1 Simplify. $$-12c^9 \div 3c^2 \div 2c^5$$ flag bookmark A $7c^{16}$ B $2c^2$ C $-7c^{16}$ D $-2c^2$ Dividing coefficients: \(-12 \div 3 \div 2 = -2\), and subtracting exponents: \(9-2-5=2\), so the result is \(-2c^2\).
2 Determine the coordinates of the midpoint of the pair of points $R(6, 10)$ and $S(-12, 8)$. flag bookmark A $(9, 1)$ B $(3, -9)$ C $(-9, 1)$ D $(-3, 9)$ Midpoint = $\left(\frac{6 + (-12)}{2}, \frac{10 + 8}{2}\right) = (-3, 9)$, so the correct option is D.
3 Diagram 1 shows a graph of a quadratic function. Determine the equation of the axis of symmetry of the graph of the quadratic function. flag bookmark A $x = 5$ B $x = 7$ C $x = 10$ D $x = 14$ T4 Chapter 1.1d Axis of Symmetry of a Quadratic Function The graph passes through (0, -10) and (14, -10), so the axis of symmetry is halfway between these x-coordinates, giving x = 7.
4 Diagram 2 shows four number cards arranged in ascending order. | 2674 | 5103 | Q | 8010 | |:---:|:---:|:---:|:---:| Which of the following represents Q? flag bookmark A $7.49 \times 10^{-4}$ B $7.49 \times 10^{-3}$ C $7.49 \times 10^{3}$ D $7.49 \times 10^{4}$ \(7.49 \times 10^{3} = 7490\), which lies between 5103 and 8010, so it fits the ascending order.
5 It is given that set $A = \{2, 3, 5, 7\}$ and set $B = \{1, 2, 4, 5, 8\}$. List all the elements of set $A \cap B$. flag bookmark A {2, 5} B {3, 8} C {2, 3, 5} D {1, 4, 7, 8} T4 Chapter 4.1a Intersection of Sets A ∩ B contains only elements that appear in both sets: 2 and 5.
6 Express $5^5 + 4$ as a number in base five. flag bookmark A $14_5$ B $41_5$ C $100004_5$ D $500004_5$ T4 Chapter 2.1c Converting Numbers from One Base to Another \(5^5\) is \(100000_5\), so adding 4 gives \(100004_5\).
7 Diagram 3 shows a triangle. Express $y$ in terms of $x$. flag bookmark A $y = \sqrt{6x - 3}$ B $y = \sqrt{6x + 3}$ C $y = \sqrt{2x^2 + 6x - 3}$ D $y = \sqrt{2x^2 + 6x - 5}$ T4 Chapter 1.1f Forming a Quadratic Function or Equation Based on a Situation By Pythagoras' theorem, \(y^2 + (x-2)^2 = (x+1)^2\). Simplifying gives \(y^2 = 6x - 3\), so \(y = \sqrt{6x - 3}\).
8 Factorise $6fg - 2fh - 3eg + eh$. flag bookmark A $(2f + e)(3g - h)$ B $(2f - e)(3g + h)$ C $(2f + e)(3g + h)$ D $(2f - e)(3g - h)$ Group the terms: \(6fg-2fh-3eg+eh = 2f(3g-h)-e(3g-h) = (2f-e)(3g-h)\). Hence D is correct.
9 Which of the following regions satisfies the linear inequality $y \geq 3x + 6$? flag bookmark A B C D T4 Chapter 6.2b Identifying the Region That Satisfies a System of Linear Inequalities Since y ≥ 3x + 6, the region above the line must be shaded. Graph D correctly shades the region above the line passing through (-2, 0) and (0, 6).
10 Diagram 4 shows a graph of a function. State the value of $x$ when $y = 25$. flag bookmark A 1 B 2 C 3 D 4 T4 Chapter 1.1i Solving Quadratic Equations by the Graphical Method From the graph, when y = 25, tracing across to the curve and down to the x-axis gives x = 2.