ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
4004/1
PAPER 1
JUNE 2023 SESSION 2 hours 30 minutes
Candidates answer on the question paper
Additional materials:
Mathematical 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.
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. 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 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 blank pages.
Copyright: Zimbabwe School Examinations Council, J2023.
Answer all questions.
NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.
Question 1
Express
(a)
54,497 correct to the nearest tenth,
Answer (a)
(b)
0,000342 in standard form,
Answer (b)
(c)
478,367 correct to two significant figures.
Answer (c)
Candidate Name Centre Number Candidate Number
Question 2
Simplify, giving the answer as common fraction in its lowest terms
(a)
\(\frac{2}{7}+\frac{1}{3}\),
Answer (a)
\_\_\_\_
(b)
\(\frac{2}{5} \div 10\),
Answer (b)
\_\_\_\_
(c)
\(\frac{18}{35} \times \frac{14}{27}\).
Answer (c)
\_\_\_\_
Question 3
(a)
Evaluate giving the answers as exact decimals
#### (i)
\(0,024 \times 0,3\),
Answer (a)(i)
\_\_\_\_
#### (ii)
\((0,4)^{3}\).
Answer (a)(ii)
(b)
Express 0,224 as a percentage.
Answer (b)
Question 4
The universal set \(\xi=\{75 ; 76 ; 77 ; 78 ; 79 ; 80\}\)
\(M\) and \(R\) are subsets \(\xi\).
\(M=\{\text{even numbers}\}\),
\(R=\{\text{multiples of 4}\}\).
(a)
#### (i)
List elements of set M.
Answer (a)(i)
#### (ii)
List elements of set R.
Answer (a)(ii)
(b)
Find \(n\left(M^{1} \cup R\right)\)
Answer (b)
Question 5
(a)
Simplify \(2(a-2)-4(a+3)\)
Answer (a)
(b)
Express \(\frac{3}{m-2}-\frac{2}{4 m+3}\) as a single fraction.
Answer (b)
Question 6
(a)
State the special name of a quadrilateral with four lines of symmetry.
Answer (a)
(b)
A quadrilateral has interior angles of \(x^{\circ}, 2 x^{\circ},(x+10)^{\circ}\) and \((x+50)^{\circ}\). Calculate the value of \(x\),
Answer (b)
Question 7
\(P\) varies directly as the cube of \(r\). Given that \(P=2\) and \(r=4\), Find the
(a)
formula connecting \(P\) and \(r\),
Answer (a)
(b)
value of \(P\) when \(r=8\).
Answer (b)
Question 8
Given that:
$$ \begin{gathered} m+3 n=5 \\ m^{2}-9 n^{2}=-15 \end{gathered} $$
find the numerical
(a)
value of \(m-3 n\),
Answer (a)
(b)
values of \(m\) and \(n\).
Answer (b)
Question 9
Given that \(p=\frac{q}{q+m}\),
(a)
make \(m\) the subject of the formula,
Answer (a)
(b)
Find \(m\) given that \(q=3\) and \(p=2\).
\_\_\_\_
Question 10
In the diagram points Q, S and R are on the circumference of a circle centre O. Line PQT is a tangent to the circle at Q.
\(P \hat{Q} S=m^{\circ}, O \hat{Q} S=n^{\circ}, Q \hat{O} R=p^{\circ}, Q \hat{S} R=70^{\circ}\) and \(O \hat{R} S=25^{\circ}\).
Calculate the value of
(a)
\(m\),
Answer (a)
(b)
\(n\),
\_\_\_\_
\_\_\_\_
(c)
\(p\).
Answer (c) \_\_\_\_
Question 11
(a)
Evaluate \(766_{9}+143_{9}\) giving the answer in base 9.
Answer (a)
\_\_\_\_
(b)
Convert \(35_{6}\) to a number in base 2.
Answer (b) \_\_\_\_
(c)
Given that \(f(x)=(4-x)(x-0,5)\),
find \(f(0)\).
Answer (c)
\_\_\_\_
Question 12
In the diagram the unshaded region \(R\) is defined by three inequalities.
Candidate Name Centre Number Candidate Number
Find the three inequalities
Answer
\_\_\_\_
\_\_\_\_
\_\_\_\_
Question 13
Two similar cylinders have heights of 16 cm and 48 cm.
(a)
Write down, in its simplest form, the ratio of
#### (i)
heights,
\_\_\_\_
#### (ii)
volumes
Answer (a)(ii)
\_\_\_\_
(b)
The curved surface area of the larger cylinder is \(500 \mathrm{~cm}^{2}\).
Calculate the curved surface area of the smaller cylinder.
Answer (b)
\_\_\_\_
Question 14
(a)
A sum of money is shared in the ratio \(2: 3: 4\). The smallest share is \(\$ 160,00\).