ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**<br>**PAPER 1**
4004/1
NOVEMBER 2021 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 25 printed pages and 3 blank page.
Copyright: Zimbabwe School Examinations Council, N2021.
Answer all questions
NEITHER MATHEMATICAL TABLES NOR SLIDE RULE NOR CALCULATORS MAY BE USED IN THIS PAPER
Question 1
Express 30,098
(a)
correct to the nearest tenth,
Answer (a)
(b)
correct to four significant figures.
Answer (b)
(c)
in standard form.
Answer (c)
Question 2
(a)
Express \(4 \frac{2}{3}\) as a recurring decimal.
Answer (a)
(b)
Find the value of \(10-10 \div 2+2 \times 2\).
Answer (b)
Question 3
(a)
Write down the next term in the sequence \(2 ; 3 ; 5 ; 8 ; 12 ; \ldots\).
Answer (a)
[1]
(b)
Simplify \(\frac{20-8}{20+8}\), giving your answer as a common fraction in its simplest form.
Answer (b)
Question 4
(a)
#### (i)
List the prime numbers between 14 and 20,
Answer (a)(i)
#### (ii)
Write the number 801008 in words.
Answer (a)(ii) in answer space
(b)
Express 6,65 hours in hours and minutes.
Answer (b)
Question 5
(a)
List the first three values of \(x\) such that \(1 \leq x \leq 4\) where \(x\) is a natural number.
Answer (a)
(b)
Express 270 as a product of its prime factors in index form.
Answer (b)
Question 6
(a)
If the bearing of P from Q is \(054^{\circ}\), find the bearing of Q from P.
(b)
Calculate the number of sides of a regular polygon with interior angles of \(162^{\circ}\) each.
Answer (b)
Question 7
Express \(\frac{1}{x^{2}-1}-\frac{1}{1+x}\) as a single fraction in its simplest form.
Question 8
(a)
Write down the largest four-digit number in base 5.
Answer (a)
(b)
Convert \(111_{8}\) to a number in base 7.
Answer (b)
Question 9
Factorise completely \(x^{2}(y+1)-y-1\).
Answer
Question 10
Evaluate
(a)
\(\log _{4} 64\),
Answer (a)
(b)
\(\frac{\log 8}{\log 16}\).
Answer (b)
Question 11
Solve the simultaneous equations:
$$ \begin{gathered} 2 x+y=4 \\ 5 y-4 x=13 \end{gathered} $$
Question 12
For the expressions \(10(x+1)\) and \(8(x+1)^{2}\), find the
(a)
H.C.F,
Answer (a)
(b)
L.C.M.
Answer (b)
Question 13
A triangle has sides of lengths \(5 \mathrm{~cm}, 8 \mathrm{~cm}\) and 12 cm. Find the cosine of the smallest angle as a common fraction in its simplest form.
Answer
Question 14
(a)
Solve the equation \(5^{x}=125\).
(b)
Simplify \(\left(\frac{98}{32}\right)^{-\frac{1}{2}}\).
Answer (b)
Question 15
Given that \(-2 \leq x \leq 5\) and \(3 \leq y \leq 10\), calculate the
(a)
greatest possible value of \(y^{2}-x^{2}\),
(b)
least possible value of \(xy\).
Answer (b)
Question 16
(a)
Solve the simultaneous inequalities \(2 x-6 \leq 4 x<10-x\).
Leave the answer in the form \(a \leq x<b\), where \(a\) and \(b\) are integers.
(b)
Represent the solution to part (a) on a number line.
Answer (b)
Question 17
(a)
Given that \(v^{2}=u^{2}+2 a s\), make \(a\) the subject of the formula,
Answer (a)
(b)
Find \(a\) when \(s=5, u=2\) and \(v=2\).
Question 18
D varies jointly as S and T.
(a)
Find an equation connecting D, S, T and a constant \(k\).
Answer (a)
(b)
Find the value of \(k\) given that \(D=24\) when \(S=4\) and \(T=2\).
Answer (b)
(c)
Find the value of T given that \(D=50\) and \(S=10\) using the value of \(k\) in (b) above.
Question 19
The universal set \(\xi\) has subsets A and B such that \(n(\xi)=45, n(A)=25, n\left(A^{\prime} \cap B\right)=9\) and \(n(A \cap B)=n(A \cup B)^{\prime}\).
(a)
Show this information on a Venn diagram.
Answer (a) on the diagram
(b)
Find \(n(B)\).
Answer (b)
Question 20
Given that \(f(x)=\frac{3}{x+2}, x \neq-2\),
find
(a)
\(f(-1)\),
(b)
the value of \(x\) for which \(f(x)=-\frac{3}{4}\).
Question 21
The diagram above shows a speed - time graph of a moving object. The object decelerates uniformly at \(3 \mathrm{~m} / \mathrm{s}^{2}\) from a speed of \(V \mathrm{~m} / \mathrm{s}\) to a speed of \(15 \mathrm{~m} / \mathrm{s}\) in 5 seconds.
It maintains the speed of \(15 \mathrm{~m} / \mathrm{s}\) for a further 5 seconds. It then decelerates uniformly until it comes to rest after 3 seconds. Calculate
(a)
\(V\),
(b)
the deceleration in the last 3 seconds,
Answer (b)
(c)
the distance travelled in the last 8 seconds.
Answer (c)
Question 22
(a)
By selling an article for \(\$ 20,00\) a dealer made a profit of \(25\%\). Calculate the cost price of the article.
Answer (a)
(b)
Given that \(\frac{7 t-s}{2}=\frac{s-5 t}{3}\), find the ratio \(t: s\)
Question 23
A straight line, \(l\) passes through the origin and the point (1;2). Find the