ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS** **4030/1** **PAPER 1** **JUNE 2017 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.
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.
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.
| Surname | Forename(s) | Centre Number | Candidate Number | | :--- | :--- | :--- | :--- | | Tsabola | leon | 558640 | 3201 |
| Centre Number | Candidate Number | | ---: | ---: | | | 3201 |
**2**
NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.
Question 1
Express 68,975 to
(a)
the nearest ten,
[1]
(b)
the nearest tenth,
[1]
(c)
one significant figure.
[1]
Answer: (a) (b) (c)
| Centre Number | Candidate Number | | :--- | :---: | | | 3201 |
**3**
Question 2
Find the exact value of
(a)
\(0,04 \times 0,3\),
[1]
(b)
\(1,44 \div 0,09\),
[1]
(c)
\(0,89-1,72\).
[1]
Answer: (a) ..... (b) ..... (c) .....
Question 3
Evaluate
(a)
\(2^{1,6} \times 2^{0,4}\),
[1]
(b)
\(\left(\frac{12}{27}\right)^{-\frac{3}{2}}\).
[2]
Answer: (a) (b)
| Centre Number | Candidate Number | | :--- | :---: | | | 3201 |
**4**
Question 4
Solve the equation
$$ x(x-3)-x+3=0 . $$
Answer: \(x=\) \_\_\_\_ or \_\_\_\_
Question 5
Express
(a)
6 minutes to 8 at night as a time in 24-hour notation,
[1]
(b)
43,35 hours in hours and minutes.
[2]
Answer: (a) (b) \_\_\_\_ hours \_\_\_\_ minutes
| Centre Number | Candidate Number | | ---: | ---: | | | 3201 |
**5**
Question 6
Evaluate
(a)
\(\log _{4} \frac{1}{4}\),
[1]
(b)
\(3 \log 5+3 \log 2-1\)
[2]
Answer: (a) ..... (b) .....
Question 7
(a)
Write down the next two terms of the pattern \(16 ; 8 ; 4 ; 2\); \_\_\_\_ : \_\_\_\_.
(b)
By selling an item for \(\$ 529\), a retailer makes a profit of \(15 \%\) on the cost price.
Calculate the cost price.
[2]
Answer: (a) \_\_\_\_ (b) \$ \_\_\_\_
| Centre Number | Candidate Number | | :--- | :---: | | | 3201 |
**6**
Question 8
(a)
Solve the inequality \(3 x+7<2 x+9\).
[2]
(b)
Illustrate the solution on a number line.
[1]
Answer: (a) (b)
Question 9
Express \(\frac{3 a}{2 a-b}+\frac{3 b}{2 b-4 a}\) as a single fraction in its simplest form.
Answer:
| Centre Number | Candidate Number | | :---: | :---: | | | 3201 |
**7**
Question 10
Solve the simultaneous equations:
$$ \begin{aligned} & x+\frac{1}{2} y=1 \\ & 3 x-4 y=14 \end{aligned} $$
Answer:
$$ \begin{aligned} & x= \\ & y= \end{aligned} $$
Question 11
(a)
Find \(12 \frac{1}{2} \%\) of \(64,8 \mathrm{~kg}\).
[1]
(b)
The determinant of a matrix \(\left(\begin{array}{cc}a-1 & 9 \\ 6 & 3\end{array}\right)\) is 9.
Find the value of \(a\).
Answer: (a) kg (b) \(a=\) \_\_\_\_
| Centre Number | Candidate Number | | ---: | ---: | | | 3201 |
**8**
Question 12
Factorise completely
(a)
\(9-36 x^{2}\),
[2]
(b)
\(a-b x+a x-b\).
[2]
Answer: (a) (b)
Question 13
(a)
State the order of rotational symmetry of a regular pentagon.
(b)
Three angles of a pentagon are \(110^{\circ}, 80^{\circ}\) and \(140^{\circ}\). The remaining two angles are such that one is twice the other.
Find the size of each of the remaining two angles.
Answer: (a) \_\_\_\_ (b) \_\_\_\_ and \_\_\_\_
| Centre Number | Candidate Number | | :---: | :---: | | | 3201 |
**9**
Question 14
It is given that \(p=3,6 \times 10^{4}\) and \(q=9 \times 10^{-4}\).
Find, giving the answer in standard form,
(a)
\(p q\),
(b)
\(\frac{p}{q}\).
Question 15
It is given that \(p=n w^{2}\left(r-\frac{w}{2}\right)\).
(a)
Make \(r\) the subject of the formula.
(b)
Find \(r\) in terms of \(\pi\) when \(w=6\) and \(p=72\).
Answer: (a) \(r=\) (b) \(r=\)
| Centre Number | Candidate Number | | ---: | ---: | | | 3201 |
**11**
Question 16
(a)
Evaluate \(\left(1 \frac{1}{5} \div 3 \frac{1}{5}\right) \times 2 \frac{2}{3}\).
(b)
Simplify \(2 \sqrt{75}+3 \sqrt{75}-\sqrt{48}\), giving the answer in the form \(a \sqrt{b}\), where \(a\) and \(b\) are integers.
| Centre Number | Candidate Number | | ---: | ---: | | | 3201 |
**12**
Question 17
A solid cone has base radius of 7 cm and a perpendicular height of 24 cm.
Find the
(a)
slant height,
(b)
volume of the cone.
(Volume of Cone \(=\frac{1}{3} \pi r^{2} h\))
Take \(\pi\) to be \(\frac{22}{7}\).
Answer: (a) \_\_\_\_ cm (b) \_\_\_\_ \(\mathrm{cm}^{3}\)
| Centre Number | Candidate Number | | :---: | :---: | | | 3201 |
**13**
Question 18
The diagram shows the speed-time graph of a car which travelled 705 metres in 60 seconds.
(a)
Calculate the acceleration during the first 10 seconds.
[1]
(b)
Find the time \(T\).