ZIMBABWE SCHOOL EXAMINATIONS
**NOVEMBER 2018 SESSION**
Additional materials: 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.
INSTRUCTIONS TO CANDIDATES
Write your Name, Centre number and candidate number in the spaces at the top of this page. Write your centre and candidate number in the box on the top right corner of every page of this paper. Check that all the pages are in the booklet and ask the invigilator for a replacement if there are duplicate or missing pages. Answer all questions in Section A and any four from Section B. 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 correct 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 and calculators may be used to evaluate explicit numerical expressions.
**SECTION A (52 Marks)**
Answer all questions in this section.
Question 1
Simplify
(a)
#### (i)
\(a x-x(a-b)+2 b x\),
Answer (a)(i)
#### (ii)
\((x-2)^{2}-x^{2}\).
(a)(ii)
(b)
Given that \(\boldsymbol{P}=\frac{1}{2}[a+d(a+d)]\),
evaluate \(\boldsymbol{P}\) when \(a=\frac{1}{2}\) and \(d=1\).
(b)
(c)
Express \(\frac{x-3}{x-2}-\frac{x+2}{x+3}\) as a single fraction in its lowest terms.
(c)
Question 2
(a)
The following is a price list from Bright Link Chemical Company.
> All prices include 15% Value Added Tax (VAT). > N.B. PROMOTION PROMOTION PROMOTION
> Place an order between 1 January and 28 February this year and get 10% discount
#### Calculate
#### (i)
the price of channel blocks per kilogram (kg),
Answer (a)(i)
#### (ii)
Value Added Tax on a twenty-litre bucket of floor polish.
(a)(ii)
Centre Number
Candidate Number
4
#### (iii)
A School ordered the following on the fourth of January of the same promotional year: Two 20 litre buckets of floor polish One 20 litre container of toilet dip Two 20 litre containers of dish washer One 20 litre container of sanitiser Three 5 kg boxes of channel blocks
Calculate the total discount the school got.
(b)
(b)
A man invested \(\$ 400\) in a bank that offers \(3 \%\) p.a compound interest.
Calculate the total amount he would get at the end of 3 years.
(c)
Question 3
(a)
#### (i)
Solve the inequality \(4 x-2 \leq 5 x+2<2 x+8\), giving your answer in the form \(a \leq x<b\), where \(a\) and \(b\) are integers.
Answer (a)(i)
#### (ii)
Illustrate the answer on a number line.
(a)(ii)
(b)
Make \(x\) the subject of the formula
\(R=\sqrt{\frac{a x-p}{Q+b x}}\)
(b)
(c)
Factorise completely \(2 m^{3} n^{2}+3 m^{2} n-2 m\).
(c)
| Candidate Name | | Candidate Number | | :--- | :--- | :--- | | | | |
6
Question 4
Answer the whole of this question below
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.
Candidate Name
\(\_\_\_\_\)
(d)
Mark and label \(X_{1}\) and \(X_{2}\), the points that are on the bisector of \(B \dot{C} A\) and are 4 cm from A .
7
Centre Number
Candidate Number
□ □
-
(d) on diagram
(e)
Describe the locus represented by the bisector of \(B \hat{C} A\).
" L " □
(e) Describe the locus represented by the bisector of \(B \hat{C} A\).
(d) on diagram " - \(\_\_\_\_\)
(f)
\(\_\_\_\_\)
\(\_\_\_\_\)
\(\_\_\_\_\)
Question 5
(a)
It is given that the universal set \(\xi=\{x: 1 \leq x \leq 10, x\) is an integer. \(\}\), has subsets A and
B such that
\(\mathbf{A}=\{\) perfect square numbers \(\}\) and
\(\mathbf{B}=\{\) multiples of 4\(\}\)
#### (i)
List all elements of set \(\mathbf{A}\),
Answer (a)(i) \(\_\_\_\_\)
#### (ii)
List all elements of set \(A \cap B\),
(a)(ii) \(\_\_\_\_\)
#### (iii)
Find \(n(A \cup B)\)
\(\_\_\_\_\)
(a)(iii)
(b)
It is given that \(P \subset Q\) and \(Q \subset R\)
#### (i)
Draw a Venn diagram to show the three sets \(P\), \(Q\) and \(R\)
(b)(i)
#### (ii)
Write in set notation the relationship between set \(\mathbf{P}\) and set \(\mathbf{R}\).
(b)(ii)
(c)
A bag contains 10 buttons that are identical except for colour. 7 of the buttons are red and 3 are blue. Two buttons are drawn at random, one after the other without replacement.
#### (i)
Complete the tree diagram.
(c)(i)
#### (ii)
Find the probability that both buttons are red.
(c)(ii)
#### (iii)
Find the probability that at least one of the buttons is red.
(c)(iii)
| Candidate Name | Centre Number | Candidate Number | | :--- | :--- | :--- | | | | |
9
**SECTION B (48 Marks)**
Answer any four questions from this section. Each question carries 12 marks.
Question 6
At a soccer match, a boy conducted a survey of the age of vehicles that were parked at the stadium. The information is displayed in the following table.
| Age \((x\) years \()\) | \(0<x \leq 5\) | \(5<x \leq 10\) | \(10<x \leq 15\) | \(15<x \leq 20\) | \(20<x \leq 25\) | | :---: | :---: | :---: | :---: | :---: | :---: | | Number of vehicles | 10 | 12 | 37 | 51 | 10 |
(a)
Calculate an estimate of the mean age of the vehicles.
Answer (a)
(b)
The same information of the survey is displayed in the following cumulative frequency table.
| Age \((x\) years \()\) | \(x<5\) | \(x<10\) | \(x<15\) | \(x<20\) | \(x<25\) | | :---: | :---: | :---: | :---: | :---: | :---: | | Cumulative frequency | 10 | 22 | \(n\) | 110 | 120 |
#### (i)
Find the value of \(n\).
(b)(i)
#### (ii)
Draw a cumulative frequency curve on the grid using a scale of 2 cm to 5 years on age axis and 2 cm to 20 on the cumulative frequency axis
|  | | :--- |
(c)
Use the graph to find the
#### (i)
median age.
#### (ii)
upper quartile.
(c)(ii) \(\_\_\_\_\)
Question 7
In the diagram, A, B and C are 3 points on level ground such that the bearing of B from A is \(075^{\circ}\) and that of C from A is \(140^{\circ}\), BC is 9 km from C and \(A \hat{B} C=80^{\circ}\).
(a)
#### (i)
Calculate \(B \hat{A} C\)
Answer (a)(i)
#### (ii)
Calculate the distance from A to C
(a)(ii)
#### (iii)
Calculate the shortest distance from B to AC
(a)(iii)
\[
\]
(b)
In the diagram P, Q, R and S are points on the circumference of a circle centre O. POR is the diameter of the circle, PT and ST are tangents to the circle, \(S \hat{Q} P=72^{\circ}\) and chords PQ and QS are equal.
Calculate
#### (i)
\(S \hat{P} Q\)
(b)(i)
#### (ii)
\(P \hat{Q} S\)
(b)(ii)
#### (iii)
\(P \hat{T} S\)