ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
PAPER 1
4028/1
JUNE 2015 SESSION
2 hours 30 minutes
Candidates answer on the question paper.
Additional materials:
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.
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 and your Centre number and Candidate number on the top right corner of every page of this paper.
Answer all questions.
Check that all the pages are in the booklet and ask the invigilator for a replacement if there are duplicate or missing pages.
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 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 28 printed pages.
Copyright: Zimbabwe School Examinations Council, J2015.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER**
Question 1
Express 0,0978
(a)
correct to two decimal places,
(b)
correct to 2 significant figures,
(c)
in standard form.
Answer (a) ..... [1]
(b) ..... [1]
(c) ..... [1]
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 2
(a)
Evaluate \(39,6+0,09\).
(b)
Simplify \(\left(\frac{2}{3}-\frac{1}{2}\right) \times \frac{3}{4}\), giving the answer in its lowest terms.
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 3
A jet plane leaves Harare for Praia at 2323. The journey takes 5 hours 33 minutes and Praia's time is 2 hours behind Harare's time.
(a)
Express 2323 in 12-hour notation.
(b)
Find the time in Praia when the jet arrives.
Answer (a) ..... [1]
(b) ..... [2]
Question 4
(a)
Write down \(1 \times 2^{4}+1 \times 2^{3}+1 \times 2^{1}\) as a number in base 2.
(b)
Given that \(a=-3, b=3\) and \(c=-1\), evaluate \(\left(\frac{c-a}{b-a}\right)^{2}\), giving the answer as a common fraction in its lowest terms.
Answer (a) ..... [1]
(b) ..... [2]
Question 5
(a)
Find \(\sqrt[3]{0,027}\).
(b)
The size of each interior angle of a regular polygon is \(168^{\circ}\).
Find the number of sides of the polygon.
Answer (a) ..... [1]
(b) ..... [2]
Question 6
Given that \(\mathbf{a}=\binom{-1}{-2}\) and \(\mathbf{b}=\binom{-3}{-4}\),
(a)
express \(\mathbf{a}-\mathbf{b}\) as a column vector,
(b)
find \(|\mathbf{b}|\).
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 7
A is a set of perfect square numbers less than 50 and \(B\) is a set of even numbers not greater than 20.
Given that the elements of sets A and B are whole numbers,
(a)
list the elements of set A,
(b)
find \(n(A \cap B)\).
Question 8
Solve the equation \(\frac{3}{x}=x-2\).
\(x =\) ..... or \(x =\) .....
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 9
(a)
If B is East of A, state the three figure bearing of A from B.
(b)
Express \(33,55^{\circ}\) in degrees and minutes.
Question 10
In the diagram P, Q, R and T are points on the circumference of a circle. PTS and QRS are straight lines. PR is a diameter, \(\mathrm{QSP}=28^{\circ}\) and \(\mathrm{RPS}=50^{\circ}\).
Calculate
(a)
\(\mathrm{P}\hat{\mathrm{R}}\mathrm{T}\),
(b)
\(\mathrm{Q}\hat{\mathrm{T}}\mathrm{S}\),
(c)
\(\mathrm{Q}\hat{\mathrm{T}}\mathrm{R}\).
Answer (a) \(\mathrm{P}\hat{\mathrm{R}}\mathrm{T}=\) ..... [1]
(b) \(\mathrm{Q}\hat{\mathrm{T}}\mathrm{S}=\) ..... [1]
(c) \(\mathrm{Q}\hat{\mathrm{T}}\mathrm{R}=\) ..... [1]
Question 11
Solve the simultaneous equations:
\[ \begin{aligned} 3x - y &= 7 \\ y &= 5 - x \end{aligned} \]
Answer \(x =\) ..... \(y =\) .....
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 12
It is given that \(y\) varies directly as the square root of \(z\).
(a)
Write down the equation connecting \(y, z\) and a constant \(k\).
(b)
Find \(k\) when \(y=3\) and \(z=4\).
(c)
Find \(y\) when \(z=16\).
Answer (a) ..... [1]
(b) ..... [1]
(c) ..... [1]
Question 13
Triangle ACD is right angled at C.
\(AD=6\) cm, \(D\hat{B}C=45^{\circ}\) and \(D\hat{A}C=30^{\circ}\). ABC is a straight line.
Using the information below, calculate
(a)
CD,
(b)
AB, giving the answer correct to 1 decimal place.
\[ \begin{aligned} & \sin 30^{\circ}=0,50; \cos 30^{\circ}=0,87; \tan 30^{\circ}=0,58; \\ & \sin 45^{\circ}=0,71; \cos 45^{\circ}=0,71; \tan 45^{\circ}=1,00; \end{aligned} \]
Answer (a) ..... cm [2]
(b) ..... cm [2]
Question 14
Simplify
(a)
\((2a)^{-2} \times 3a^{2}\),
(b)
\(\log 8 + \log 4\).
Answer (a) ..... [2]
(b) ..... [2]
Question 15
Given that \(\mathbf{A}=\begin{pmatrix} x-1 & 2 \\ x+1 & -1 \end{pmatrix}\) and \(\mathbf{B}=\begin{pmatrix} 3 & 4 \end{pmatrix}\),
Find in terms of \(x\)
(a)
the determinant of \(\mathbf{A}\) in its simplest form,
(b)
\(\mathbf{BA}\) in its simplest form.
Question 16
(a)
On a day when the exchange rate was R9,03 to 1 USD, a trader exchanged 600 USD for rands.
Find the amount, in rands, the trader received.
(b)
Given that \(f=\frac{mv - mu}{t}\), express \(m\) in terms of \(f, v, u\) and \(t\).
Answer (a) R ..... [2]
(b) \(m =\) ..... [2]
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 17
An object starts from rest and accelerates at \(4\) m/s\(^2\) for 5 seconds until it reaches a speed of \(20\) m/s. It then travels at this speed for 30 seconds, after which it decelerates uniformly and comes to rest in a further 10 seconds.
(a)
Draw a velocity-time graph on the grid.
(b)
Calculate the total distance travelled.
(b) ..... m
| Centre Number | Candidate Number | | :--- | :--- | | | |
Question 18
18 white and 6 yellow identical tennis balls are placed in a box. Kuda picks balls at random one at a time.
Find the probability that the first and second balls picked are