ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
PAPER 2
4004/2
NOVEMBER 2023 SESSION
2 hours 30 minutes
Additional materials:
Mathematical Instruments
Mathematical Tables
Non programmable Electronic Calculator
Plain Paper (1 sheet)
Graph Paper (4 sheets)
Answer Paper
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 four questions from Section B.
Write your answers on the separate answer paper provided.
If you use more than one sheet of paper, fasten the sheets together.
All working must be clearly shown 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 correct to three significant figures. Answers in degrees should be given correct to one decimal place.
Mathematical tables and Non-programmable electronic calculators may be used to evaluate explicit numerical expressions.
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 9 printed pages and 3 blank pages.
Copyright: Zimbabwe School Examinations Council, N2023.
**SECTION A [52 Marks]**
Answer all questions in this section
Question 1
(a)
#### (i)
The price of a packet of sweets was \(\$ 1,20\). The price increased to \(\$ 1,50\). Calculate the percentage increase.
#### (ii)
A new cereal packet contains \(20 \%\) more cereal than the old packet. If the new packet now has a mass of 264 g, calculate the mass of the cereal in the old packet.
#### (iii)
A painter got a \(7 \%\) discount after buying a large amount of paint. If the discount was \(\$ 91\), find the value of paint he bought.
(b)
\(A B\) is a diameter of a circle centre O and \(C\) is a point on the circumference such that \(A C=7,5 \mathrm{~cm}\) and \(B C=5 \mathrm{~cm}\). Calculate the length of \(A B\).
Question 2
(a)
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 arcs.
On a single diagram, construct
#### (i)
triangle ABC with \(\mathrm{AB}=6 \mathrm{~cm}, \mathrm{AC}=5,8 \mathrm{~cm}\) and \(\mathrm{B} \hat{\mathrm{A}} \mathrm{C}=135^{\circ}\).
#### (ii)
the perpendicular from C to BA produced.
#### (iii)
a line parallel to AB passing through C.
#### (iv)
the locus of points \(4,5 \mathrm{~cm}\) from B.
(b)
The line parallel to AB passing through C represents a certain locus. Describe this locus fully.
Question 3
The universal set \(\xi\) has subsets P and Q such that:
\(\xi=\{x: x\) is an integer and \(30 \leq x \leq 40\}\)
\(\mathrm{P}=\{x: x\) is a prime number \(\}\)
\(\mathrm{Q}=\{x: x\) is a multiple of 4\(\}\)
(a)
#### (i)
Find \(n(P)\).
#### (ii)
List the members of \(Q \cap P^{1}\), where \(\mathrm{P}^{1}\) is the complement of set P.
(b)
In triangle \(X Y Z, X Y=17 \mathrm{~cm}, X Z=8 \mathrm{~cm}\) and \(Y \hat{X} Z=65^{\circ} 30^{\prime}\). Calculate the area of triangle XYZ.
(c)
There are 25 red sweets and \(x\) blue sweets in a box. One sweet is selected at random. Given that the probability that it is blue is \(\frac{3}{8}\), find \(x\).
(d)
\(\mathrm{P}\) varies directly as q and inversely as the square of \(r\). Given that \(P=15, q=9\) and \(r=6\), find \(P\) when \(q=7\) and \(r=2\).
Question 4
(a)
Remove the brackets and simplify
#### (i)
\(4(3-2 p)-3(1-p)\),
#### (ii)
\((3 q-r)(q+2 r)\).
(b)
Factorise completely
#### (i)
\(8 a b+6 a b^{2}\)
#### (ii)
\(18 t^{2}-2\)
(c)
Given that \(y=18+3 x^{2}\)
#### (i)
Find the value of \(y\) when \(x=-2\),
#### (ii)
Find the values of \(x\) when \(y=93\),
#### (iii)
Express \(x\) in terms of \(y\).
Question 5
(a)
Express \(\frac{4}{y-3}-\frac{3}{y+4}\) as a single fraction in its simplest form.
(b)
Solve the equation.
\(\frac{y-1}{8}=\frac{2}{y-1}\)
(c)
Solve the inequality \(21<4 n-3 \leq 27\).
(d)
Points \(P, Q\) and \(R\) have coordinates at (9; 8), (12; 4) and (4; -2) respectively.
Find the
#### (i)
gradient of \(Q P\).
#### (ii)
equation of a line passing through \(R\) and parallel to \(P Q\).
**SECTION B [48 Marks]**
Answer any four questions from this section.
Each question carries 12 marks.
Question 6
The ages of 40 learners were recorded. The results are shown in the table below.
| Age (x years) | \(8 \leq x<10\) | \(10 \leq x<11\) | \(11 \leq x<12\) | \(12 \leq x<14\) | \(14 \leq x<16\) | \(16 \leq x<19\) | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | Frequency | 7 | 8 | 6 | 10 | 3 | 6 | | Frequency Density | 3,5 | 8 | 6 | 5 | 1,5 | 2 |
(a)
State the modal class.
(b)
Draw a histogram on a sheet of graph paper using a scale of 2 cm to 2 units on both axes.
(c)
Calculate an estimate of the mean age of the learners.
(d)
One learner is chosen at random from this group.
Calculate the probability that the learner is below the age of
#### (i)
8 years,
#### (ii)
16 years.
(e)
If two learners are chosen at random, find the probability that they are both in the age group \(14 \leq x<16\).
Question 7
(a)
The following table gives the values of \(y=6-x-x^{2}\)
| \(x\) | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | \(y\) | \(p\) | 0 | 4 | 6 | \(q\) | 4 | 0 | -6 |
Find the value of \(p\) and the value of \(q\).
Answer the whole of this part of the question on graph paper. Use a scale of 2 cm to 1 unit on the \(x\)-axis in the range \(-4 \leq x \leq 3\) and 2 cm to 2 units on the \(y\)-axis in the range \(-6 \leq y \leq 7\).
(b)
Draw the graph of \(y=6-x-x^{2}\).
(c)
Use the graph to find the,
#### (i)
maximum value of \(6-x-x^{2}\),
#### (ii)
equation of the line of symmetry,
#### (iii)
gradient of the graph when \(x=-2\),
#### (iv)
area bounded by the graph, the \(x\)-axis, the \(y\)-axis and the line \(x=-2\).
Question 8
(a)
The diagram shows a solid right cone with a base radius of 8 cm and a height of 15 cm.
In this question take \(\pi\) to be \(\frac{22}{7}\).
Calculate the
#### (i)
slant height of the cone.
#### (ii)
volume of the cone.
#### (iii)
curved surface area of the cone.
#### (iv)
total surface area of the cone.
(b)
A boy made several different objects from modelling clay. He used \(50 \mathrm{~cm}^{3}\) of clay for each object.
#### (i)
He made a square based cuboid of height 2 cm. Find the length of the side of the square base.
#### (ii)
He made a pyramid with a base area of \(15 \mathrm{~cm}^{2}\). Find the height of the pyramid.
#### (iii)
He made a sphere. Calculate the radius of the sphere.
[Volume of a sphere \(=\frac{4}{3} \pi r^{3}\)]
Question 9
Answer the whole of this question on a sheet of graph paper. Use a scale of 2 cm to 2 units on both axis in the ranges \(-8 \leq x \leq 10\) and \(-10 \leq y \leq 6\).
Triangle \(A\) has vertices at \((2 ; 2),(4 ; 2)\) and \((4 ; 5)\)
Triangle \(B\) has vertices at \((-4 ; 3),(-2 ; 3)\) and \((-2 ; 6)\)
(a)
Draw and label triangle A and triangle B.
(b)
Triangle A is mapped onto triangle C by an enlargement centre (0; 0) scale factor -2.
Draw and label triangle C.
(c)
Triangle D is the image of triangle A under a clockwise rotation of \(90^{\circ}\) about the point (2; -2).
Draw and label triangle D.