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**JUNE 2018 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. 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 three 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. Answers in degrees should be given correct 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 and 2 blank pages. Copyright: Zimbabwe School Examinations Council, J2018.
**Section A [64 marks]** Answer all the questions in this section.
Question 1
(a)
Simplify \(0,8+7,2 \div 0,24\).
Answer: (a)
(b)
By selling an article for \(\$ 45\), a shopkeeper made a loss of \(10 \%\) on the cost price.
Calculate the cost price.
| Centre Number | Candidate Number | | :--- | :--- | | | |
(c)
It is given that \(f(\mathrm{k})=2 \mathrm{k}^{2}-8\).
Calculate
#### (i)
\(f(-3)\),
#### (ii)
the values of \(k\) for which \(f(k)=0\).
Answer:
(i)
[2]
(ii) \(\_\_\_\_\) or \(\_\_\_\_\) [2]
Question 2
(a)
In the diagram, PAB is a straight line and is parallel to CD . \(\mathrm{P} \widehat{\mathrm{A}} \mathrm{C}=132^{\circ}\) and \(\mathrm{B} \widehat{\mathrm{C}} \mathrm{D}=43^{\circ}\).
Calculate \(\mathrm{A} \widehat{\mathrm{C}} \mathrm{B}\).
Answer:
(a) \(\_\_\_\_\) [2]
| Centre Number | Candidate Number | | :--- | :--- | | | |
(b)
Factorise completely
#### (i)
\(4 a^{2} b-20 a b^{2}\),
#### (ii)
\(3 a^{2}+7 a-6\).
Answer:
(i)
[1]
(ii)
[2]
(c)
It is given that \(H=m p+\frac{1}{2} f^{2} p\).
#### (i)
Calculate the value of \(H\) when \(m=2, p=3\) and \(f=-4\).
#### (ii)
Make \(f\) the subject of the formula.
Answer:
(i)
\(\_\_\_\_\)
(ii)
\(\_\_\_\_\)
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 3
(a)
The cost of 3 kg of apples and 7 kg of bananas is \(\$ 16\). The cost of 4 kg of apples and 5 kg of bananas is \(\$ 17\). Calculate the cost per kg of apples and the cost per kg of bananas.
Answer: (a) apples \$ \(\_\_\_\_\)
bananas \$ \(\_\_\_\_\)
(b)
\(\mathrm{W}\) varies directly as \(x\) and inversely as the square root of \(u\).
\(\mathrm{W}=6\), when \(x=2\) and \(u=9\).
#### (i)
Express W in terms of \(x\) and \(u\).
#### (ii)
Find W when \(x=8\) and \(u=4\).
(i)
(ii)
(c)
Matrix \(\mathbf{A}=\left(\begin{array}{ll}4 & 2 \\ 3 & 1\end{array}\right)\) and matrix \(\mathbf{B}=\left(\begin{array}{rr}2 & 0 \\ 1 & -3\end{array}\right)\).
Calculate
#### (i)
\(\mathbf{A}-2 \mathbf{B}\),
#### (ii)
AB ,
#### (iii)
\(\mathbf{A}^{-1}\), the inverse of matrix \(\mathbf{A}\).
(ii)
(iii)
Question 4
(a)
In the diagram, \(\mathrm{B}, \mathrm{C}, \mathrm{D}\) and E are points on the circumference of a circle centre O . TB is a tangent to the circle at \(\mathrm{B}, \mathrm{C} \widehat{\mathrm{B}} \mathrm{D}=67^{\circ}\) and \(\mathrm{E} \widehat{\mathrm{B}} \mathrm{T}=40^{\circ}\).
Calculate
#### (i)
\(\mathrm{E} \widehat{\mathrm{B}} \mathrm{D}\),
#### (ii)
\(\mathrm{B} \widehat{\mathrm{C}} \mathrm{E}\),
#### (iii)
\(\mathrm{B} \widehat{\mathrm{E}} \mathrm{C}\),
#### (iv)
\(\mathrm{B} \overline{\mathrm{D}} \mathrm{C}\).
Answer (a) (i) ..... [1]
(ii) ..... [1]
(iii) ..... [1]
(iv) ..... [1]
| Centre Number | Candidate Number | | :--- | :--- | | | |
(b)
It is given that the Universal set, \(\xi\) is such that \(\xi=\{x:-3 \leq x \leq 3, x\) is an integer \(\}\).
\(\mathbf{A}\) and \(\mathbf{B}\) are subsets of \(\xi\) such that
\(\mathbf{A}=\{x:-2 \leq x<2\}\) and
\(\mathbf{B}=\{x:-1 \leq x \leq 3\}\).
#### (i)
List the elements of
1. A,
2. \(\mathbf{A}^{\prime} \cup \mathbf{B}^{\prime}\). where \(\mathrm{A}^{\prime}\) is the complement of set \(\mathbf{A}\).
#### (ii)
Find \(n(A \cap B)\).
Answer (b) (i) 1.
2.
(ii)
| Centre Number | Candidate Number | | :--- | :--- | | | |
(c)
A polygon has \(n\) sides. The sum of the interior angles is equal to the sum of the exterior angles.
#### (i)
Find the value of \(n\).
#### (ii)
State the name of the polygon.
Question 5
(a)
Peter, John and James share a certain amount of money.
Peter gets \(\frac{2}{3}\) of the amount of money,
John gets \(\frac{3}{4}\) of the remainder and James gets \(\$ 3,00\).
Calculate the total amount of money shared.
| Centre Number | Candidate Number | | :--- | :--- | | | |
(b)
Three men working at the same rate can dig a trench, 5 m long, in 4 hours.
Calculate the time that two men working at the same rate would take to dig a similar trench, 5 m long.
(c)
Find the value of \(n\) given that
$$ 111_{n}=7_{10} . $$
| Centre Number | Candidate Number | | :--- | :--- | | | |
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 arcs.
All constructions should be done on a single diagram. Line PQ has been drawn on page 13.
(a)
Construct
#### (i)
triangle PQR in which \(\mathrm{PQ}=7,5 \mathrm{~cm}, \mathrm{R} \widehat{\mathrm{PQ}}=90^{\circ}\) and \(\mathrm{P} \widehat{\mathrm{Q}} \mathrm{R}=30^{\circ}\),
#### (ii)
the locus of points equidistant from \(Q\) and \(R\),
#### (iii)
a circle with diameter QR .
(b)
#### (i)
Measure and write down the length of the
1. radius of circle in a(iii),
2. side PR in triangle PQR .
#### (ii)
Mark and label the points X and Y on the circle which are equidistant from Q and R .
#### (iii)
Write down the special name given to quadrilateral PRYQ.
| Centre Number | Candidate Number | | :--- | :--- | | | |
Answer
(a)
#### (i)
On the diagram
[4]
#### (ii)
On the diagram
[2]
#### (iii)
On the diagram
[1]
(b)
#### (i)
1.
1. \(\_\_\_\_\)
2. \(\_\_\_\_\) [1]
#### (ii)