Download and practise with this ZIMSEC O-Level Mathematics Paper 2 June 2020 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 2020. Use it for exam practice under timed conditions. The paper code is 4004/2. Time allowed: 2 hours 30 minutes.
# ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
PAPER 2
JUNE 2020 SESSION
Candidates answer on the question paper
Additional materials:
Mathematical Instruments
Mathematical Tables
Non programmable Electronic Calculator
4004/2
2 hours 30 minutes
Allow candidates 5 minutes to count pages before the examination.
This booklet should not be punched or stapled and pages should not be removed.
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. Write your Centre and Candidate number in the box on the top right corner of every page of this paper.
Check that all the pages are in the booklet and ask the invigilator for a replacement if there are duplicate or missing pages.
Answer all questions in Section A and any four questions from Section B.
Write your answers in the spaces provided on the question paper using black or blue pens. 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.
Decimal answers in degrees should be given correct to one decimal place.
Mathematical tables and Electronic calculators may be used to evaluate explicit numerical expressions.
### 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 2 blank page(s).
Copyright: Zimbabwe School Examinations Council, J2020.
**SECTION A (52 Marks)**
Answer all questions in this section
## Question 1
### (a)
The difference between two fractions is \(3 \frac{2}{3}\). The smaller fraction is \(2 \frac{1}{4}\).
Find the other fraction.
Answer (a) \_\_\_\_
### (b)
The population of a certain country is 24,9 million.
Express this population in standard form.
Answer (b) \_\_\_\_
### (c)
Increase \($ 40,00\) in the ratio 8:5.
Answer (c) \_\_\_\_
### (d)
Evaluate \((7 \sqrt{5})^{2}\).
Answer (d) \_\_\_\_
### (e)
Simplify \(11011_{2}+243_{5}\), giving the answer in base five.
Answer (e) \_\_\_\_
## Question 2
### (a)
Two similar cups have diameters of 6 cm and 10 cm.
#### (i)
Write down the ratio of their volumes.
Answer (a)(i) \_\_\_\_
#### (ii)
Given that the volume of the smaller cup is \(100 \mathrm{~cm}^{3}\), calculate the volume of the larger cup.
Answer (a)(ii) \_\_\_\_
### (b)
A wooden block is in the form of a prism whose cross-section is a parallelogram with base 35 cm, perpendicular height 20 cm and length \(1,2 \mathrm{~m}\).
Calculate the
#### (i)
surface area of the cross-section of the block.
Answer (b)(i) \_\_\_\_
#### (ii)
volume of the block.
Answer (b)(ii) \_\_\_\_
#### (iii)
mass of the block if \(3 \mathrm{~cm}^{3}\) of the block weigh \(2,5 \mathrm{~g}\).
Answer (b)(iii) \_\_\_\_ [2]
## Question 3
### (a)
Find the value of \(y\) for which
$$
\left(\begin{array}{ll}
y | 4
\end{array}\right)\binom{-2}{3}=\left(\begin{array}{l}
-2
\end{array}\right)
$$
Answer (a) \_\_\_\_ [2]
### (b)
Find the matrix \(\mathbf{P}\) such that
$$
P\left(\begin{array}{cc}
3 | -4
2 | 0
\end{array}\right)=\left(\begin{array}{ll}
1 | 0
0 | 1
\end{array}\right)
$$
Answer (b) \_\_\_\_
### (c)
The equation of a straight line is \(y+3 x=-4\)
Find the
#### (i)
coordinates of the point where the line crosses the \(y\)-axis.
Answer (c)(i) \_\_\_\_
#### (ii)
gradient of the line.
Answer (c)(ii) \_\_\_\_
#### (iii)
equation of a line parallel to the line \(y+3 x=-4\) and passing through the point (3;5).
Answer (c)(iii) \_\_\_\_
## Question 4
Answer the whole of this question on the blank space below.
Use ruler and compasses only for all constructions and show clearly all construction lines and arcs.
All constructions should be done on a single diagram.
### (a)
Construct
#### (i)
triangle ABC in which \(\mathrm{AB}=7 \mathrm{~cm}, B \hat{A} C=45^{\circ}, \mathrm{BC}=8 \mathrm{~cm}\).
Answer (a)(i) on the diagram
#### (ii)
the locus of points equidistant from B and C.
Answer (a)(ii) on the diagram
| Candidate Name | Centre Number | Candidate Number |
| :--- | :--- | :--- |
| | | |
#### (iii)
the locus of points 5 cm from C.
Answer (a)(iii) on the diagram
### (b)
A point R in triangle ABC is such that it is nearer B than C and is less than 5 cm from C.
Show by shading, the region in which R must lie.
Answer (b) on the diagram
### (c)
Measure and write down the size of \(A \hat{B} C\).
Answer (c) \_\_\_\_
## Question 5
### (a)
Show that the equation \(x-3=\frac{5}{3 x}\) reduces to \(3 x^{2}-9 x-5=0\).
Answer (a) \_\_\_\_
### (b)
Solve the equation \(3 x^{2}-9 x-5=0\).
Give the answers correct to 2 decimal places.
Answer (b) \_\_\_\_
### (c)
In the diagram, ABCD is a cyclic quadrilateral with centre O. AB is produced to M.
\(M \hat{B} C=70^{\circ}\) and \(B \hat{D} C=40^{\circ}\).
Find
#### (i)
\(B \hat{C} D\).
Answer (c)(i) \_\_\_\_ [1]
#### (ii)
\(A \hat{B} D\).
Answer (c)(ii) \_\_\_\_
**SECTION B (48 Marks)**
Answer any four questions from this section.
## Question 6
Each question carries 12 marks
In the diagram, ABO is a triangle in which M is the mid-point of OB and N lies on AB such that \(A N=\frac{1}{5} A B\). ON and AM intersect at X. \(\overrightarrow{O A}=a\) and \(\overrightarrow{O B}=b\).
### (a)
Express, in terms of …