2014_maths_olevel_nov_paper2

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z

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4028/2
PAPER 2
NOVEMBER 2014 SESSION 2 hours 30 minutes

Additional materials:
Answer paper
Geometrical instruments

Graph paper (2 sheets)
Mathematical tables
Plain paper (2 sheet

TIME 2 hours 30 minutes

INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the
answer paper/answer booklet.

Answer all questions in Section A and any three questions from Section B.

Write your answers on the separate answer paper provided.
Tf you use more than one sheet of paper, fasten the sheets together.

All working must be clearly shown. It should be done on the same sheet as the rest of the
answer.

Omission of essential working will result in loss of marks.

if the degree of accuracy is not specified in the question and if the answer is not exact, the
answer should be given to three significant figures. Answers in degrees should be given
to one decimal place.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ } at the end of each question or part
question. Mathematical tables or electronic calculators may be used to evaluate
explicit numerical expressions.

This question paper consists of 11 printed pages and | blank page.

Copyright: Zimbabwe School Examinations Council, N2014.
©ZIMSEC N2014 {Turn ay

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2 Section A [64 marks]

Answer all the questions in this section.

1 (a) Simplify 3,27 x.0,59 giving your answer correct to three significant
figures. [2]
(b) —_‘ Find the Lowest Common Multiple (L.C.M) of 72 and 96. [3]
(c) Express 101112 as a number in base 5. [3]
(d) A train that is scheduled to arrive in Bulawayo at 0027 is delayed by
3 hours 47minutes.
Find the time at which it arrives in Bulawayo. (2]
2 (a) Solve the equation
x 4 5x
(b) Factorise completely
(i) Tx? -28x,
(ii) 3y? -Sy +2.
[5]
x+2 4 . Ceca lca ray 22
(c) Express dn-3 x as a single fraction in its simplest form. [4]
x

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(a) A rectangle measures 8 cm by 6 cm to the nearest centimetre. Calculate
the least possible value of the area of the rectangle. B]

(b) It is given that
E=[x :8<xs16,x isan integer],
A= {x: x is a square number} and
B = {x: x is an even number}.

(i) List all the elements of A.
(ii) Find n(B).

(iii) | Show this information on a fully labelled Venn diagram.

[7]

(a) ,

s

iN 9 P

In the diagram, ALMN is right-angled at L and LP is an altitude.
PN = 9 cm and LM =6cm.

(ji) Name two triangles which are similar to ALMN.
(ii) = Find PM.
[5]

(b) The annual premium, $P, for a funeral insurance scheme varies jointly
as the square-root of the age, ¥, years and the number of dependants,
D, of the applicant.

Ifa 25 year old applicant with 6 dependants pays $150,00, calculate the
monthly premium for a 49 year-old applicant with 4 dependants. (5]

4028/2 N2014
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on

4

Mrs Shoko decides to erect a durawall around her rectangular stand measuring
20 m by 11m. Three metres are to be left for a gate.

(a)

(b)

(c)
(d)

Find the perimeter of the durawall.
She has two options, A or B, to consider for erecting the durawall.
Option A

She could engage a contractor who charges $12 per metre on a fix-and-
supply basis.

Calculate the total cost of erecting the durawall using option A.
Option B

She could buy the following materials as shown in the table below and
engage a builder who charges $100 for the job.

3)

[2]

item quantity cost per unit |
bricks 5.000 $80,00 for 1 000
cement 10 x 50 kg bag $10 per bag

_ brick force 5 bundles $5 per bundle

{pit sand [2 loads [$30 per load

Calculate the total cost of erecting the durawall using option B.

Mrs Shoko decides to use the cheaper option. Calculate the amount
she saves by using that option.

13]

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5 Answer the whole of this question on a sheet of plain paper.

Use ruler and compasses only for all constructions and show clearly all the
construction lines and ares.

A triangular field PQR has dimensions PQ = 30 m, POR = 60° and
RPQ = 45°.

(a) Using a scale of 1 cm to represent 3 m, construct the triangle PQR. [6]

(b) A well is to be dug in the field such that it is equidistant from PQ and PR
and 15 m from R.

Construct the locus of points which are
(0) equidistant from PQ and PR,

(ii) 15 m from R.

[3]
(c) Mark and label the point W, the position of the well. {1]
(d) Find the actual distance of the well from Q. [2]

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Section B_ [36 marks] Answer any three questions in this section.

Each question carries 12 marks.

A farmer has a square orchard of side 10 m. He decides to extend it by
increasing the length of one side by x metres and the other by 2x metres as
shown in the diagram below.

(a)

(b)
(c)

(@)

(e)

10 2x

10

x

Po

Write down an expression for the total area of the extended orchard and
show that it simplifies to 2x° + 30x +100.

Write down and simplity an expression for the area of the extension.

Given that the area has increased by 87,5 m’, form an equation in x and
show that it reduces to 2x° + 30x - 87,5 =0.

Solve the equation
2x? + 30x - 87,5 =0.

Write down the actual length of the extended orchard.

(2]

(2]

[4]

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Answer the whole of this question on a sheet of graph paper.

A triangle PQR has vertices at P(1; 1), Q(3; 4) and R(4; 0).

Using a scale of 2 cm to represent 2 units on both axes, draw the x and y axes
for -10<s x10 and -6s y<6.

(a)
(b)

Draw and label triangle PQR. 1

Triangle PQR is mapped onto triangle P}Q;R; by a transformation, N,
-1 0

where N is represented by the matrix i}

(i) Draw and label triangle P}QiRu.

(ii) Describe fully the single transformation represented by matrix N.

[6]
Triangle PQR is mapped onto triangle P2Q.R> by a translation T which
is represented by the vector _ and then followed by the transformation
N.
(0) Calculate the coordinates of the vertices of AP2Q2Ro.
(ii) Draw and label AP2Q)R>.
[5]

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Answer the whole of this question on a sheet of plain paper.

The table shows the number of books borrowed from a University library in

one week.

subject | Geography | Science Maths Shona Theory of

Education
number of 30 45 25 20 60
books

(a) Find the total number of books borrowed in that week.

(b) Express the number of Theory of Education books as a fraction of all
the books borrowed in its lowest terms.

(c) Show this information on a clearly labelled pie-chart.

(d) Two students borrowed books from the library during that week.

Calculate the probability that the first student borrowed a Science book
and the second a Maths book.

[2]

[2]

[2]

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10

9

Answer the whole of this question on a sheet of graph paper.

The velocity, v m/s, of a moving body, at time ¢ seconds, is given by the formula

v=P-3t+5.

Below is an incomplete table of values for v.

i(sec) lo |i (2 {3 4 [5 6
a ee Cea

[7
n 4 [15 23 [33

(a) Find the value of m and the value of n.

(b) Using a scale of 2 cm to represent | second on the horizontal axis and
2 cm to represent 5 m/s on the vertical axis, draw the ¢ and v axes for
Osts7.

Draw the graph of v=? - 3f+5.

(c) Use your graph to estimate

(i) the values of ¢t when v = 4,

(ii) the acceleration when t = 3,

(iii) — the distance travelled from t= 4 to t= 6.

[2]

[6]

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(a)

(b)

10

A regular polygon has an interior angle that is twice the exterior angle.

Find
(i) the number of sides of the polygon,

dai the sum of the interior angles of the polygon.

(\

A B 6 Cc
In the diagram, the points A, B, C and D lie on level ground. ABC is
a straight road which runs in a west-east direction. AD = BD = 9 km,
ABD = 40° and BC = 6 km.
Calculate
(6) the bearing of A from D,

(ii) the distance CD,

(iii) the area of ABCD.

[8]

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sa}

12

Cc xX
In the diagram, ABC is a triangle in which AB = q and AC =p. Mis the mid-
point of AB and X is a point on BC such that BX : XC = 4:1. CM and AX
intersect at Y.

(a) Express, in terms of p and/or q

(i) BC,
(ii) CX,
(iii) CM,
(iv) AX.

(b) Given that CY = kCM, express CY in terms of Pp, q and k.
(c) Given also that AY = HAX, express CY in terms of p, q and A.
(d) Using the results of (b) and (c), find the value of 4 and the value of k.

Hence express AY in terms of pand q.

[5]
(Y
[2]

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