ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary Level **MATHEMATICS** **PAPER 1** 4004/1
**NOVEMBER 2018 SESSION** 2 hours 30 minutes
Additional materials: Candidates answer on the question paper Geometrical Instruments Allow candidates 5 minutes to count pages before the examination. This booklet should not be punched or stapled and pages should not be removed.
INSTRUCTIONS TO CANDIDATES
Write your Name, Centre number and candidate number in the spaces at the top of this page. Write your centre and candidate number in the box 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. 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 bought 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 20 printed pages and 0 blank page(s). Copyright: Zimbabwe School Examinations Council, N2018.
Answer all questions.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
(a)
Simplify \(\frac{2^{3}}{5^{2}}\) giving the answer as a fraction.
Answer (a) \(\_\_\_\_\)
(b)
Express
#### (i)
\(\frac{6}{25}\) as a decimal fraction,
(b)(i) \(\_\_\_\_\)
#### (ii)
0,125 in standard form.
(b)(ii) \(\_\_\_\_\)
Question 2
The following is a list of real numbers: \(\frac{3}{7} ; 11 ; \sqrt{\frac{3}{2}} ; 121 ;-19 ; \pi ; \sqrt{64}\).
Choose from the list
(a)
a square number,
Answer (a) \(\_\_\_\_\)
(b)
irrational numbers.
(b) \(\_\_\_\_\)
Question 3
(a)
Express \(4 \times 5^{3}+3 \times 5^{2}+2\) as a number in base 5.
(a) \(\_\_\_\_\)
(b)
#### (i)
\(512^{7}-435^{7}\) giving the answer in base 7.
(b)(i) \(\_\_\_\_\)
#### (ii)
\(\_\_\_\_\)
Question 4
(a)
Express 0045 in 12 hour notation.
(a) \(\_\_\_\_\)
(b)
Gortha's local time is 3 hours 45 minutes ahead of Harare's local time.
Find the time in Harare when the time in Gortha is 2123.
(b) \(\_\_\_\_\)
(c)
Convert \(5 \mathrm{~km}^{2}\) to hectares.
(c) \(\_\_\_\_\)
Question 5
(a)
Express \(6,07 \times 10^{4}\) in ordinary form.
Answer (a) \(\_\_\_\_\)
(b)
Evaluate \(2,53 \times 10^{1}+6,1 \times 10^{-1}\), giving the answer in standard form.
(b) \(\_\_\_\_\)
Question 6
In the diagram \(A Q\) and \(B S\) are parallel lines such that \(\mathrm{PQ}=\mathrm{PR}, A \hat{P} R=84^{\circ}\) and \(R \hat{Q} S=90^{\circ}\).
Find
(a)
\(P \dot{R} Q\),
Answer (a) \(\_\_\_\_\)
(b)
\(Q \hat{R} B\),
(b) \(\_\_\_\_\)
(c)
\(Q \hat{S} R\).
(c) \(\_\_\_\_\)
Question 7
Solve the simultaneous equations:
\(2 x+3 y=11\)
\(3 x-5 y=-12\)
Question 8
The wave length, \(w\), is inversely proportional to its frequency, \(f\).
When \(f=90, w=675\).
Find
(a)
an equation connecting \(f\) and \(w\),
Answer (a) \(\_\_\_\_\)
(b)
the value of \(f\) when \(w=500\).
(b) \(\_\_\_\_\)
Question 9
(a)
Write 45,3981 correct to 4 significant figures.
Answer (a) \(\_\_\_\_\)
(b)
A student spends 8 seconds, correct to the nearest second, to solve a problem.
Find the limits between which this time lies in the form \(a \leq t<b\) where \(a\) and \(b\) are constants and \(t\) is the time.
(b) \(\_\_\_\_\)
Question 10
(a)
Factorise \(3 x^{2}-15 x\) completely.
Answer (a) \(\_\_\_\_\)
(b)
Find the Highest Common Factor (H.C.F.) of \(8 k l^{2} m, 28 k^{2} l^{3} m\) and \(36 l^{2} m n\).
(b) \(\_\_\_\_\)
Question 11
The points \(A(6 ; 2)\) and \(B(8 ; 5)\) lie on a straight line.
Find the
(a)
gradient of the line AB ,
Answer (a) \(\_\_\_\_\)
(b)
equation of the line AB , giving the answer in the form \(y=m x+c\).
(b) \(\_\_\_\_\)
Question 12
(a)
Simplify \(\frac{2 a+6}{a-3} \div \frac{a+3}{a^{2}-2 a-3}\).
(a) \(\_\_\_\_\)
(b)
In 2010 a farmer harvested 45 tonnes of maize. This was \(20 \%\) more than what he had harvested in 2015.
Find the number of tonnes of maize the farmer harvested in 2015.
(b) \(\_\_\_\_\) tonnes
Question 13
(a)
Solve the inequality
\(4-5 x<2 x+8\).
Answer (a) \(\_\_\_\_\)
(b)
Write down the smallest integer that satisfies the inequality
\(4-5 x<2 x+8\).
(b) \(\_\_\_\_\)
Question 14
If \(\log a=3\) and \(\log b=7\),
calculate
(a)
\(\log a b\),
(a) \(\_\_\_\_\)
(b)
\(\log \frac{1}{b}\),
(b) \(\_\_\_\_\)
(c)
\(\log \sqrt[3]{a}\).
(c) \(\_\_\_\_\)
Question 15
(a)
If a function \(f(x)=(x+4)(2 x-1)\), find \(f(3)\).
(a) \(\_\_\_\_\)
(b)
Solve the equation
\(\frac{3 m}{4}-\frac{m}{3}=2 \frac{1}{2}\).
(b) \(\_\_\_\_\)
Question 16
It is given that vector \(p=\binom{0}{-3}\) and vector \(q=\binom{x}{1}\).
Find
(a)
\(p-q\) in terms of \(x\) in its simplest form,
Answer (a) \(\_\_\_\_\)
(b)
the possible values of \(x\) given that \(|p-q|=5\).
(b) \(\_\_\_\_\)
Question 17
(a)
State the special name given to a regular polygon with 4 sides.
Answer (a) \(\_\_\_\_\)
(b)
The angles of a hexagon are \(115^{\circ}, 89^{\circ}, x^{\circ}, x^{\circ}, x^{\circ}\) and \(x^{\circ}\).
Find the value of \(x\).
(b) \(\_\_\_\_\)
Question 18
In the diagram, triangle \(\mathbf{A B C}\) is right angled at \(\mathbf{B}, \mathbf{B C D}\) is a straight line, \(\mathbf{A C}=12 \mathrm{~cm}\) and \(B \hat{C} A=45^{\circ}\).
\(\left[\operatorname{Sin} 45^{\circ}=\frac{\sqrt{2}}{2}, \operatorname{Cos} 45^{\circ}=\frac{\sqrt{2}}{2}\right]\)
Using as much of the information given above as is necessary, calculate
(a)
BC, leaving the answer in surd form,
Answer (a) \(\_\_\_\_\)
(b)
\(\operatorname{Sin} A \hat{C} D\) leaving the answer in surd form,
(b) \(\_\_\_\_\)