1 Express 395 000 in standard form. flag bookmark A $3.95 \times 10^4$ B $3.95 \times 10^5$ C $39.5 \times 10^4$ D $39.5 \times 10^5$ Move the decimal point 5 places to the left: $395\,000 = 3.95 \times 10^5$. In standard form the first number must be between 1 and 10, so 39.5 is not allowed.
2 $0.000034 - 2.2 \times 10^{-6} =$ flag bookmark A $3.18 \times 10^{-6}$ B $3.18 \times 10^{-5}$ C $3.18 \times 10^5$ D $3.18 \times 10^6$ $0.000034 = 34 \times 10^{-6}$. So $34 \times 10^{-6} - 2.2 \times 10^{-6} = 31.8 \times 10^{-6} = 3.18 \times 10^{-5}$.
3 The total population of a country Y in the year 2011 is 49.50 million. It is given that the number of people who are 60 years old and above is 9.9% of the total population. Calculate the number of people who are below 60 years old. [1 million = $10^6$] flag bookmark A $4.46 \times 10^6$ B $4.46 \times 10^7$ C $4.9 \times 10^6$ D $4.9 \times 10^7$ People below 60 = 100% − 9.9% = 90.1% of the population. $0.901 \times 49.50 \times 10^6 = 44.6 \times 10^6 = 4.46 \times 10^7$.
4 Convert $3 \times 8^4 + 2 \times 8^2 + 5$ to a number in base eight. flag bookmark A $3025_8$ B $3250_8$ C $30205_8$ D $30250_8$ T4 Chapter 2.1c Converting Numbers from One Base to Another Write a digit for every place value: $3 \times 8^4 + 0 \times 8^3 + 2 \times 8^2 + 0 \times 8^1 + 5 \times 8^0 = 30205_8$.
5 $10011_2 + 111_2 =$ flag bookmark A $10010_2$ B $10100_2$ C $10110_2$ D $11010_2$ T4 Chapter 2.1d Addition and Subtraction of Numbers in Various Bases $10011_2 = 19$ and $111_2 = 7$. $19 + 7 = 26 = 16 + 8 + 2 = 11010_2$.
6 In Diagram 1, PQUV is part of an 8-sided regular polygon. PQR is a straight line. The value of $x$ is flag bookmark A 120 B 135 C 145 D 150 Each interior angle of a regular octagon is 135°, so ∠PQU = 135° and ∠UQR = 180° − 135° = 45°. By symmetry, ∠QRS = 45° too. The sum of the interior angles of the pentagon QUTSR is (5 − 2) × 180° = 540°. The three equal angles at U, T and S share 540° − 45° − 45° = 450°, so x = 450° ÷ 3 = 150°.
7 In Diagram 2, JKL is a tangent to the circle with centre O at point K. Find the value of $x + y$. flag bookmark A 122 B 151 C 212 D 273 By the alternate segment theorem, ∠KNM = ∠LKM = 61°. KM = MN, so ∠MKN = ∠MNK = 61° and ∠KMN = 180° − 122° = 58°. y is the reflex angle KON: the minor angle KON = 2 × 58° = 116°, so y = 360° − 116° = 244°. The radius OK is perpendicular to the tangent, so x = ∠OKM = 90° − 61° = 29°. x + y = 29 + 244 = 273.
8 In Diagram 3, XYZ is a right-angled triangle and XY = 5 cm, YZ = 4 cm. Find the length of XZ, in cm. Express your answer correct to 4 significant figures. flag bookmark A 3 B 6.400 C 6.403 D 6.4031 $XZ = \sqrt{5^2 + 4^2} = \sqrt{41} = 6.40312...$ = 6.403 cm (4 significant figures).
9 Diagram 4 shows five quadrilaterals drawn on a grid of squares. Which of the quadrilaterals, A, B, C or D, is the image of quadrilateral G under an anticlockwise rotation of 90° about the centre P? flag bookmark A A B B C C D D T5 Chapter 5.3a Combined Transformation: Determining the Image and Object G lies above and to the left of P. Turning it 90° anticlockwise about P moves it to below and to the left of P, with each side turned through 90°. This is quadrilateral A.
10 Diagram 5 shows two quadrilaterals, PQRS and KLMN, drawn on a grid of equal squares. KLMN is the image of PQRS under an enlargement with centre O. Find the scale factor of the enlargement. flag bookmark A $\frac{1}{2}$ B $\frac{1}{3}$ C $2$ D $3$ T5 Chapter 5.2b Enlargement: Meaning, Scale Factor and Centre of Enlargement Compare a pair of corresponding distances from the centre O: OK is twice OP (P is 2 squares above O, K is 4 squares above O). The image is larger, so the scale factor is 2.