ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary Level
**MATHEMATICS** **PAPER 1**
4028/1
**NOVEMBER 2015 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.
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.
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.
This question paper consists of 28 printed pages.
Copyright: Zimbabwe School Examinations Council, N2015.
NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.
Question 1
(a)
Find the value of \(\frac{8}{0,04}\).
(b)
Simplify \(1 \frac{1}{2}-\frac{4}{7} \div \frac{2}{3}\) giving the answer as a fraction in its simplest form.
Question 2
Given that \(p=-4, q=3\) and \(r=-1\), evaluate
(a)
\(\frac{p+q}{r}\),
(b)
\(\sqrt{p^{2} q-r}\).
Question 3
In an athletics competition, under 20 boys compete in a 5000 m race, while under 16 boys compete in a 3000 m race.
(a)
Calculate the difference in the distances they run giving the answer in standard form.
(b)
A lap is 400 m long.
Find the number of laps in the 5000 m race.
Question 4
It is given that \(\overrightarrow{\mathrm{OP}}=\binom{-2}{7}\) and \(\overrightarrow{\mathrm{OQ}}=\binom{12}{-5}\) where O is the origin.
(a)
Express \(\overrightarrow{\mathrm{PQ}}\) as a column vector.
(b)
Find
#### (i)
\(|\overrightarrow{\mathrm{OQ}}|\),
#### (ii)
the co-ordinates of \(M\), the midpoint of \(P Q\).
Question 5
(a)
Express \(1 \times 3^{5}+2 \times 3^{3}+3\) as a number in base 3.
(b)
Convert \(101_{10}\) to a number in base 9.
(c)
Evaluate \(203_{7}-154_{7}\) giving the answer in base 7.
Question 6
Solve the simultaneous equations:
\[ \begin{array}{r} 2 x+3 y=28 \\ x+5 y=35 \end{array} \]
Answer \(x=\) \_\_\_\_
\(y=\) \_\_\_\_
Question 7
Solve the equation:
\[ \frac{2 y+5}{3 y-2}=\frac{9}{4} \]
Question 8
Make \(a\) the subject of the formula \(\frac{1}{a}+\frac{1}{b}=3\).
Question 9
When baking scones, a baker mixes six cups of flour, one cup of sugar, two cups of water and half a cup of milk, together with other ingredients.
(a)
Express the quantities of flour, sugar, water and milk as a ratio in its simplest form.
(b)
Calculate the number of cups of water needed if the baker uses four cups of flour.
Question 10
The probability that Sihle will bring a calculator is \(\frac{5}{6}\) while the probability that Yemurai will bring a calculator is \(\frac{3}{5}\).
Giving the answer as a fraction in its simplest form, find the probability that,
(a)
Sihle will not bring a calculator for the lesson,
(b)
only one of them will bring a calculator for the lesson.
Question 11
(a)
Write down the special name given to a polygon with five sides.
(b)
State, for a regular five sided polygon,
#### (i)
the number of lines of symmetry,
#### (ii)
the order of rotational symmetry.
Question 12
Solve the inequality \(2-x \leq 2 x-1<11\), giving your answer in the form \(a \leq x<b\), where \(a\) and \(b\) are integers.
Question 13
In the diagram, A, B and C are positions of 3 boreholes where BA = BC. The borehole at C has a bearing of \(116^\circ\) from the borehole at B.
Calculate
(a)
\(\mathrm{A} \hat{\mathrm{C}} \mathrm{B}\),
(b)
the bearing of the borehole at A from the borehole at C.
Question 14
(a)
If \(\log _{10} 7=0,8451\), evaluate
#### (i)
\(\log _{10} 0,07\),
#### (ii)
\(\log _{10} 49\).
(b)
Evaluate \(\log _{2}\left(\frac{1}{64}\right)\).
Question 15
| Earnings | \$ | Deductions | \$ | | :--- | :--- | :--- | :--- | | transport allowance | 100,00 | pension contribution | 6,00 | | housing allowance | 129,00 | union subscription | 10,00 | | | | medical aid | 8,00 | | | | Insurance | 17,50 | | basic salary | 275,00 | total deductions | - | | net salary | | | |
(a)
Calculate
#### (i)
the total deductions,
#### (ii)
the net salary.
(b)
Express the pension contribution as a percentage of her basic salary.
Question 16
(a)
Evaluate \(81^{\frac{3}{4}}\).
(b)
Find \(x\) if \(9^{x-1} \times 3^{3 x-2}=3\).
Question 17
Given that \(y\) is inversely proportional to \((x-1)^{2}\) and that \(y=2\) when \(x=7\),
(a)
express \(y\) in terms of \(x\),
(b)
calculate the values of \(x\) when \(y=8\).
Question 18
A luxury coach leaves Bulawayo for Harare every morning at 7.30 am and arrives in Harare at 1.00 pm.
(a)
Express the departure time as a time in the 24 hour notation.
(b)
Calculate the total time taken to travel from Bulawayo to Harare.
(c)
Calculate the average speed of the bus to the nearest whole number if the distance from Bulawayo to Harare is 439 km.
Question 19
Factorise completely
(a)
\(c g-d g-c h+d h\),
(b)
\(5 d^{2}-d-4\).
Question 20
The pie chart shows the distribution of an athlete's daily exercise programme.
(a)
Calculate the value of \(x\).
(b)
If the athlete spent 18 minutes jogging, calculate
#### (i)
the time the athlete spent on weight lifting,
#### (ii)
the total time spent exercising.
Question 21
In the diagram, PQR is an isosceles triangle such that \(\mathrm{PQ}=\mathrm{PR}=7 \mathrm{~cm}\) and \(\hat{\mathrm{PRQ}}=35^\circ\).
Using as much of the information given below as is necessary, calculate
(a)
QR,
(b)
the area of triangle PQR.
\[ \left[\begin{array}{lll} \sin 35^\circ=0,57 & \cos 35^\circ=0,82 & \tan 35^\circ=0,70 \\ \sin 70^\circ=0,94 & \cos 70^\circ=0,34 & \tan 70^\circ=2,75 \end{array}\right] \]
Question 22
It is given that, \(\xi=\{x: 31 \leq x<37\) and \(x\) is an integer \(\}\) has subsets P, Q and R such that \(\mathrm{P}=\{x: x\) is a multiple of 3\(\}\), \(\mathrm{Q}=\{x: x\) is a factor of 99\(\}\) and \(\mathrm{R}=\{x: x\) is a prime number \(\}\).
(a)
List all the elements of R.
(b)
Write down \(n(P \cup R)^{\prime}\).
(c)
List all elements of \((\mathrm{P} \cup \mathrm{Q} \cup \mathrm{R})^{\prime}\).
Question 23
A map is drawn to a scale of 1: 75000.
(a)
Calculate in km the actual distance between two towns which are 40 cm apart on the map.
(b)
An airport has an actual area of \(22,5 \mathrm{~km}^{2}\).
Calculate in \(\mathrm{cm}^{2}\) the area of the airport on the map.
