1 Round off 0.05268 correct to three significant figures. flag bookmark A 0.0527 B 0.0526 C 0.053 D 0.052 The significant figures start at 5: keep 5, 2, 6. The next digit is 8, so round up: 0.0527.
2 The average number of cars manufactured by factory P, factory Q and factory R in the year 2020 is 25 000. Factory Q manufactured 19 000 cars. The production of factory R is three times that of factory P. Calculate the number of cars manufactured by factory R in the year 2020. Express the answer in standard form. flag bookmark A $4.02 \times 10^3$ B $4.20 \times 10^3$ C $4.02 \times 10^4$ D $4.20 \times 10^4$ Total = 3 × 25 000 = 75 000. P + R = 75 000 − 19 000 = 56 000 and R = 3P, so 4P = 56 000, P = 14 000 and R = 42 000 = $4.20 \times 10^4$.
3 Express $32_7$ as a number in base two. flag bookmark A $10111_2$ B $11100_2$ C $11110_2$ D $100110_2$ T4 Chapter 2.1c Converting Numbers from One Base to Another $32_7 = 3 \times 7 + 2 = 23 = 16 + 4 + 2 + 1 = 10111_2$.
4 A factory melts ten cuboid steel blocks with sides 5.2 m, 6.3 m and 4.8 m and makes three cube-shaped steel blocks. Calculate the length of the side of a cube-shaped steel block, correct to three significant figures. flag bookmark A 5.24 B 8.06 C 5.240 D 8.060 Volume of ten cuboids = 10 × 5.2 × 6.3 × 4.8 = 1 572.48 m³. Each cube = 1 572.48 ÷ 3 = 524.16 m³. Side = $\sqrt[3]{524.16} = 8.0623...$ = 8.06 m (three significant figures; 8.060 has four).
5 Given that $3122_4 + 13_4 = 3311_4 - P_6$. Find the value of P. flag bookmark A 20 B 32 C 60 D 110 T4 Chapter 2.1d Addition and Subtraction of Numbers in Various Bases $3122_4 = 218$, $13_4 = 7$ and $3311_4 = 245$ in base ten. So $P_6 = 245 - 225 = 20$, and $20 = 3 \times 6 + 2 = 32_6$. P = 32.
6 Table 1 shows the mass of sugar, in kg, sold by Kilang Gula Bestari for the months of June, July and August. | Month | June | July | August | |---|---|---|---| | Mass (kg) | $2.55 \times 10^4$ | 76 000 | x | Given that the mass of sugar in August is equal to the sum of the mass of sugar in July and 20% of the mass of sugar in June. Calculate the value of x. flag bookmark A $4.07 \times 10^4$ B $8.11 \times 10^4$ C $1.02 \times 10^5$ D $2.70 \times 10^5$ x = 76 000 + 0.2 × 25 500 = 76 000 + 5 100 = 81 100 = $8.11 \times 10^4$.
7 Given $rs + 5 = 6 + 8r$, express r in terms of s. flag bookmark A $r = \frac{1}{s - 8}$ B $r = \frac{1}{s + 8}$ C $r = \frac{-1}{s - 8}$ D $r = \frac{-1}{s + 8}$ $rs - 8r = 6 - 5 = 1$, so $r(s - 8) = 1$ and $r = \frac{1}{s - 8}$.
8 Factorise $\frac{1}{4}p^2 - 9$. flag bookmark A $\left(\frac{1}{2}p + 3\right)\left(\frac{1}{2}p - 3\right)$ B $(p - 3)\left(\frac{1}{4}p + 3\right)$ C $(4p + 3)\left(\frac{1}{4}p - 3\right)$ D $\left(\frac{1}{2}p + 3\right)^2$ $\frac{1}{4}p^2 - 9 = \left(\frac{1}{2}p\right)^2 - 3^2 = \left(\frac{1}{2}p + 3\right)\left(\frac{1}{2}p - 3\right)$.
9 A bank offers a 4% interest rate per annum for savings in a fixed deposit account. Mr Faiz saves RM15 000 at the beginning of the year and the interest is compounded every 4 months. Calculate the total savings at the end of the second year. flag bookmark A RM15 600.00 B RM16 200.00 C RM16 240.72 D RM16 892.43 Compounded every 4 months means 3 times a year, so n = 3 and t = 2: $MV = 15\,000\left(1 + \frac{0.04}{3}\right)^{6} = 16\,240.72$. Total savings = RM16 240.72.
10 The premium for travel insurance is influenced by the following factors except flag bookmark A number of insured persons B travel duration C destination D health history T5 Chapter 3.1a Risk, Insurance, Life Insurance and General Insurance Travel insurance premiums depend on the number of people insured, the length of the trip and the destination. Health history affects life or medical insurance premiums, not travel insurance.