1 Which of the following is a quadratic expression in one variable? flag bookmark A $r^2 + r^{-1} - 6$ B $\frac{1}{x^2} + x + 7$ C $3t^2 - 6t = 7$ D $2n^2 + 4n^2 - 3$ T4 Chapter 1.1a Quadratic Expressions in One Variable $2n^2 + 4n^2 - 3 = 6n^2 - 3$: one variable, highest power 2, and it is an expression. A and B have negative powers; C is an equation, not an expression.
2 Convert $110_7$ to a number in base two. flag bookmark A $101000_2$ B $111000_2$ C $100100_2$ D $111100_2$ T4 Chapter 2.1c Converting Numbers from One Base to Another $110_7 = 49 + 7 = 56 = 32 + 16 + 8 = 111000_2$.
3 Which of the following is a statement? flag bookmark A $m^2 = 16$ B $7^2 = 14$ C $2x^2 + 3x - 5$ D $\frac{a}{b} = 3$ T4 Chapter 3.1a Statements and Truth Value A statement can be judged true or false. $7^2 = 14$ is false (7² = 49), so it is a statement. A and D depend on unknown values; C is an expression.
4 Table 1 shows Irfan's marks for four subjects. | Subject | Marks | |---|---| | Mathematics | $37_8$ | | Science | $85_{10}$ | | History | $68_9$ | | English | $59_{10}$ | Calculate the average mark for the four subjects in base ten. flag bookmark A 54.25 B 59.25 C 238.00 D 249.00 T4 Chapter 2.1e Solving Problems Involving Number Bases $37_8 = 31$, $68_9 = 62$. $\frac{31 + 85 + 62 + 59}{4} = \frac{237}{4} = 59.25$.
5 Puan Mary deposited RM3 000 in her savings account with an interest rate of 4% per annum compounded quarterly. How much money is in her account at the end of the second year? flag bookmark A RM3 240.00 B RM3 244.88 C RM3 280.40 D RM3 248.57 T4 Chapter 10.1b Evaluating Financial Status and Creating a Financial Plan $3000\left(1 + \frac{0.04}{4}\right)^{4 \times 2} = 3000(1.01)^8 = 3248.57$.
6 Diagram 1 shows an incomplete argument. Premise 1: If $S = \{a, b, c\}$, then the number of subsets of S is 8. Premise 2: ______ Conclusion: ______ Which of the following completes a deductive argument that is valid and sound? flag bookmark A Premise 2: The number of subsets of S is 8. Conclusion: $S \neq \{a, b, c\}$ B Premise 2: The number of subsets of S is 8. Conclusion: $S = \{a, b, c\}$ C Premise 2: The number of subsets of S is not 8. Conclusion: $S \neq \{a, b, c\}$ D Premise 2: $S \neq \{a, b, c\}$ Conclusion: The number of subsets of S is not 8. T4 Chapter 3.2c Forming a Valid Deductive Argument Form III: "If p, then q; not q; so not p." Here not q is "the number of subsets of S is not 8", giving "$S \neq \{a, b, c\}$". A, B and D use invalid forms.
7 Diagram 2 shows the Venn diagram for the universal set $\xi$, set P, set Q and set R. Which of the following represents the shaded region? flag bookmark A $P \cup Q \cap R'$ B $P' \cap Q \cap R'$ C $P \cap Q \cap R'$ D $P' \cup Q \cap R'$ T4 Chapter 4.3a Combined Operations on Sets The shaded region is inside Q but outside both P and R: $P' \cap Q \cap R'$.
8 The variance of a set of data is 2.8. If each value is reduced by 2 and then divided by 3, determine the new variance. flag bookmark A 0.089 B 0.267 C 0.311 D 0.933 T4 Chapter 8.2e Effect of Data Changes on Measures of Dispersion Subtracting 2 does not change the variance; dividing by 3 divides the variance by $3^2$: $\frac{2.8}{3^2} = \frac{2.8}{9} = 0.311$.
9 Table 2 shows the games taken part in by 40 pupils. Each pupil took part in at least one game: chess, carrom or scrabble. | Game | Number of pupils | |---|---| | Chess | 18 | | Scrabble | 20 | | Carrom | 27 | | Chess and scrabble | 7 | | Scrabble and carrom | 12 | | Chess, carrom and scrabble | 4 | Calculate the number of pupils who took part in chess and carrom only. flag bookmark A 6 B 10 C 14 D 20 T4 Chapter 4.3c Solving Problems Involving Combined Operations on Sets Let x = number in chess and carrom (including all three). 40 = 18 + 20 + 27 − 7 − 12 − x + 4, so x = 10. Chess and carrom only = 10 − 4 = 6.
10 Which of the following graphs is a tree? flag bookmark A B C D T4 Chapter 5.1d Subgraphs and Trees A tree is connected and has no cycle (edges = vertices − 1). Graph A has 6 vertices, 5 edges and no cycle. B, C and D each contain a closed loop (cycle).