ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS <br> PAPER 2**
JUNE 2016 SESSION 2 hours 30 minutes Candidates answer on the question paper. Additional materials: Geometrical instruments Mathematical tables/ Electronic calculator 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 and your Centre number and Candidate number on the top right corner of every page of this paper.
Answer all questions in Section A and any three from Section B. Check that all the pages are in the booklet and ask the invigilator for a replacement if there are duplicate or missing pages. 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. 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 26 printed pages.**
Copyright: Zimbabwe School Examinations Council, J2016.
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2
**Section A [64 marks]** Answer all the questions in this section.
Question 1
(a)
Simplify \(7 \frac{1}{2}+\frac{1}{2} \times 8-2\).
Answer (a)
(b)
Find the Lowest Common Multiple (L.C.M) of 60 and 84.
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3
(c)
Mary, Peter and John share a total amount of \(\$ 500\) in the ratio 3:2:5. Mary uses part of her share to buy a pair of shoes costing \(\$ 30\).
#### (i)
Calculate Mary's share.
Answer (c) (i) § [2]
#### (ii)
Calculate the percentage of Mary's share that is left.
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Question 2
(a)
Factorise completely
#### (i)
\(4 c^{2}+12 c n\),
Answer (a) (i) [1]
#### (ii)
Factorise completely \(k^{2}+k h-k p-h p\).
Answer (ii) [2]
(b)
Solve the equation \(\frac{12-y}{3}=5-2 y\).
Answer (b) \(y=\) [2]
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5
(c)
The mass, \(m\) grams, of a solid, is inversely proportional to its volume, \(v \mathrm{~cm}^{3}\).
#### (i)
Find the formula connecting \(m\) and \(v\), given that \(m=3,5 \mathrm{~g}\) when \(v=4 \mathrm{~cm}^{3}\).
Answer (c) (i) [2]
#### (ii)
Find \(m\) when \(v=6 \mathrm{~cm}^{3}\).
Answer (ii) \(m=\) [1]
(d)
Make \(x\) the subject of the formula \(w x^{2}=n\).
Answer (d) \(x=\) [2]
6
Question 3
(a)
In the diagram, \(L \hat{M} N=90^{\circ}, M N=x c m, M L=(x+3) \mathrm{cm}\) and \(L N=7 \mathrm{~cm}\).
#### (i)
Form an equation in \(x\) and show that it reduces to \(x^{2}+3 x-20=0\).
Answer (a) (i)
#### (ii)
Solve the equation \(x^{2}+3 x-20=0\), giving the answers correct to 2 significant figures.
Answer (ii) \(x=\) \(\_\_\_\_\) or \(\_\_\_\_\) [4]
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#### (iii)
Hence calculate the perimeter of the triangle LMN.
Answer (iii)
cm [2]
(b)
A form four class has 40 pupils. All of them were asked whether they would like to study Mathematics or Physics after form four. Some of the results are shown in the Venn diagram.
The Universal set, \(\boldsymbol{\xi}\) is the set of all pupils in the class. M is the set of pupils who like Mathematics. P is the set of pupils who like Physics.
#### (i)
Find \(\mathrm{n}(M \cup P)\),
Answer (b) (i) [1]
#### (ii)
Find the number of pupils who do not like either subject,
Answer (ii) [1]
8
#### (iii)
Find \(\mathrm{n}\left(M^{l} \cap P\right)\).
Answer (iii) \(\_\_\_\_\)
Question 4
In the diagram, J, K, M and L lie on the circumference of a circle. JM and KL intersect at \(\mathrm{H} . \mathrm{JHK}=97^{\circ}, \mathrm{J} \hat{\mathrm{KH}}=48^{\circ}, \mathrm{KH}=20 \mathrm{~cm}, \mathrm{JH}=25 \mathrm{~cm}\) and \(\mathrm{HM}=6 \mathrm{~cm}\).
(a)
Find HL̂M.
Answer (a) \(\mathrm{H} \hat{\mathrm{L} M}=\) \(\_\_\_\_\) [3]
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(b)
Name, in the correct order, the triangle which is similar to triangle JKH.
Answer (b) [1]
(c)
Calculate
#### (i)
the length of JK,
Answer (c) (i) \(\mathrm{JK}=\) \(\_\_\_\_\) cm [3]
#### (ii)
the area of the triangle JKH ,
Answer (ii) \(\_\_\_\_\) \(\mathrm{cm}^{2}\) [2]
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#### (iii)
the area of triangle HLM.
Answer (iii) \(\_\_\_\_\) \(\mathrm{cm}^{2}\) [3]
Question 5
(a)
Given that \(\mathbf{A}=\left(\begin{array}{cc}2 & 5 \\ -3 & y\end{array}\right), \mathbf{B}=\left(\begin{array}{ll}-4 & 3\end{array}\right)\) and \(\mathbf{C}=\left(\begin{array}{cc}5 & -4 \\ 2 & -9\end{array}\right)\),
#### (i)
find the value of \(y\) for which \(\mathbf{A}\) has no inverse,
Answer (a) (i) \(y=\) \(\_\_\_\_\) [2]
#### (ii)
evaluate \(\mathbf{A}+\mathbf{C}\), using the value of y in (i).
Answer (a) (ii) \(\_\_\_\_\)
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#### (iii)
evaluate \(\mathbf{C}^{-1}\),
Answer (ii) [2]
#### (iv)
evaluate \(\mathbf{B C}\),
Answer (iii) \(\_\_\_\_\) [2]
(b)
If \(\log _{x} 27=1,5\), find \(x\).
Answer (b) \(x=\) \(\_\_\_\_\) [2]
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Question 6
Answer the whole of this question on page 13.
Use ruler and compasses only for all constructions and show clearly all the construction lines and ares.
(a)
#### (i)
Construct triangle ABC in which \(\mathrm{AB}=\mathrm{BC}=8 \mathrm{~cm}\) and \(\hat{A B C}=60^{\circ}\).
Line AB has been drawn on page 13.
#### (ii)
Bisect \(A \hat{B C}\)
#### (iii)
Mark point N on the bisector of \(\mathrm{A} \hat{\mathrm{B}} \mathrm{C}\) such that \(\mathrm{BN}=12 \mathrm{~cm}\).
#### (iv)
Complete the quadrilateral ABCN .
(b)
#### (i)
State the special name given to the quadrilateral.
#### (ii)
Describe fully the locus represented by the bisector BN.
(c)
Measure and write down
#### (i)
the length of CN ,
#### (ii)
the size of \(B \hat{C} N\).
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(a)
Answer (a) (i) On diagram ..... [3] (ii) On diagram ..... [2] (iii) On diagram ..... [1] (iv) On diagram ..... [1]
(b)
#### (i)
\(\_\_\_\_\) ..... [1]
#### (ii)
\(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\)
(c)
#### (i)
\(M N=\)
\(\_\_\_\_\) ..... cm [1]
#### (ii)
\(B \hat{C} N=\) ..... [1]
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**Section B [36 marks]** Answer any three questions in this section.
**Each question carries 12 marks.**
Question 7
