ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
PAPER 1 NOVEMBER 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. 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 27 printed pages and 1 blank page.
Copyright: Zimbabwe School Examinations Council, N2013.
| Centre Number | Candidate's Number | | :--- | :--- | | | |
2
NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.
Question 1
Evaluate, giving each answer as a fraction in its lowest terms.
(a)
\(\frac{1}{5}+\frac{1}{6}\),
(b)
\(\quad \frac{2}{5} \div 4\),
(c)
\(\frac{3}{4}-\frac{1}{4} \times \frac{2}{3}\).
Answer
(a)
[1]
(b)
[1]
(c)
[1]
| | | | :--- | :--- |
3
Question 2
Evaluate \(\frac{(0,3)^{3} \times 0,02}{0,0008}\), giving your answer in standard form.
| Centre Number | Candidate's Number | | :--- | :--- | | | |
Question 3
(a)
The temperature inside a freezer is \(-8^{\circ} \mathrm{C}\). During a power cut the temperature rose by \(12^{\circ} \mathrm{C}\). Find the temperature after the rise.
(b)
Write down the next two terms in the following sequence; \(1 ; \frac{1}{2} ; \frac{1}{4} ; \frac{1}{8} ; \cdots\).
(a)
(b)
\(\_\_\_\_\) ; [2]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
5
Question 4
(a)
Write 3,35 minutes in minutes and seconds.
(b)
If 1 kilometre is \(\frac{5}{8}\) of a mile, convert 75 miles to kilometres.
Answer
(a)
\(\_\_\_\_\) minutes \(\_\_\_\_\) seconds [1]
(b)
\(\_\_\_\_\) km [2]
6
Question 5
A shopper spent \(\$ \frac{c}{d}\) on one item and half of that amount on each of three other items.
Find how much she spent altogether.
Question 6
Simplify
(a)
\(\frac{\left(3^{3}\right)^{4}}{27^{3}}\),
(b)
\(\quad\left(4 x^{2} y^{6}\right)^{\frac{1}{2}}\),
(c)
\(\quad x^{0}+x^{-2}\).
Answer
(a)
[1]
(b)
[1]
(c)
[1]
8
Question 7
(a)
Express \(\frac{7}{8}\) as a decimal fraction.
(b)
A car loses \(55 \%\) of its value after four years.
If it cost \(\$ 8500\) when new, find its value after the four years.
Answer
(a)
(b)
\(\$\)
| Centre Number | Candidate's Number | | :--- | :--- | | | |
Question 8
(a)
Simplify \(5 m-2(x-3 m)\).
(b)
Solve the equation \(\frac{x+5}{7}=\frac{3}{2}\).
Answer
(a)
..... [1]
(b)
\(x=\) \(\_\_\_\_\)
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10
Question 9
(a)
Express \(200 \mathrm{~km} / \mathrm{h}\) as a speed in \(\mathrm{km} / \mathrm{min}\).
(b)
Find the time taken for a racing driver to cover a 120 km race if he travels at a speed of \(200 \mathrm{~km} / \mathrm{h}\), giving your answer in minutes.
Answer
(a)
\(\_\_\_\_\) km / minute [1]
(b)
\(\_\_\_\_\) minutes [2]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
11
Question 10
Factorise completely
(a)
\(\quad 4 y-4\),
(b)
\(\quad x y^{2}-4 x+2 y^{2}-8\).
(a)
\(\_\_\_\_\)
(b)
\(\_\_\_\_\) [2]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
12
Question 11
Solve the simultaneous equations \(5 d-3 e=-1\) \(2 d+3 e=8\).
\(e=\) \(\_\_\_\_\)
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13
Question 12
(a)
Solve the equation \((x+3)^{2}=49\).
(b)
Write down the prime numbers between 20 and 30 .
Answer
(a)
\(x=\) \(\_\_\_\_\) or \(\_\_\_\_\)
(b)
Question 13
(a)
Simplify \(\frac{x^{2}+3 x+2}{x+2}\).
(b)
Find the order of rotational symmetry of a right-angled isosceles triangle.
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15
Question 14
(a)
Given that \(n(\mathbf{A})=10\) and \(n(\mathbf{B})=15\), find the greatest possible value of
#### (i)
\(\quad n(\mathrm{~A} \cup \mathrm{~B})\),
#### (ii)
\(\quad n(\mathrm{~A} \cap \mathrm{~B})\).
(b)
Use set notation to describe the shaded region in the above diagram in terms of sets \(\mathbf{P}, \mathbf{Q}\) and \(\mathbf{R}\).
Answer
(a)
#### (i)
\(\_\_\_\_\) [1]
#### (ii)
\(\_\_\_\_\) [1]
(b)
\(\_\_\_\_\) [2]
| Centre Number | Candidate's Number | | :--- | :--- | | | |
Question 15
Given that \(\mathbf{A}=\left(\begin{array}{cc}-2 & -1 \\ 6 & 2\end{array}\right)\) and \(\mathbf{B}=\left(\begin{array}{cc}0 & -1 \\ 4 & 3\end{array}\right)\).
Find
(a)
\(3 \mathbf{A}-\mathbf{B}\),
(b)
\(\quad \mathrm{B}^{2}\).
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17
Question 16
(a)
Write down the largest four-digit number in base eight.
(b)
Convert \(111_{8}\) to a number in base two.