MATHEMATICS
PAPER 1 JUNE 2013 SESSION
**4008/1**
2 hours 30 minutes
Candidates answer on the question paper.
Additional materials:
Geometrical instruments
Allow candidates 5 minutes to count pages before the examination.
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.
If you need additional working space, use the lined pages at the back and number your work correctly.
Answer all questions.
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.
Mathematical tables, slide rules and calculators should not be brought into the examination room.
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 lined pages.
Copyright: Zimbabwe School Examinations Council, J2013.
| Centre Number | Candidate's Number | | :--- | :--- | | | |
2
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
(a)
Subtract -2 from 2.
(b)
Leaving your answer as a common fraction, find, in its lowest terms, the value of \(\frac{8}{15} \div \frac{2}{3}\).
| Centre Number | Candidate's Number | | :--- | :--- | | | |
3
Question 2
(a)
Express \(3 \frac{4}{5}\) as a decimal number.
(b)
Find the exact value of \(\frac{0,83+8,368}{0,42}\).
Answer (a) ..... [1]
(b)[2]
4
Question 3
(a)
Find \(n\) such that \(0,0075=7,5 \times 10^{n}\).
(b)
In the diagram ACE and BCD are straight lines intersecting at C. Given that \(\hat{C E D}=90^{\circ}\), calculate \(\hat{A B C}\).
$$ \text { Answer } \quad \text { (a) } \quad n= $$
\_\_\_\_
(b) \(\mathrm{A} \hat{\mathrm{B}} \mathrm{C}=\) \_\_\_\_
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 4
(a)
Write down the square of 4.
(b)
Evaluate \(125^{\frac{1}{3}} \times \sqrt{144}\).
| Centre Number | Candidate's Number | | :--- | :--- | | | |
6
Question 5
Express
(a)
\(3 \mathrm{~m}^{2}\) in \(\mathrm{cm}^{2}\),
(b)
\(32,5 \mathrm{~m} / \mathrm{s}\) in km/h.
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 6
In the diagram, \(A B C D\) is a quadrilateral in which \(A B\) is parallel to \(D C, A B=12 \mathrm{cm}, \mathrm{CD}=18 \mathrm{~cm}, \mathrm{BX}=7 \mathrm{~cm}\) and \(\mathrm{B} \hat{\mathrm{X}} \mathrm{C}=90^{\circ}\).
(a)
State the special name given to the quadrilateral \(A B C D\).
(b)
Calculate the area of the quadrilateral.
Answer
(a) \_\_\_\_ [1]
(b) \_\_\_\_ \(\mathrm{cm}^{2}\) [2]
8
Question 7
Simplify \(\frac{x^{2}+7 x+6}{x^{2}-36}\).
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 8
In the diagram \(\mathrm{P}, \mathrm{Q}, \mathrm{R}\) and S are points on the circumference of a circle and arcs QR and RS are equal. TP is a tangent to the circle at \(\mathrm{P}, \mathrm{T} \hat{\mathrm{PS}}=70^{\circ}\) and \(\mathrm{RPS}= 30^{\circ}\).
Calculate
(a)
\(\mathrm{Q} \hat{\mathrm{P}} \mathrm{R}\),
(b)
\(P \hat{R} S\),
(c)
\(\mathrm{PQ} \mathrm{Q}\).
Answer (a) QPR ..... [1]
(b) \(\mathrm{P} \hat{\mathrm{R}} \mathrm{S}\) ..... [1]
(c) \(\quad \mathrm{P} \hat{\mathrm{Q}} \mathrm{R}\) ..... [1]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 9
E varies directly as the square of \(V\).
(a)
Express \(E\) in terms of \(V\) and a constant \(m\).
(b)
Given that \(E=3\) when \(V=2\) find \(m\).
\_\_\_\_
(b) \(m=\) \_\_\_\_
Question 10
Evaluate
(a)
\((-3)^{\circ}\),
(b)
\(\left(\frac{16}{81}\right)^{-\frac{3}{4}}\).
Answer
(a) \_\_\_\_ [1]
(b) \_\_\_\_
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 11
In the diagram GHJ is a straight line. \(\mathrm{HJK}=90^{\circ}, \mathrm{JK}=5 \mathrm{~cm}\) and \(\mathrm{HK}=10 \mathrm{~cm}\).
(a)
Find sin GHK,
(b)
Calculate HJ leaving your answer in surd form.
(a)
(b) \_\_\_\_ [2]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 12
Given that \(\mathbf{M}=\left(\begin{array}{ll}5 & 5 \\ 3 & x\end{array}\right)\) and \(\mathbf{N}=\binom{3}{4}\)
find
(a)
the determinant of \(\mathbf{M}\) in terms of \(x\),
(b)
the modulus of the vector \(\mathbf{N}\),
(c)
the value of \(x\) given that \(\operatorname{det} \mathrm{M}=|\mathbf{N}|\).
Answer (a) \(\operatorname{det} \mathrm{M}=\) ..... [1]
(b) \(|\mathbf{N}|=\) ..... [1]
(c) \(x=\)[1]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 13
(a)
Write down the gradient of the line whose equation is \(3 x+2 y=18\).
(b)
Find the equation of the straight line which is parallel to the line \(3 x+2 y=18\) and passes through ( \(-2 ; 3\) ).
Answer (a)
\_\_\_\_ ..... [1]
(b)
\_\_\_\_ ..... [2]
15
Question 14
Given that \(h\binom{3}{5}+k\binom{2}{-1}=\binom{14}{6}\), find the scalars \(h\) and \(k\).
$$ \begin{aligned} & h=\text { _ [2] } \\ & k=\text { [2] } \end{aligned} $$
| Centre Number | Candidate's Number | | :--- | :--- | | | |
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Question 15
Given that \(\log _{10} 3=0,4771\) and \(\log _{10} 5=0,6991\), find
(a)
\(\quad \log _{10} 1 \frac{2}{3}\),
(b)
\(\quad \log _{10} 30\).
Answer
(a)
[2]
(b)
[2]
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Question 16
In the diagram, OAB is a sector of a circle of radius 7 cm and \(\mathrm{AOB}=30^{\circ}\).
Calculate
(a)
the length of the arc AB ,
(b)
the area of the sector AOB .