paper.
A particle moves along a straight line so that after t seconds its velocity, \(\mathrm{v} \mathrm{m} / \mathrm{s}\), is given by the formula
$$
v=5+7 t-2 t^{2}.
$$
Corresponding values of t and v are given in the table below.
| \(\mathrm{t}(\mathrm{s})\) | 0 | 1 | 2 | 3 | 4 | 5 |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: |
| \(\mathrm{v}(\mathrm{m} / \mathrm{s})\) | 5 | 10 | 11 | 8 | p | -10 |
### (a)
Calculate the value of p.
### (b)
Taking 2 cm to represent 1 second on the horizontal axis and 2 cm to represent \(4 \mathrm{~m} / \mathrm{s}\) on the vertical axis, draw the graph of \(\mathrm{v}=5+7 \mathrm{t}-2 \mathrm{t}^{2}\) for \(0 \leq \mathrm{t} \leq 5\).
### (c)
Use the graph to estimate,
#### (i)
the maximum velocity of the particle,
#### (ii)
the value of t when the particle is stationary,
#### (iii)
the acceleration of the particle when \(t=5\),
#### (iv)
the …