1 Calculate $$\frac{5+(-1)-(-8)}{7-10}$$ flag bookmark A $-4$ B $-1$ C $3$ D $8$ Numerator: \(5+(-1)-(-8)=12\); denominator: \(7-10=-3\). \(12 \div (-3)=-4\).
2 Ali filled up his motorcycle with $\frac{3}{4}$ litres of fuel in the morning. In the evening, he used $\frac{5}{6}$ litres of fuel to deliver goods. Later, he refilled the tank with another $\frac{1}{2}$ litres of fuel. Calculate the latest amount of fuel in the tank of Ali's motorcycle. flag bookmark A $\frac{13}{12}$ B $\frac{10}{12}$ C $\frac{7}{12}$ D $\frac{5}{12}$ He started with \(\frac{3}{4}\), used \(\frac{5}{6}\), then added \(\frac{1}{2}\): \(\frac{3}{4}-\frac{5}{6}+\frac{1}{2}=\frac{9-10+6}{12}=\frac{5}{12}\).
3 Diagram 1 shows a triangle RST. Given the ratio of $RT : ST : RS = 1 : 2 : \frac{1}{2}$. Calculate the perimeter, in cm, of triangle RST. flag bookmark A 104 B 112 C 224 D 256 RS is half a part, so one part is 64 cm. Thus RT is 64 cm and ST is 128 cm, giving perimeter 64 + 128 + 32 = 224 cm.
4 Determine the Lowest Common Multiple (LCM) of 8 and 12. flag bookmark A 12 B 24 C 36 D 48 The LCM is the smallest number divisible by both 8 and 12: 24 is divisible by both, while 12 is not divisible by 8.
5 There are 15 cylindrical steel rods, each 14 cm in diameter and 1 m long, which have been melted to form 70 steel balls of the same size. Calculate the volume, in cm³, of each steel ball. [Use $\pi = \frac{22}{7}$] flag bookmark A $1.32 \times 10^{4}$ B $3.3 \times 10^{3}$ C $1.32 \times 10^{2}$ D $3.3 \times 10^{1}$ Total volume of rods = \(15 \times \frac{22}{7} \times 7^2 \times 100 = 231000\) cm³. Divided by 70 balls gives \(3300\) cm³ each = \(3.3 \times 10^3\).
6 Encik Tajul's active income and passive income are RM4 500 and RM755 respectively. The estimated total expenditure is RM4 850. Calculate Encik Tajul's surplus income in base 6. flag bookmark A $1513_6$ B $1512_6$ C $1152_6$ D $1151_6$ T4 Chapter 2.1e Solving Problems Involving Number Bases T4 Chapter 10.1b Evaluating Financial Status and Creating a Financial Plan Total income = RM4 500 + RM755 = RM5 255. Surplus = RM5 255 − RM4 850 = RM405 = \(1513_6\).
7 Given $x_9 = 9^3 + (3 \times 9^2) + (2 \times 9^0)$. Find the value of $x$. flag bookmark A 123 B 132 C 1032 D 1302 T4 Chapter 2.1b Determining the Number Value of a Number in Various Bases Write the digits for each place: 9³ gives 1, 9² gives 3, no 9¹ term gives 0, and 9⁰ gives 2. So the base-9 numeral is 1302, i.e., x = 1302.
8 Which of the following is **not** a common factor for the terms $4k$ and $6kh$? flag bookmark A $1$ B $2$ C $2k$ D $4k$ 4k is not a common factor because 6kh ÷ 4k = 1.5h, which is not a whole number.
9 Diagram 2 shows 3 balls of the same size. The total surface area of the 3 balls is 1039.5 cm². Calculate the radius, in cm, of a ball. [Use $\pi = \frac{22}{7}$] flag bookmark A 5.25 B 9.09 C 27.56 D 82.69 Total surface area of one ball is 1039.5 ÷ 3 = 346.5. Substituting into 4πr² = 346.5 with π = 22/7 gives r² = 27.5625, so r = 5.25 cm.
10 Diagram 3 shows right-angled triangles PQR and SRT. PSR is a straight line. Given that $\cos x = \frac{3}{4}$ and the ratio of the length of SR to PQ is $1 : 2$. Calculate the length of PS. flag bookmark A 12 B 20 C 28 D 32 T5 Chapter 6.1d Solving Problems Involving Sine, Cosine and Tangent From cos x = 3/4 and RT = 9, SR = 12. Since SR:PQ = 1:2, PQ = 24, so PR = 32. Thus PS = PR - SR = 20.