ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary Level MATHEMATICS PAPER 1 4008/1, 4028/1
NOVEMBER 2009 SESSION 2 hours 30 minutes 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 **24** printed pages. Copyright: Zimbabwe School Examinations Council, N2009.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
Find the value of
(a)
#### (i)
\(\frac{7}{8}-\frac{5}{6}\), giving your answer as a common fraction in its lowest terms,
#### (ii)
\(0,004 \div 0,8\), giving your answer as a decimal.
(b)
Express 0,085 as a percentage.
Answer
(a)
#### (i)
[1]
#### (ii)
\(\_\_\_\_\) [1]
(b)
\(\_\_\_\_\) \% [1]
Question 2
(a)
State the number of significant figures in the number 0,000320.
(b)
A rectangle measures \((x+2) \mathrm{cm}\) by \((2 x-1) \mathrm{cm}\). Given that \(x=3\), correct to the nearest whole number, find the minimum possible area of the rectangle.
(a)
\(\_\_\_\_\)
(b)
\(\_\_\_\_\) \(\mathrm{cm}^{2}\)
Question 3
Factorise completely
(a)
\(x^{2}-12 x+27\),
(b)
\(c x-d x-4 c y+4 d y\).
(a)
[1]
(b)
[2]
Question 4
ABCDEF is a regular polygon. AB and DC are produced to meet at X.
(a)
Calculate
#### (i)
\(\mathrm{XBC}\),
#### (ii)
\(\mathrm{B}\hat{\mathrm{X}}\mathrm{C}\).
(b)
Give the special name for triangle BXC.
Answer
(a)
#### (i)
\(\_\_\_\_\) [1]
#### (ii)
[1]
(b)
\(\_\_\_\_\) [1]
Question 5
Simplify
(a)
\((2 x)^{3}\),
(b)
\(\left(8^{-\frac{2}{3}}\right)^{\frac{1}{2}}\).
Answer
(a)
[1]
(b)
[2]
Question 6
\(\mathbf{X}=\left(\begin{array}{ll}2 & 0 \\ 0 & 6\end{array}\right)\) and \(\mathbf{Y}=\left(\begin{array}{cc}p & q \\ 0 & r\end{array}\right)\).
Given that \(\mathbf{X Y}=\mathbf{X}+\mathbf{Y}\), find
(a)
\(p\),
(b)
\(q\),
(c)
\(r\).
Answer
(a)
\(p=\) \(\_\_\_\_\) [1]
(b)
\(q=\) \(\_\_\_\_\) [1]
(c)
\(r=\) \(\_\_\_\_\) [1]
Question 7
A bicycle wheel has a diameter of 70 cm. Taking \(\pi\) to be \(\frac{22}{7}\), calculate
(a)
the circumference of the wheel,
(b)
the number of revolutions made by the wheel in travelling 55 km.
Answer
(a)
\(\_\_\_\_\) [1]
(b)
\(\_\_\_\_\) [2]
Question 8
From the following list of numbers, write down the irrational numbers:
\(0,5 ; \quad 36 ; \quad \pi ; \quad \sqrt{81} ; \quad \sqrt{2} ; \quad \sqrt{5} ; \quad-6,392 ; \quad \frac{3}{4}\)
Answer \(\_\_\_\_\) [3]
Question 9
(a)
Solve the inequality \(5 x-5 \leq 10 x<8 x+10\).
(b)
Illustrate your solution to (a) on the number line below.
Answer
(a)
\(\_\_\_\_\) \(\leq x<\) \(\_\_\_\_\)
(b)
Question 10
A shop assistant is paid a basic wage of \(\$ 3600000\) per week. In addition she is paid a commission of \(2 \frac{1}{2} \%\) of the value of the goods which she sells.
During a certain week she sells goods worth \(\$ 52000000\). Calculate
(a)
the amount of commission she gets,
(b)
her total earnings for that week.
Answer
(a)
\(\$\) \(\_\_\_\_\)
(b)
\(\$\) \(\_\_\_\_\)
Question 11
Two towns \(X\) and \(Y\) are such that the bearing of \(X\) from \(Y\) is \(031^{\circ}\).
(a)
Find the bearing of Y from X.
(b)
A third town Z is on a bearing of \(300^{\circ}\) from Y. Find \(Z \hat{Y X}\).
Answer
(a)
[1]
(b)
\(\mathrm{Z} \hat{\mathrm{Y} \mathrm{X}}=\) [2]
Question 12
The diagram above is a regular pentagonal star.
(a)
State the order of rotational symmetry of the pentagonal star.
(b)
Draw in all the lines of symmetry of the pentagonal star.
Answer
(a)
[1]
(b)
on the diagram.
Question 13
Solve the following simultaneous equations.
$$ \begin{aligned} & 3 x+2 y=0 \\ & 2 x+y=-1 \end{aligned} $$
Answer
$$ \begin{aligned} & x= \\ & y= \end{aligned} $$
\(\_\_\_\_\)
Question 14
Given that \(\overrightarrow{\mathrm{OA}}=\binom{10}{-2}, \overrightarrow{\mathrm{OB}}=\binom{1}{10}\) and X is the midpoint of OA,
(a)
express \(\overrightarrow{\mathrm{OX}}\) as a column vector,
(b)
find \(|\overrightarrow{\mathrm{AB}}|\).
Answer
(a)
\(\_\_\_\_\)
(b)
\(\_\_\_\_\) [1]
Question 15
In the diagram, \(A B C\) and \(A O M\) are straight lines and \(O\) is the centre of the circle. Given that \(\mathrm{NBC}=68^{\circ}\) and \(\mathrm{NAB}=40^{\circ}\), calculate
(a)
\(\hat{\mathrm{AMN}}\),
(b)
MAN,
(c)
BÔM.
Answer