ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
**General Certificate of Education Ordinary Level** **MATHEMATICS** **PAPER 1** **4028/1R** **NOVEMBER 2014 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.
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 26 printed pages.**
Copyright: Zimbabwe School Examinations Council, N2014.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
Express 0,07649
(a)
in standard form,
(b)
correct to 2 significant figures,
(c)
correct to the nearest hundredth.
| Centre Number | Candidate Number | | :--- | :--- |
Question 2
(a)
Write down the next term in the sequence \(-2 ; 1 ; 6 ; 13 ; 22 ; \ldots\).
(b)
Given the expression \(\frac{(3,65+5,49) \times 9,84}{5,16 \times(12,1-8,52)}\), rewrite the expression, giving each number correct to the nearest whole number.
(c)
Estimate, using the answer to (b), the value of the given expression correct to the nearest whole number.
Question 3
In the diagram, TA and TB are tangents to the circle, centre O, at A and B respectively. C is a point on the major arc ACB and D is a point on the minor arc ADB such that TDO is a straight line and \(\mathrm{ATO}=36^\circ\).
(a)
Name the two congruent triangles.
(b)
Calculate
#### (i)
\(\hat{\mathrm{O}} \mathrm{D}\),
#### (ii)
\(A \hat{O} B\).
Question 4
Triangle ABC is mapped onto triangle EBD by a combination of two transformations.
(a)
Name the two transformations.
(b)
Write down the ratio AB : BE in its simplest form.
Question 5
(a)
Write down the smallest prime number.
(b)
Express 5292 as a product of its prime factors in index form.
| Centre Number | Candidate Number | | :--- | :--- |
Question 6
The population of town A is \(4,5 \times 10^{4}\) and that of town B is \(3,9 \times 10^{4}\).
(a)
Calculate the difference between the two populations.
(b)
The population of town A is \(125\%\) greater than what it was forty years ago.
Calculate the population of town A forty years ago. Give the answer in standard form.
Question 7
(a)
If \(32=2^{m}\), find the value of \(m\).
(b)
Simplify \(\left(\frac{1}{27}\right)^{\frac{2}{3}}\).
| Centre Number | Candidate Number | | :--- | :--- |
Question 8
In the diagram, the bearing of B from A is \(060^\circ\) and the bearing of C from B is \(100^\circ\).
(a)
Find the bearing of B from C.
(b)
If AB and BC are adjacent sides of a regular polygon, find the number of sides of the polygon.
Question 9
It is given that \(w\) is inversely proportional to \(f\) and when \(f=20, w=150\).
(a)
Find an equation connecting \(f\) and \(w\).
(b)
Find the value of \(f\) when \(w=60\).
Question 10
Express \(\frac{6 x+5}{7}-\frac{4 x-6}{21}\) as a single fraction in its simplest form.
Question 11
If \(\log (2 x+21)-\log 5 x=0\), find the value of \(x\).
| Centre Number | Candidate Number | | :--- | :--- |
Question 12
The dimensions of a rectangle, correct to the nearest centimetre, are 9 cm by 7 cm.
Calculate the minimum possible area of the rectangle.
\(cm^2\)
Question 13
(a)
Convert \(372_{8}\) to a number in base 10.
(b)
A quadrilateral has a rotational symmetry of order 1 and one line of symmetry.
State the name of the quadrilateral.
(c)
A lake has a surface area of \(36 km^2\). On a map, drawn to scale, the lake has an area of \(9 cm^2\).
Calculate the scale used in drawing the map giving the answer in the form 1 : \(n\).
Question 14
\(\overrightarrow{\mathrm{AB}}=\binom{14}{6}\) and \(\overrightarrow{\mathrm{AC}}=\binom{12}{8}\). M and N are the mid-points of AB and AC respectively.
(a)
Find
#### (i)
\(\overrightarrow{\mathrm{MN}}\),
#### (ii)
\(\overrightarrow{\mathrm{BC}}\).
(b)
Explain why MN is parallel to BC.
| Centre Number | Candidate Number | | :--- | :--- |
Question 15
The diagram shows the velocity-time graphs of two cars. Car A and car B start moving from the same point at the same time.
Find the
(a)
acceleration of car A,
(b)
time the two cars have equal velocities,
(c)
distance covered by car A in the 8 seconds,
(d)
average velocity of car A during the 8 seconds.
Question 16
The equation of a straight line is given as \(5 x+4 y-30=0\).
(a)
Make \(y\) the subject of the equation.
(b)
Write down the gradient of the straight line.
(c)
Write down the coordinates of the point where the line crosses the \(x\)-axis.
| Centre Number | Candidate Number | | :--- | :--- |
Question 17
(a)
Below is a list of some of the units used in measuring quantities.
hour; hectare; kilometre; kilogramme; degree.
Write down the unit of area from the given list.
(b)
Find the capacity, in litres, of a cylindrical tank of height \(3,5 m\) and diameter 4 m.
[Take \(\pi\) to be \(\frac{22}{7}\)].
Question 18
Given that \(f(x)=x^{2}-5 x-12\), find
(a)
\(f(-2)\),
(b)
the values of \(x\) for which \(f(x)=12\).
| Centre Number | Candidate Number | | :--- | :--- |
Question 19
Represent the following inequalities on the Cartesian plane in the answer space.
(a)
\(y>-6\)
(b)
\(x \geq 2\)
(c)
\(x+y \leq 0\)
Question 20
It is given that \(n(\xi)=14, n(P)=7, n(P \cap Q)=2\) and \(n(P \cup Q)=11\).
(a)
Show this information on the Venn diagram in the answer space.
(b)
Find
#### (i)