1 State $2^7 + 2^6 + 2^3 + 2 + 1$ as a number in base two. flag bookmark A $11001011_2$ B $11011011_2$ C $11010101_2$ D $10011011_2$ T4 Chapter 2.1c Converting Numbers from One Base to Another Write a digit for every power of 2 from $2^7$ down to $2^0$: $2^7, 2^6$ → 1, 1; $2^5, 2^4$ → 0, 0; $2^3$ → 1; $2^2$ → 0; $2^1, 2^0$ → 1, 1. So the number is $11001011_2$.
2 Arrange the following numbers in ascending order. $2110_3,\ 310_4,\ 209_5,\ 101101_2$ flag bookmark A $209_5,\ 310_4,\ 2110_3,\ 101101_2$ B $209_5,\ 101101_2,\ 310_4,\ 2110_3$ C $101101_2,\ 2110_3,\ 310_4,\ 209_5$ D $101101_2,\ 310_4,\ 209_5,\ 2110_3$ T4 Chapter 2.1b Determining the Number Value of a Number in Various Bases Convert to base ten: $2110_3 = 54 + 9 + 3 = 66$, $310_4 = 48 + 4 = 52$, $209_5 = 50 + 9 = 59$, $101101_2 = 32 + 8 + 4 + 1 = 45$. Ascending: 45, 52, 59, 66, i.e. $101101_2, 310_4, 209_5, 2110_3$.
3 Express 0.00078 in standard form. flag bookmark A $7.8 \times 10^4$ B $7.8 \times 10^{-4}$ C $7.8 \times 10^5$ D $7.8 \times 10^{-5}$ Move the decimal point 4 places to the right to get 7.8, so $0.00078 = 7.8 \times 10^{-4}$.
4 Mokhtar has a plot of rectangular land measuring 239 m long and 329 m wide. Find the area, in m², of the land correct to three significant figures. flag bookmark A 786 B 787 C 78 600 D 78 700 Area = 239 × 329 = 78 631 m². Correct to three significant figures: 78 600 m².
5 Encik Hafiz, a fashion designer, found that the number of shirts sold, $N$, varies directly as the advertising budget, $D$, and inversely as the price of a shirt, $P$. When RM4 500 is allocated for advertising and the price of a shirt is RM100, 450 shirts are sold. Express $N$ in terms of $D$ and $P$. flag bookmark A $N = \frac{D}{P}$ B $N = \frac{10D}{P}$ C $N = \frac{100D}{P}$ D $N = \frac{1000D}{P}$ T5 Chapter 1.3a Combined Variation $N = \frac{kD}{P}$: $450 = \frac{4500k}{100} = 45k$, so $k = 10$ and $N = \frac{10D}{P}$.
6 It is given that $p$ varies inversely as $\sqrt{q}$. If $p = 3$ when $q = 16$, calculate the value of $q$ when $p = 10$. flag bookmark A 5.76 B 2.40 C 1.44 D 1.20 T5 Chapter 1.2b Worked Examples: Finding the Constant and Solving Inverse Variation Equations $p = \frac{k}{\sqrt{q}}$: $3 = \frac{k}{4}$, so $k = 12$. When $p = 10$: $\sqrt{q} = \frac{12}{10} = 1.2$, so $q = 1.44$.
7 Azhan plans to take part in Kayuhan Perdana organised by Taman Tasik. Diagram 7 shows his cycling route during a training session, starting from point P. State the route with the maximum distance, in km, that Azhan cycles if he passes through all the points. flag bookmark A P – Q – R – S – T B P – Q – T – R – S C P – S – R – T – Q D P – S – R – Q – T T4 Chapter 5.1f Solving Problems Involving Networks Add the distances along each route: A: 5 + 3 + 8 + 5 = 21 km B: 5 + 3 + 2 + 8 = 18 km C: 9 + 8 + 2 + 3 = 22 km D: 9 + 8 + 3 + 3 = 23 km The longest route is P – S – R – Q – T.
8 Which of the following is true about the statement below? "Graph H is a subgraph of graph G" I The edge set of graph H is not a subset of the edge set of graph G II The vertex set of graph H is a subset of the vertex set of graph G III The vertex pairs of the edges of graph H are the same as the edges of graph G IV The vertex pairs of the edges of graph H are not the same as the edges of graph G flag bookmark A I and II B I and IV C II and III D III and IV T4 Chapter 5.1d Subgraphs and Trees A subgraph uses only vertices of G (its vertex set is a subset of the vertex set of G, II) and only edges of G (each edge of H joins the same pair of vertices as an edge of G, III). So II and III.
9 Diagram 9 shows a speed-time graph for the movement of a particle for a period of 32 seconds. Calculate the distance, in m, travelled by the particle with uniform speed. flag bookmark A 120 B 400 C 520 D 640 T4 Chapter 7.2b Area Under a Speed-Time Graph Represents Distance Travelled The speed is uniform (20 m s$^{-1}$) from 12 s to 32 s, i.e. for 20 s. Distance = 20 × 20 = 400 m.
10 Which of the following coordinates is a solution of the system of linear inequalities $x < 5$ and $x + 3y < 9$? flag bookmark A (6, 0) B (4, 1) C (3, 2) D (−1, 4) T4 Chapter 6.1b Points in the Region That Satisfy a Linear Inequality Test each point: (6, 0): 6 < 5 ✗ (4, 1): 4 < 5 ✓, 4 + 3 = 7 < 9 ✓ (3, 2): 3 + 6 = 9, not < 9 ✗ (−1, 4): −1 + 12 = 11 ✗