ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
**PAPER 1**
4008/1, 4028/1
2 hours 30 minutes
NOVEMBER 2010 SESSION
Candidates answer on the question paper.
Additional materials:
Geometrical instruments
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.
Answer all questions.
Write your answers in the spaces provided on the question paper.
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.
FOR EXAMINER'S USE
□
This question paper consists of 26 printed pages and 6 blank pages.
Copyright: Zimbabwe School Examinations Council, N2010. CALCULATORS MAY BE USED IN THIS PAPER.
Question 1
Evaluate
(a)
\(\quad\left(16^{\frac{1}{2}}\right)^{\frac{3}{2}}\),
(b)
\(\quad 7^{-\frac{1}{4}} \times 7^{\frac{5}{4}} \times 7\),
(c)
\(\left(\frac{1}{5}\right)^{-2}\)
Answer:
(a) ..... [1]
(b) ..... [1]
(c) ..... [1]
Question 2
Factorise completely
(a)
\(\quad x^{2}+5 x-6\),
(b)
\(\quad 8 m^{3} n-2 m n^{3}\).
Answer:
(a)
[1]
(b)
[2]
Question 3
Given that \(m=2 \times 10^{3}\) and \(n=5 \times 10\), evaluate, giving your answer in standard form.
(a)
\(m+n\),
(b)
\(\frac{n}{m}\).
Answer:
(a)
(b)
[2]
Question 4
(a)
In a certain month \(£ 1402\) was equivalent to US \(\$ 2000\).
Calculate the exact value of the exchange rate in the form \(\mathrm{USS} 1=£ n\).
(b)
In another month the exchange rate was \(\mathrm{US} \$ 1=£ 0,69\). Calculate the equivalent of \(£ 2760\) in US\$.
(a) USS1 \(=£\) \_\_\_\_
(b) USS \_\_\_\_
Question 5
The dimensions of a rectangle measuring 32 cm by 24 cm are enlarged in the ratio \(5: 2\). Find the new dimensions.
Answer: \_\_\_\_ cm by \_\_\_\_ cm
[3]
Question 6
Given that \(\overrightarrow{\mathrm{AB}}=\binom{10}{-4}\) and \(\overrightarrow{\mathrm{BC}}=\binom{2}{-8}\),
(a)
write down \(\overrightarrow{\mathrm{AC}}\) as a column vector,
(b)
find \(|\overrightarrow{\mathrm{BC}}|\) leaving your answer in surd form.
(a)
[1]
(b)
[2]
Question 7
(a)
Find the gradient of the line \(\ell\) which passes through (6;8) and (0; 5).
(b)
Find the equation of the line which is parallel to line \(\ell\) in (a) and passes through \((4 ;-5)\).
Answer:
(a)
(b)
[1]
[2]
Question 8
By correcting each number to 1 significant figure, estimate the value of
$$ \frac{371 \div 849}{\sqrt{668-643}} . $$
Answer:
Question 9
D is proportional to the cube of \(n\).
(a)
Express D in terms of \(n\) and a constant \(k\).
(b)
Given that \(n=3\) when \(\mathrm{D}=21,6\); find D when \(n=5\).
Answer:
(a) \(\mathrm{D}=\)
(b) \(\mathrm{D}=\)
Question 10
A map has a scale of 1 : 250 .
(a)
A building on the map has a length of 6 cm . Calculate the actual length of the building in metres.
(b)
The area of a pool on the map is \(10 \mathrm{~cm}^{2}\). Calculate the actual area of the pool in \(\mathrm{m}^{2}\).
Answer:
(a) \_\_\_\_ m
(b)
\_\_\_\_ \(\mathrm{m}^{2}\)
Question 11
(a)
The bearing of A from B is \(243^{\circ}\). Write down the three-figure bearing of B from A .
(b)
From the list of numbers below, choose the rational numbers.
\(\frac{22}{7} ; \quad \pi ; \quad 2,3 ; \quad \sqrt{48} ; \quad \sqrt[3]{-8}\)
Answer:
(a)
[1]
(b)
[2]
4008/4028/1 N2010
Question 12
Express \(\frac{3}{x-2}-\frac{4}{x+1}\) as a single fraction in its simplest form.
Answer:
Question 13
Solve the simultaneous equations
$$ \begin{array}{r} 0,4 x+3 y=2,6 \\ x-2 y=4,6 \end{array} $$
Answer:
$$ \begin{aligned} & x= \\ & y= \end{aligned} $$
Question 14
In the diagram PQ and RS are parallel tangents to the circle AQBR . Chord AB is also parallel to the two tangents and \(\mathrm{PQ} \hat{\mathrm{Q}}=63^{\circ}\).
(a)
Find
#### (i)
\(\quad \mathrm{Q} \hat{\mathrm{AB}}\),
#### (ii)
\(\quad \hat{A} \hat{A}\).
(b)
Write down the special name of the cyclic quadrilateral AQBR .
Answer: (a) (i) \(\mathrm{QAB}=\)
(ii) \(\hat{\mathrm{BAR}}=\) \_\_\_\_
(b)
Question 15
Write the 4 inequalities which define the unshaded region D.
Answer:
(a) \_\_\_\_ [1]
(b) \_\_\_\_
(c) \_\_\_\_
(d) \_\_\_\_ [1]
4008/4028/1 N2010
[Turn over
Question 16
The length, \(\ell \mathrm{cm}\), of the edge of a cube is given as \(5,1 \mathrm{~cm}\) correct to one decimal place.
(a)
Give the limits for \(\ell\).
(b)
Find the least possible surface area of the cube.
Answer:
(a) \_\_\_\_
\_\_\_\_
(b) \_\_\_\_ \(\mathrm{cm}^{2}\)
Question 17
It is given that \(\mathrm{n}(\mathrm{A})=18, \mathrm{n}(\mathrm{B})=11\) and \(\mathrm{n}(\mathrm{A} \cup \mathrm{B})^{I}=0\).
(a)
If this information was shown on the Venn diagram below, write down the values of \(p, q\) and \(r\), the number of elements in each region.
(b)
For the same given information, complete the Venn diagram to show the number of elements in each region where \(\mathrm{n}(\mathrm{A} \cup \mathrm{B})=29\).
Answer:
(a) \(p=\) \_\_\_\_
\(q=\) \_\_\_\_
\(r=\)
\_\_\_\_
