1 Factorise completely the expression $5x^2 - 5$. flag bookmark A $5(x^2 + 1)$ B $5(x^2 - 1)$ C $5(x + 1)(x - 1)$ D $5(x - 1)(x - 1)$ Take out the common factor 5: $5(x^2 - 1)$. Then $x^2 - 1$ is a difference of two squares: $5(x + 1)(x - 1)$.
2 Given that $\frac{3a + 4}{5} = a + 2b$, express $a$ in terms of $b$. flag bookmark A $a = \frac{4 - b}{2}$ B $a = \frac{2b - 9}{2}$ C $a = -2 + 5b$ D $a = 2 - 5b$ $3a + 4 = 5(a + 2b) = 5a + 10b$, so $4 - 10b = 2a$ and $a = 2 - 5b$.
3 Which of the following is **not true**? flag bookmark A $3x^0 y^0 = 3$ B $\left(\frac{a}{b}\right)^{-3} = \left(\frac{b}{a}\right)^3$ C $5m^{-2} = \frac{1}{5m^2}$ D $(3x^3)^2 = 9x^6$ $5m^{-2} = \frac{5}{m^2}$, not $\frac{1}{5m^2}$ (only $m$ has the negative index). The others are true: $3x^0y^0 = 3 \times 1 \times 1 = 3$, $\left(\frac{a}{b}\right)^{-3} = \left(\frac{b}{a}\right)^3$, $(3x^3)^2 = 9x^6$.
4 If $p \times p \times p \times p \times p \times p = (-2)^{\frac{q}{2}}$, state the value of $p$ and of $q$. flag bookmark A $p = 2,\ q = 12$ B $p = 2,\ q = 5$ C $p = -2,\ q = 3$ D $p = -2,\ q = 12$ $p^6 = (-2)^{\frac{q}{2}}$. With $p = -2$: $(-2)^6 = (-2)^{\frac{q}{2}}$, so $\frac{q}{2} = 6$ and $q = 12$. Note that $p = 2$, $q = 12$ also works, because $2^6 = 64 = (-2)^6$, so both A and D are accepted.
5 Round off 396.4 correct to two significant figures. flag bookmark A 40 B 400 C 400.0 D 400.4 The first two significant figures of 396.4 are 3 and 9; the next digit is 6, so round up: 39 becomes 40, giving 400.
6 Diagram 1 shows a durian orchard, $PQRS$, in the shape of a trapezium. Given that the area of the orchard is 690 m$^2$, calculate the perimeter, in m, of the orchard. flag bookmark A $1.18 \times 10^2$ B $1.18 \times 10^3$ C $1.27 \times 10^2$ D $1.27 \times 10^3$ Convert to metres: $PQ = 2.4 \times 10^{-2}$ km = 24 m, $SR = 4.5 \times 10^{-2}$ km = 45 m, $QR = 2.9 \times 10^3$ cm = 29 m. Area: $\frac{1}{2}(24 + 45)h = 690$, so $h = 20$ m. Perimeter $= 24 + 29 + 45 + 20 = 118 = 1.18 \times 10^2$ m.
7 Which of the following is **not** an investment? flag bookmark A Shares B Unit trust C Inheritance D Real estate Shares, unit trusts and real estate are bought with money in the hope of returns. An inheritance is property passed on after someone dies — it is not an investment you make.
8 Zainal takes a personal loan of RM30 000 from Bank Cemerlang with an interest rate of 4.5% per annum on the balance. The repayment period is 9 years and the monthly instalment is RM245. What is the total amount of interest, in RM, payable by Zainal for the first two months? flag bookmark A 112.00 B 112.50 C 224.50 D 225.00 Monthly rate $= 4.5\% \div 12 = 0.375\%$. Month 1 interest $= 30\,000 \times 0.00375 =$ RM112.50; balance $= 30\,000 - (245 - 112.50) = 29\,867.50$. Month 2 interest $= 29\,867.50 \times 0.00375 \approx$ RM112.00. Total $= 112.50 + 112.00 =$ RM224.50.
9 The following is a sequence in base 7. $3165_7,\ 3166_7,\ p_7,\ \dots$ Determine the value of $p_7$. flag bookmark A 3210 B 3200 C 3170 D 3167 T4 Chapter 2.1d Addition and Subtraction of Numbers in Various Bases Each term goes up by 1. In base 7, $6 + 1 = 10_7$, so $3166_7 + 1$: the last digit becomes 0 and carries 1; the next 6 also becomes 0 and carries 1; $1 + 1 = 2$. So $p = 3200_7$.
10 Firdaus is a data analyst with a monthly income of RM7 000 and plans to get married in three years. The wedding expenses are estimated at RM50 000. Therefore, he wants to save RM1 500 a month for three years. Based on the situation above, which one fulfils the realistic component of the SMART concept for achieving his financial goal? flag bookmark A The wedding expenses are RM50 000. B The saving period is three years. C Save RM1 500 monthly. D Monthly saving of RM1 500 out of a total income of RM7 000. T4 Chapter 10.1a The Financial Management Process and Setting SMART Financial Goals "Realistic" means the goal fits his means. Saving RM1 500 out of an income of RM7 000 shows the saving is affordable, so D is the realistic component (A is specific, B is time-bound, C is measurable).