MATHEMATICS PAPER 2
**4028/2**
2 hours 30 minutes
Candidates answer on the question paper.
Additional materials: Geometrical instruments
Mathematical tables/ Electronic calculator
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 in Section A and any three from Section B.
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. 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 30 printed pages and 2 blank pages.
Copyright: Zimbabwe School Examinations Council, N2015.
| Centre Number | Candidate Number | | :--- | :--- |
2
**Section A [64 marks]**
Answer all the questions in this section.
Question 1
(a)
Find the value of \(\left(1 \frac{3}{4}+2 \frac{1}{3}\right) \div \frac{5}{6}\).
Answer (a)
(b)
#### (i)
Factorise completely \(y^{2}+10 y-24\).
Answer (b) (i)
#### (ii)
Factorise completely \(27-3 x^{2}\).
Answer (b) (ii)
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(c)
It is given that \(f(x)=10+3 x-x^{2}\).
#### (i)
Find \(f(2)\).
Answer (i)
#### (ii)
Find the values of \(x\) when \(f(x)=0\).
Answer (ii) \(x=\) \_\_\_\_ or \_\_\_\_
Question 2
(a)
The diagram shows a quadrilateral ABCD with \(\mathrm{BC}=8 \mathrm{~cm}, \mathrm{AC}=12 \mathrm{~cm}, \hat{C A D}=46,5^{\circ}\) and \(A \hat{B C}=A \hat{C} D=90^{\circ}\).
#### (i)
Calculate AB.
Answer (i) \(\mathrm{AB}=\) \_\_\_\_ cm
5
#### (ii)
Calculate CD.
Answer (ii) \(\mathrm{CD}=\) \_\_\_\_ [2]
#### (iii)
Calculate the area of quadrilateral \(A B C D\).
Answer (iii) \_\_\_\_ \(\mathrm{cm}^{2}\)
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(b)
Four interior angles of a nonagon have a sum of \(460^{\circ}\). The remaining interior angles are equal. Find the size of each of the equal angles.
Answer (b)
(c)
A shop sells a refrigerator at \(\$ 540\). In the previous year the same type of a refrigerator cost \(8 \%\) less.
Calculate the cost price of the same type of refrigerator in the previous year.
Question 3
(a)
It is given that \(\mathrm{M}=\left(\begin{array}{rr}8 & -4 \\ -5 & 3\end{array}\right)\) and \(\mathrm{N}=\binom{1}{3}\).
#### (i)
Find MN.
Answer (a) (i)
#### (ii)
Find the inverse of M.
Answer (a) (ii)
#### (iii)
Find \(\mathrm{M}^{2}\).
Answer (a) (iii)
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(b)
Express \(\frac{2 x-1}{4}-\frac{3 x-5}{12}\) as a single fraction in its simplest form.
Answer (b)
(c)
The area of a trapezium is \(63 \mathrm{~cm}^{2}\) and the sum of the lengths of its two parallel sides is \(22,5 \mathrm{~cm}\).
Calculate the perpendicular distance between the two parallel sides.
Answer (c) \_\_\_\_ cm
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Question 4
(a)
In a survey, a class of 40 music students were taught to play mbira, piano and guitar. At the end of their course they were asked to state at least one of the three instruments they found enjoyable to play.
The table shows the students' choices.
| type of instrument indicated as enjoyable | number of students | | :--- | :--- | | mbira | 18 | | piano | 14 | | guitar | 20 | | mbira only | 10 | | piano only | 8 | | mbira and guitar | 6 | | piano and mbira | 5 | | guitar and piano | 4 | | all the three | 3 |
The Venn diagram shows some of the number of students in each subset.
| Centre Number | Candidate Number | | :--- | :--- |
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#### (i)
Find the values of \(w, x, y\) and \(z\).
Answer (a) (i) \(w=\) \_\_\_\_
\[ \begin{aligned} & x= \\ & y= \\ & z= \end{aligned} \]
#### (ii)
If two students were selected at random from the class, find the probability that both enjoyed playing the guitar.
(b)
Solve the equation \(9^{m-1}=27\).
Answer (b) \_\_\_\_
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Question 5
(a)
Make \(x\) the subject of the formula \(y=\frac{p-2 x}{x}\).
Answer (a) \(x=\) \_\_\_\_
(b)
In the diagram, ABCD is a circle with centre \(\mathrm{O}\). \(\mathrm{CD}\) is a diameter of the circle, \(A O D=50^{\circ}\) and \(O A\) is parallel to \(C B\).
#### (i)
Find \(O \hat{C A}\).
Answer (b) (i) OCA = \_\_\_\_
13
#### (ii)
Find \(O \hat{A} P\).
Answer (ii) \(\mathrm{OA} \hat{\mathrm{A}} \mathrm{D}=\)
#### (iii)
Find \(A \hat{B} C\).
Answer (iii) \(\mathrm{A} \hat{\mathrm{B}} \mathrm{C}=\) \_\_\_\_
#### (iv)
Find \(C \hat{A} B\).
Answer (iv) \(\mathrm{C} \hat{\mathrm{A}} \mathrm{B}=\) \_\_\_\_
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Question 6
Answer the whole of this question on page 15.
Use ruler and compasses only for all constructions and show clearly all construction lines and arcs.
All constructions should be done on a single diagram.
(a)
Construct on a single diagram
#### (i)
parallelogram ABCD with \(\mathrm{AB}=8 \mathrm{~cm}, \mathrm{BC}=10 \mathrm{~cm}\), and \(\mathrm{A} \hat{\mathrm{B}} \mathrm{C}=120^{\circ}\), line AB has been drawn on page 15.
#### (ii)
the locus of points equidistant from B and C,
#### (iii)
the bisector of \(A \hat{B} C\).
(b)
Mark and label the point X that lies on the bisector of \(\mathrm{A} \hat{\mathrm{B}} \mathrm{C}\) and is equidistant from B and C.
(c)
Describe the locus that the bisector of angle ABC represents.
DO NOT WRITE ON THIS SPACE
15
Answer (a) (i) on diagram ..... [5]
(ii) on diagram ..... [2]
(iii) on diagram ..... [2]
(b) on diagram ..... [1]
(c)
\_\_\_\_
\_\_\_\_
\_\_\_\_
| Centre Number | Candidate Number | | :--- | :--- |
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**Section B [36 marks]**
Answer any three questions in this section
Each question carries 12 marks.
Question 7
The table shows values for the function \(y=\frac{1}{2} x(5-x)\).
| \(x\) | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | \(y\) | -3 | 0 | 2 | 3 | \(p\) | 2 | 0 | -3 |
(a)
Calculate the value of \(p\).
Answer (a) \(p=\) \_\_\_\_
Answer this part of the question on the grid on page 17.
(b)
Draw the graph of \(y=\frac{1}{2} x(5-x)\)