1 What is the value of the digit 7, in base ten, for the number $2753_8$? flag bookmark A 7 B 56 C 448 D 3584 T4 Chapter 2.1b Determining the Number Value of a Number in Various Bases In $2753_8$ the digit 7 is in the $8^2$ place. Its value = $7 \times 8^2 = 7 \times 64 = 448$.
2 The length and width of a rectangle are $4.5 \times 10^5$ cm and $2.4 \times 10^4$ cm respectively. Find the perimeter, in cm, of the rectangle. Give your answer in standard form. flag bookmark A $1.08 \times 10^{10}$ B $4.32 \times 10^{10}$ C $4.98 \times 10^5$ D $9.48 \times 10^5$ Perimeter = $2(4.5 \times 10^5 + 2.4 \times 10^4) = 2(450\,000 + 24\,000) = 948\,000 = 9.48 \times 10^5$ cm.
3 Diagram 1 shows the distance-time graph of a runner. Given that the speed of the runner is 5 m s$^{-1}$, state the value of $x$. flag bookmark A 118 B 110 C 108 D 90 Speed = gradient: $\frac{x - 8}{20} = 5$, so $x - 8 = 100$ and $x = 108$.
4 Diagram 2 shows five straight lines drawn on a Cartesian plane. Which of the following is true? flag bookmark A The equation of QR is $x = -4$. B The equation of PR is $x = 4$. C The gradient of PS is equal to the gradient of QS. D The gradient of PR is zero. P = (0, 4) and R lies directly above Q(4, 0) at the same height as P, so PR is a horizontal line ($y = 4$) and its gradient is zero. QR is $x = 4$, not $x = -4$; PR is $y = 4$, not $x = 4$; PS and QS have different gradients.
5 A trader sells three types of products P, Q and R in the ratio $2 : y : 6$. When the data is represented in a pie chart, the sector angle for product R is 240°. State the value of $y$. flag bookmark A 4 B 3 C 2 D 1 $\frac{6}{2 + y + 6} = \frac{240°}{360°} = \frac{2}{3}$, so $8 + y = 9$ and $y = 1$.
6 Diagram 3 shows a polygon. Which of the following statements is NOT true about the exterior angles and interior angles of a polygon? flag bookmark A An interior angle is an angle formed by two adjacent sides inside a polygon. B An exterior angle is an angle formed when one side of a polygon is extended. C Angles $a$, $b$ and $c$ are interior angles. D Angles $x$, $y$ and $z$ are interior angles. x, y and z are formed outside the triangle where a side is extended, so they are exterior angles, not interior angles. Statements A, B and C are true.
7 Diagram 4 shows a combination of a right prism with a rectangular base and a right pyramid with a triangular base on a horizontal plane. AD and BC are vertical sides. Which of the following shows the elevation as viewed from X? flag bookmark A B C D From X we look at the side ABCD of the prism. It appears as a rectangle (12 cm by 8 cm), and the pyramid BCEG behind it to the right adds a triangle on the right with a slanted edge from C down to the base. This is elevation B.
8 Diagram 5 shows a circle with centre O. If the circle is drawn using a scale of $1 : \frac{1}{2}$, find the circumference of the new circle. (Use $\pi = \frac{22}{7}$) flag bookmark A 1414.29 cm B 188.57 cm C 94.29 cm D 47.14 cm T5 Chapter 5.2b Enlargement: Meaning, Scale Factor and Centre of Enlargement A scale of $1 : \frac{1}{2}$ means 1 cm on the drawing represents $\frac{1}{2}$ cm of the real circle, so the drawing is 2 times larger. New radius = 2 × 15 = 30 cm. Circumference = $2 \times \frac{22}{7} \times 30 = 188.57$ cm.
9 Diagram 6 shows two circles. QRS is the common tangent to both circles. Given KR = LR, ∠KLR = 65° and ∠PMR = 42°. Calculate the value of $x$. flag bookmark A 60° B 68° C 80° D 88° KR = LR, so ∠LKR = 65° and ∠KRL = 180° − 130° = 50°. ∠MRN = ∠KRL = 50° (vertically opposite angles). ∠MPN = ∠MRN = 50° (angles in the same segment, both standing on MN). In the triangle formed by PN, RM and PM: x = 180° − 50° − 42° = 88°.
10 Diagram 7 shows the transformation of a regular polygon. Which transformations represent X and Y, describing the change from Shape I to Shape II and then to Shape III? flag bookmark A X: Rotation 90° clockwise; Y: Rotation 180° B X: Reflection; Y: Rotation 90° clockwise C X: Rotation 180°; Y: Translation D X: Reflection; Y: Translation T5 Chapter 5.3c Describing a Combined Transformation Shape II is a mirror image of Shape I, so X is a reflection. Shape III is Shape II turned through 90° clockwise, so Y is a rotation of 90° clockwise.