1 Round off the product of 0.1989 and 0.4 correct to two significant figures. flag bookmark A 0.07 B 0.079 C 0.08 D 0.080 0.1989 × 0.4 = 0.07956. The first two significant figures are 7 and 9; the next digit is 5, so round up: 0.080. The final zero must be written to show two significant figures.
2 Simplify: $\dfrac{(h^2k^2)^{\frac{1}{2}} \times h^{-4}k^3}{(3hk^2)^2}$ flag bookmark A $\dfrac{1}{9h^5}$ B $\dfrac{1}{9h^4}$ C $\dfrac{1}{6h^5}$ D $\dfrac{1}{6h^4}$ $(h^2k^2)^{\frac{1}{2}} = hk$, so the numerator is $hk \times h^{-4}k^3 = h^{-3}k^4$. The denominator is $9h^2k^4$. So the expression is $\dfrac{h^{-3}k^4}{9h^2k^4} = \dfrac{h^{-5}}{9} = \dfrac{1}{9h^5}$.
3 Diagram 1 shows a Venn diagram with the universal set $\xi = E \cup F \cup G$. Which of the following are the elements of $E \cup G'$? flag bookmark A $\{2, 3, 4\}$ B $\{2, 3, 4, 10\}$ C $\{1, 2, 3, 4, 6, 9, 10\}$ D $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ T4 Chapter 4.3a Combined Operations on Sets $\xi = \{1, 2, \ldots, 10\}$ and $G = \{1, 5, 6, 7, 8, 9\}$, so $G' = \{2, 3, 4, 10\}$. $E = \{1, 2, 3, 4, 6, 9\}$. $E \cup G' = \{1, 2, 3, 4, 6, 9, 10\}$.
4 Find the values of $x$ for the following equation: $(625)^{\frac{1}{4}x^2} \div \dfrac{1}{(\sqrt[3]{125})^{-5x}} = 15\,625$ flag bookmark A −1 and 6 B −2 and 3 C 1 and −6 D 2 and 3 $625^{\frac{1}{4}x^2} = (5^4)^{\frac{1}{4}x^2} = 5^{x^2}$. $\sqrt[3]{125} = 5$, so $\dfrac{1}{5^{-5x}} = 5^{5x}$. The left side is $5^{x^2 - 5x}$ and $15\,625 = 5^6$. So $x^2 - 5x - 6 = 0$, $(x - 6)(x + 1) = 0$, giving $x = -1$ or $6$.
5 Diagram 2 shows an irregular polygon. The name of the polygon is flag bookmark A hexagon B octagon C nonagon D decagon Count the corners (vertices) of the double-headed arrow: 2 arrow tips, 4 outer corners of the arrow heads and 4 corners where the heads meet the middle bar. That makes 10 sides, so it is a decagon.
6 A bag contains 25 blue and yellow marbles. The number of yellow marbles exceeds the number of blue marbles by 7. A marble is chosen at random from the bag. Calculate the probability that a blue marble is chosen. flag bookmark A $\frac{7}{25}$ B $\frac{9}{25}$ C $\frac{16}{25}$ D $\frac{18}{25}$ Let the number of blue marbles be $b$. Then $b + (b + 7) = 25$, so $b = 9$. P(blue) = $\frac{9}{25}$.
7 Diagram 3 shows the relation between set V and set W. What is the type of relation? flag bookmark A One-to-one B One-to-many C Many-to-one D Many-to-many T4 Chapter 1.1b Quadratic Function as a Many-to-One Relation 1 is mapped to 5 only, while 2 is mapped to both 6 and 7. One object has more than one image and no image comes from two objects, so the relation is one-to-many.
8 The digit value of 6 in the number $7632_9$ is $6 \times 9^m$. State the value of $m$. flag bookmark A 0 B 1 C 2 D 3 T4 Chapter 2.1b Determining the Number Value of a Number in Various Bases In $7632_9$ the place values from the right are $9^0, 9^1, 9^2, 9^3$. The digit 6 is third from the right, in the $9^2$ place, so $m = 2$.
9 If $p^3 - 4q = 6$ and $5px = -15$, find the value of $p^3 - (5px + 4q)$. flag bookmark A 21 B 9 C −9 D −21 $p^3 - (5px + 4q) = (p^3 - 4q) - 5px = 6 - (-15) = 21$.
10 Sarimah deposits RM9 200 in a bank with a simple interest rate of 4% per annum. Calculate Sarimah's total savings at the end of the third year. flag bookmark A RM1 104 B RM9 568 C RM10 304 D RM10 349 Simple interest $I = Prt = 9200 \times 0.04 \times 3 = $ RM1 104. Total savings = RM9 200 + RM1 104 = RM10 304.