Download and practise with this ZIMSEC O-Level Mathematics Paper 2 June 2011 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 2011. Use it for exam practice under timed conditions. The paper code is 4028/2. Time allowed: 2 hours 30 minutes.
# ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
4028/2
PAPER 2
JUNE 2011 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.
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 or electronic calculators 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, J2011.
**Section A [64 marks]**
Answer all the questions in this section.
## Question 1
### (a)
Simplify \(\left(3 \frac{1}{2}-1 \frac{3}{5}\right)+1 \frac{2}{3}\).
### (b)
Find the exact value of
#### (i)
\(10,03 \times 0,17\);
#### (ii)
\(7,2+0,018\).
### (c)
Three farmers share 120 hectares of land in the ratio \(3: 4: 5\).
Calculate the area of the largest piece of land.
### (d)
Find the Highest Common Factor (H.C.F) of
\(27 x^{2} y z\),
\(72 x y^{3} z^{2}\) and
\(108 x y z^{3}\).
## Question 2
### (a)
It is given that \(\mathrm{r}=2 q-5\) and \(q=3 p+2\).
#### (i)
Express \(r\) in terms of \(p\).
#### (ii)
Given also that \(p=-3\), find the numerical value of \(r\).
### (b)
#### (i)
Express \(\frac{x}{3}+\frac{x-4}{5}\) as a single fraction in its simplest form.
#### (ii)
Hence or otherwise solve the equation \(\frac{x}{3}+\frac{x-4}{5}=4\).
### (c)
Express 150 g as a percentage of 3 kg.
## Question 3
### (a)
The diagram shows points \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D on the circumference of a circle such that \(\mathrm{BC}=\mathrm{CD} . \mathrm{AC}\) and BD intersect at F and CD is produced to E . \(\hat{A C D}=33^{\circ}\) and \(A \hat{D} E=87^{\circ}\). Calculate
#### (i)
\(\mathrm{A} \hat{\mathrm{B}} \mathrm{D}\),
#### (ii)
\(\mathrm{CBD}\),
#### (iii)
\(B \hat{A} C\),
#### (iv)
\(\mathrm{A} \hat{\mathrm{D} B}\),
#### (v)
\(\mathrm{CFD}\).
### (b)
Take \(\pi\) to be 3,142.
The diagram shows a sector of a circle centre \(\mathrm{O} . \mathrm{PO} \mathrm{Q}=37^{\circ}, \mathrm{PO}=8 \mathrm{~cm}\) and PT is perpendicular to QO. Calculate
#### (i)
\(\mathrm{PT}\),
#### (ii)
area of the sector,
#### (iii)
area of triangle PQO ,
#### (iv)
the area of the shaded segment.
## Question 4
### (a)
Factorise completely
#### (i)
\(3 n p-6 n q+a p-2 a q\),
#### (ii)
\(12-4 g-g^{2}\).
### (b)
In a survey of 72 girls, it was found that every girl watched at least one of the following TV programmes, Teen Scene or Fashion Show. Fifty girls watched Teen Scene and 62 girls watched Fashion Show. Find the number of girls who watched
#### (i)
both programmes,
#### (ii)
Fashion Show only.
## Question 5
### (a)
#### (i)
Convert \(112_{3}\) to a number in base 5 .
#### (ii)
Evaluate \(1101_{2}+1011_{2}\), giving your answer in base 2 .
### (b)
#### (i)
Show that \(2 \log _{5}(3 x+2)-\log _{5} 2=1\) reduces to \(3 x^{2}+4 x-2=0\).
#### (ii)
Solve the equation \(3 x^{2}+4 x-2=0\), giving your answers correct to two decimal places.
## Question 6
Answer the whole of this question on a sheet of plain paper.
Use ruler and compasses only and show clearly all construction lines and arcs. All constructions should be in a single diagram.
A secondary school, Boterekwa, is to be built to service three primary schools Tugwi, Shinga and Hlangu. Shinga is 16 km from Tugwi on a bearing of \(150^{\circ}\). Hlangu is 15 km North-East of Shinga.
### (a)
Using a scale of 1 cm to represent 2 km , construct a diagram to show the positions of the three primary schools.
### (b)
Boterekwa is 8 km from Shinga and equidistant from Tugwi and Hlangu.
#### (i)
Construct the locus of points 8 km from Shinga and the locus of points equidistant from Tugwi and Hlangu
#### (ii)
Mark and label \(B_{1}\) and \(B_{2}\) the possible positions of Boterekwa.
### (c)
Use your diagram to find the shorter distance between Boterekwa and Tugwi.
**Section B [36 marks]**
Answer any three questions in this section.
Each question carries **12 marks**.
## Question 7
### (a)
Given that \(\mathbf{A}=\left(\begin{array}{ll}3 | -4 1 | -2\end{array}\right)\),
#### (i)
find the inverse of matrix \(\mathbf{A}\),
#### (ii)
hence or otherwise solve the equations
$$
\begin{aligned} | 3 x-4 y=-3, | x-2 y=-2 .
\end{aligned}
$$
### (b)
The diagram shows a trapezium OABC where OC is parallel to AB , with \(\overrightarrow{\mathrm{OA}}=x\) and \(\overrightarrow{\mathrm{OC}}=y\). Diagonals OB and AC intersect at D such that \(\mathrm{AD}: \mathrm{DC}=3: 2\).
Express, in terms of \(\boldsymbol{x}\) and/or \(\boldsymbol{y}\),
#### (i)
(a) \(\overrightarrow{\mathrm{AC}}\),
(b) \(\overrightarrow{\mathrm{AD}}\).
#### (ii)
Given that \(\overrightarrow{\mathrm{AB}}=k …