ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS**
**PAPER 1**
NOVEMBER 2011 SESSION
2 hours 30 minutes
Candidates answer on the question paper.
Additional materials:
Geometrical instruments
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.
Answer all questions.
Write your answers in the spaces provided on the question paper.
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.
FOR EXAMINER'S USE
□
This question paper consists of 21 printed pages and 3 blank pages.
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.**
Question 1
Giving your answer as a common fraction in its lowest terms, find the value of
(a)
\(\frac{3}{5}-\frac{5}{9}\),
(b)
\(\quad \frac{2}{3 \frac{2}{5}}\).
Answer:
(a)
(b)
[1]
[2]
Question 2
Given \(\mathrm{P}=\frac{0.00274 \times 3460}{(9.88+23.8)^{2}}\)
(a)
Rewrite this expression with each number correct to one significant figure.
(b)
Estimate the value of P correct to one significant figure.
| Answer: | (a) \(\frac{x}{(+-)^{2}}\) | [2] | | :--- | :--- | :--- | | | (b) | [1] |
Question 3
(a)
Simplify \(\left(27 x^{6}\right)^{\frac{1}{3}}\).
(b)
If \(32^{-\frac{2}{5}}=2^{p}\), find p.
| Answer: (a) | [1] | | :--- | :--- | :--- | | | (b) \(p=\) | [2] |
Question 4
Evaluate \(3.25 \times 10^{4} \times 10^{-6}\) giving the answer
(a)
in standard form,
(b)
as a decimal fraction,
(c)
as a common fraction in its lowest terms.
Answer:
(a)
[1]
(b)
[1]
(c)
[1]
Question 5
(a)
State the number of lines of symmetry of an equilateral triangle.
(b)
Factorise completely \(3 x^{3}-12 x\).
Answer:
(a)
[1]
(b)
[2]
Question 6
Solve the simultaneous equations
$$ \begin{aligned} & x-6 y=-4 \\ & 9 x+3 y=-17 \end{aligned} $$
Answer: \(\quad x=\) \_\_\_\_
$$ y= $$
Question 7
A and B are sets. Write the following sets in their simplest form.
(a)
\(\mathrm{A} \cap \mathrm{A}^{I}\)
(b)
\(\mathrm{A} \cup \mathrm{A}^{I}\)
(c)
\((\mathrm{A} \cap \mathrm{B}) \cup\left(\mathrm{A} \cap \mathrm{B}^{l}\right)\)
Answer:
| (a) | [1] | | :--- | ---: | | (b) | | | (c) | [1] | | | [1] |
Question 8
It is given that \(y\) varies inversely as the square of \((x-1)\). When \(y=2\), \(x=2\).
Find the value of \(y\) when \(x=4\).
Answer: \(\quad y=\) \_\_\_\_
Question 9
(a)
If A is a non-singular matrix, simplify \(\mathbf{A A}^{-1}\)
(b)
If \(\mathbf{B}=\left(\begin{array}{ll}1 & 3 \\ 5 & 2\end{array}\right)\binom{2}{6}\), write down the order of matrix \(\mathbf{B}\).
Answer:
(a)
[1]
(b) \_\_\_\_ [2]
Question 10
In the diagram AC is 10 units and BA is parallel to \(\mathrm{CD}\). \(\mathrm{BA}\) is the line \(y=3 x+4\).
(a)
Write down
#### (i)
the value of \(y\) at C,
#### (ii)
the equation of the line CD which is parallel to \(y=3 x+4\).
(b)
Find the coordinates of the point D where the line in part (a)(ii) crosses the \(x\)-axis.
Answer:
(a)
(i)
- [1]
(ii) \_\_\_\_
(b) \_\_\_\_ ; \_\_\_\_ )
Question 11
(a)
Evaluate \(765_{8}-567_{8}\), giving your answer in base eight.
(b)
Express \(5^{3}+4\) as a number in base five.
(c)
Convert \(13_{10}\) to a number in base two.
Answer: (a) ..... [1]
(b) ..... [1]
(c) ..... [1]
Question 12
A rectangle is \(9.1 \mathrm{~cm}\) long and \(5.7 \mathrm{~cm}\) wide correct to one decimal place.
(a)
State the least possible width of the rectangle.
(b)
Find the limits within which the perimeter of the rectangle lies.
Answer:
(a) \_\_\_\_
(b) \_\_\_\_ \(\mathrm{cm} \leq\) perimeter < \_\_\_\_ cm
[2]
Question 13
In the diagram ABC and \(\mathrm{A}^{1} \mathrm{~B}^{1} \mathrm{C}^{1}\) are congruent triangles and \(\mathrm{BCC}^{1} \mathrm{~B}^{1}\) is a straight line.
Describe fully a single transformation that maps triangle ABC onto triangle \(A^{1} B^{1} C^{1}\).
Answer: \_\_\_\_
\_\_\_\_
Question 14
Solve the equations
(a)
\(\frac{2 y}{3}-9=0\),
(b)
\(\quad x^{2}-5 x-6=0\).
Answer:
(a) \(y=\) \_\_\_\_
(b) \(x=\) \_\_\_\_ or \_\_\_\_
Question 15
A car manufacturer makes a scale model of one of his real cars.
(a)
The capacity of the fuel tank of the real car is 64 litres and that of the model car is 0.512 litres.
Find the ratio of the length of the real car: the length of model car.
(b)
The area of the front window of the model is \(0.0484 \mathrm{~m}^{2}\). Find the area of the front window of the real car.
Answer:
(a) \_\_\_\_
(b) \_\_\_\_
Question 16
(a)
Given that \(y=m^{2}-4 n^{2}\), find the value of \(y\) when \(m=4\) and \(n=2\).
(b)
If \(\frac{x}{a}+\frac{y}{b}=1\), make \(x\) the subject.
Answer:
(a) \_\_\_\_
(b) \(x=\) \_\_\_\_
[1]
Question 17
Evaluate
(a)
\(\quad \log _{3} 9\),
(b)
\(\quad \log _{5}\left(\frac{1}{25}\right)\),
(c)
\(\quad \log _{29} 1\).
Answer: