1 Express $1153.6 \times 10^3$ in standard form. flag bookmark A $1.1536 \times 10^6$ B $1.1536 \times 10^3$ C $1.1536 \times 10^{-3}$ D $1.1536 \times 10^{-6}$ $1153.6 = 1.1536 \times 10^3$, so $1153.6 \times 10^3 = 1.1536 \times 10^3 \times 10^3 = 1.1536 \times 10^6$.
2 Zuhdi has 168 kg of sand. He used 60% of the sand to make a wall. The remaining sand is divided equally into 3 bags. Find the mass, in g, of the sand in each bag. flag bookmark A $2.24 \times 10^{-4}$ B $2.24 \times 10^4$ C $3.36 \times 10^{-4}$ D $3.36 \times 10^4$ Remaining sand = 40% × 168 kg = 67.2 kg. Each bag = 67.2 ÷ 3 = 22.4 kg = 22 400 g = $2.24 \times 10^4$ g.
3 Given $\frac{x+1}{5} = \frac{2x-1}{2}$, calculate the value of $x$. flag bookmark A $\frac{1}{4}$ B $\frac{3}{4}$ C $\frac{7}{9}$ D $\frac{7}{8}$ Cross-multiply: $2(x+1) = 5(2x-1)$, so $2x + 2 = 10x - 5$, $8x = 7$ and $x = \frac{7}{8}$.
4 The area of a square is 289 cm$^2$. Find the perimeter, in cm, of the square. flag bookmark A 17 B 34 C 60 D 68 Side = $\sqrt{289} = 17$ cm. Perimeter = 4 × 17 = 68 cm.
5 Simplify: $$\frac{3^2x^3y^5 \times (-8x^2y)}{24xy^4}$$ flag bookmark A $-3x^6y^{10}$ B $-3x^4y^2$ C $-\frac{3x^2}{y}$ D $-\frac{3}{x^2y}$ Numerator: $9x^3y^5 \times (-8x^2y) = -72x^5y^6$. Divide by $24xy^4$: $-\frac{72}{24}x^{5-1}y^{6-4} = -3x^4y^2$.
6 Given $t = \frac{2}{3} + \frac{m}{4}$, express $m$ in terms of $t$. flag bookmark A $m = \frac{3t - 2}{3}$ B $m = \frac{3t + 3}{3}$ C $m = \frac{4(3t - 2)}{3}$ D $m = \frac{4(2 + 3t)}{3}$ $\frac{m}{4} = t - \frac{2}{3} = \frac{3t - 2}{3}$, so $m = \frac{4(3t - 2)}{3}$.
7 Diagram 1 shows a hall and two classrooms. The length and the width of the hall are 56 m and 42 m respectively, while the width of a classroom is $\frac{2}{3}$ of the width of the hall. If the area of the hall is the same as the area of two classrooms, find the length, in m, of a classroom. flag bookmark A 56 m B 37 m C 42 m D 28 m Area of hall = 56 × 42 = 2 352 m². Width of a classroom = $\frac{2}{3}$ × 42 = 28 m. Two classrooms: 2 × 28 × L = 2 352, so L = 42 m.
8 Which of the following statements is true about a regular polygon? flag bookmark A A regular polygon has irregular sides. B The interior angles of a regular polygon are unequal. C The number of axes of symmetry of a regular polygon is equal to the number of sides of the polygon. D The sum of the exterior angles and interior angles of a regular polygon is 360°. A regular polygon has equal sides and equal angles, and a regular n-sided polygon has n axes of symmetry. At each vertex, the exterior angle plus the interior angle is 180°, not the whole sum being 360°.
9 In Diagram 2, XYZ is a tangent to the circle with centre O. Find ∠ABY. flag bookmark A 50° B 60° C 70° D 100° Angle at the centre is twice the angle at the circumference: ∠AYB = ½ × 100° = 50°. By the alternate segment theorem, ∠YAB = ∠BYZ = 70°. In triangle AYB: ∠ABY = 180° − 50° − 70° = 60°.
10 Diagram 3 shows two straight lines KL and MN. Find the value of $x$. flag bookmark A 15° B 20° C 25° D 30° ∠KOM and ∠NOL are vertically opposite, so ∠NOL = 85°. ∠NOL is made of the 60° angle and x: 60° + x = 85°, so x = 25°.