NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER.
Question 1
(a)
Simplify \(0-(-3)\)
Answer (a) \_\_\_\_
(b)
Express 8 as a recurring decimal.
Answer (b) \_\_\_\_
(c)
Find \(\sqrt{1 \frac{11}{25}}\).
Answer (c) \_\_\_\_
Question 2
(a)
Simplify \(2 \frac{2}{3} \div 2\).
Answer (a) \_\_\_\_
(b)
Find the value of \(9+6 \div 3\).
Answer (b) \_\_\_\_
(c)
Evaluate \(0,032 \div 0,4\).
Answer (c) \_\_\_\_
Question 3
Three learners A, B and C contributed \(\$ 20, \$ 30\) and \(\$ 50\) respectively. They bought a packet of sweets with 150 sweets worth \(\$ 100\).
(a)
Write down the ratio of the money they contributed in an ascending order in its simplest form.
Answer (a) \_\_\_\_
(b)
If the three learners shared the sweets in the ratio of the money they contributed.
Calculate the number of sweets C got.
Answer (b) \_\_\_\_
Question 4
Two hills A and B are 3 km apart. Hill A is 150 metres above sea level. The person on top of the hill A sees the peak of hill B at an angle of elevation of \(15^{\circ}\). Use as much information given below as is necessary: \([ \operatorname{Sin} 15 = 0.2588; \operatorname{Cos} 15^{\circ} = 0.9659; \operatorname{Tan} 15^{\circ} = 0.0875 ]\) Find the height of hill B above sea level.
Answer \_\_\_\_ [3]
Question 5
In the diagram points P, Q and R are on the circumference of a circle, centre O. \(P \hat{O} R = 300^{\circ}, Q \hat{P} O = Q \hat{R} O = x^{\circ}\),
(a)
\(P \hat{Q} R\)
Answer (a) \_\_\_\_
(b)
\(x\).
Answer (b) \_\_\_\_
Question 6
Solve the simultaneous equations:
$$ \begin{aligned} & x = 3 - 3y \\ & 2y = x - 8 \end{aligned} $$
Answer \_\_\_\_
| | Candidate Name | Candidate Number | | :--- | :--- | :--- | | | | |
Question 7
A rectangular wall measuring 6 m by 5 m has a window measuring 1.5 m by \(1.2 \mathrm{~m}\). The wall needs to be painted. Calculate the area of the wall to be painted.
Answer \_\_\_\_
Question 8
The Universal set \(\xi\) has subsets A and B, such that, \(\xi = \{x: 1 \leq x \leq 20, x \text{ is an integer}\}\), \(\mathrm{A} = \{x: x < 10\}\), \(\mathrm{B} = \{x: x \text{ is a perfect cube}\}\).
(a)
List all elements of,
#### (i)
B,
Answer (a)(i) \_\_\_\_
#### (ii)
\(\mathrm{A} \cap \mathrm{B}\),
Answer (a)(ii) \_\_\_\_
(b)
Hence or otherwise state the relationship between sets A and B.
Answer (b) \_\_\_\_
Question 9
(a)
Express \(732 \times 10^{-1}\) in standard form.
Answer (a) \_\_\_\_
| | Candidate Name | Candidate Number | | :--- | :--- | :--- | | | | |
(b)
Three towns A, B and C are situated along a straight road, such that town C is \(\left(4 \times 10^{2}\right) \mathrm{km}\) from town A and town B is \(\left(1.88 \times 10^{2}\right) \mathrm{km}\) from town A. Find the distance of town B from town C. Give the answer in standard form.
Answer (b) \_\_\_\_
Question 10
(a)
Round off,
#### (i)
\(\$ 9995.85\) correct to the nearest \(\$ 10\).
Answer (a)(i) \_\_\_\_
#### (ii)
\(3 \frac{1}{5} \mathrm{~cm}\) correct to the nearest centimetre.
Answer (a)(ii) \_\_\_\_
(b)
#### (i)
Express 432 as a product of its prime factors.
Answer (b)(i) \_\_\_\_
#### (ii)
Hence find the smallest number by which 432 must be multiplied to get a result which is a perfect square.
Answer (b)(ii) \_\_\_\_
Question 11
(a)
A greengrocer bought 80 oranges for \(\$ 640\) and sold them at \(\$ 15\) each. Find the percentage profit made.
Answer (a) \_\_\_\_
(b)
A woman invested \(\$ 4000\) in a bank at \(3\%\) simple interest. The money earned an interest of \(\$ 240\). Find the time her money was in the bank.
Answer (b) \_\_\_\_
Question 12
Learner P walks to school every day which is 5 km from the learner's home. In order for the learner to reach the school at 0715, the time at which the lessons commence, the learner leaves home at 0545.
(a)
Write 0545 as a time in 12-hour notation.
Answer (a) \_\_\_\_
(b)
On one of the days, learner P arrived at school at 0725.
#### (i)
Find the time by which learner P was late for the lessons.
Answer (b)(i) \_\_\_\_
#### (ii)
Calculate the average speed, in \(\mathrm{km/h}\), at which learner P was walking on the day that the learner was late.
Answer (b)(ii) \_\_\_\_
Question 13
In the diagram triangle PSR is such that QT is parallel to RS, \(\hat{Q R S} = 50^{\circ}, \hat{Q S R} = 30^{\circ}\) and \(\mathrm{PQ} = \mathrm{QS}\). Find
(a)
\(S \hat{Q} T\),
Answer (a) \_\_\_\_
(b)
\(T \hat{Q} P\),
Answer (b) \_\_\_\_
(c)
\(P \hat{T} Q\)
Answer (c) \_\_\_\_
Question 14
Two learners P and Q write a Mathematics test. The probability that P passes the test is \(\frac{3}{5}\). The probability that Q passes the test is \(\frac{2}{3}\).
(a)
Complete the tree diagram below by inserting the probabilities not given.
Answer (a) on the diagram \_\_\_\_
(b)
Find the probability that only one of the learners passes the test.
Answer (b) \_\_\_\_
Question 15
(a)
Factorise completely,
#### (i)
\(4x - 2y\),
Answer (a)(i) \_\_\_\_ [1]
#### (ii)
\(4x^{2} - y^{2}\).
Answer (a)(ii) \_\_\_\_ [2]
(b)
Hence or otherwise, find L.C.M of \(4x - 2y\) and \(4x^{2} - y^{2}\).
Answer (b) \_\_\_\_
Question 16
The table below contains distance covered, in km, per given litres of fuel.
| Number of litres \((l)\) | 0.5 | 10 | 30 | 50 | | :--- | :---: | :---: | :---: | :---: | | Distance (D) in km | 7.5 | 150 | 450 | 750 |
(a)
State the type of variation connecting the two quantities.
Answer (a) \_\_\_\_
(b)
Express D in terms of \(l\),
Answer (b) \_\_\_\_
(c)
Calculate amount of fuel in litres, that will be required for a distance of 480 km.
Answer (c) \_\_\_\_
Question 17
In the diagram above, school F is 8 km due north of school E. School G is 5 km from school E on a bearing of \(240^{\circ}\).
(a)
Find the compass bearing of school E from school G.
Answer (a) \_\_\_\_
(b)
Calculate the distance of school F from school G, leaving the answer in surd form.
Answer (b) \_\_\_\_
Question 18
(a)
Given that, \(\left(\begin{array}{ll}1 & 2 \\ 6 & 3\end{array}\right) - \left(\begin{array}{cc}4 & 7 \\ 3y & 10\end{array}\right) = \left(\begin{array}{cc}-3 & -5 \\ 9 & -7\end{array}\right)\) find the value of \(y\).
Answer (a) \_\_\_\_
(b)
Simplify \(\binom{2}{3}\left(\begin{array}{ll}1 & -3\end{array}\right)\)
Answer (b) \_\_\_\_
(c)
Given that \(\left(\begin{array}{cc}1 & -x \\ -2 & 9\end{array}\right)\) is the inverse of \(\left(\begin{array}{ll}9 & x \\ 2 & 1\end{array}\right)\), find the value of \(x\).
Answer (c) \_\_\_\_
| Candidate Name | Centre Number | Candidate Number | | :--- | :--- | :--- |
Question 19
(a)
Write down the value of 1 in the number \(610_{7}\).