Mathematics (9-1) - iGCSE 2018-20 Year 09 Unit 07 – Answers

7 - Prior knowledge check Page 651 400 a. 3.6 b. 2.1 c. 5.0 a. 9.40 b. 13.98 Teaspoon 5ml, drink can 300ml, bucket 5 litres, juice carton 1 litre. a. 520cm b. 240mm c. 1000mm d. 3410m e. 327ml f. 2,4 litres

7 - Prior knowledge check Page 651 a. 18 b. 521 c. 480 d. 2 a. x = 1 c y b. x = a bz c. x = 2𝑚 y Suitable circle with correct centre, radius and diameter labelled.

7 - Prior knowledge check Page 651 a. b. 108cm2

7 - Prior knowledge check Page 651 a. b. c. 48cm3

7 - Prior knowledge check Page 651 40cm2 370cm3 Students' own answers. The boxes will fit exactly into a cuboid box with dimensions 9cm x 12cm x 12cm.

7.1 – Perimeter and Area a. 12cm2,16cm b. 30cm2, 30cm c. 96cm2, 44cm Page 651 a. 12cm2,16cm b. 30cm2, 30cm c. 96cm2, 44cm a. 1 = 4 b. 1 = 12 c. z = 5 a. Area = 46.5 m2, perimeter = 29m b. 1548mm2 c. 1406 mm2 a. 60cm2 b. 30cm2 c. 26.6m2 d. 373.5cm2 Area = 276cm2, perimeter = 72cm

7.1 – Perimeter and Area Page 651 £34.93 4350 m2 a. 96 = 1 2 (9 + 15)h b. 96 = 12h c. h = 8cm 4cm a. a = 6cm b. b = 2.8m (1 d.p.) 100cm

7.2 – Units and Accuracy a. 3.6 b. 320 c. 8.50 d. 15.7 Page 651 a. 3.6 b. 320 c. 8.50 d. 15.7 a. i. 2.5 kg ii. 22.5 kg iii. 27.5 kg b. i. 2m ii. 38m iii. 42m a. 1 cm = 10 mm, so they have same side length 1cm2 and 100mm2 1 cm2 = 100 mm2 a. Suitable sketch of the squares 1m2 = 10000cm2 Divide by 10000

7.2 – Units and Accuracy Page 651 a. 2.5cm2 b. 52000cm2 c. 0.7m2 d. 340mm2 e. 88,500cm2 f. 12.46cm2 g. 370,000mm2 h. 2.8m a. 0.6m2 b. 544 mm2 c. 468mm2 d. 21600cm2 24.2 ha 1,600,000 a. 33 mm, 27 m b. 27mm ≤ length ≤ 33mm

7.2 – Units and Accuracy Page 651 19g ≤ mass ≤ 21g a. i. 35.5cm ii. 111.5cm a. 17.5m ≤ x ≤ 18.5 m b. 24.45 kg ≤ x ≤ 24.55 kg c. 1.35 m ≤ x ≤ 1.45 m d. 5.255 km ≤ x ≤ 5.265 km

7.2 – Units and Accuracy Page 651 a. i. 7.5cm ii. 8.5cm b. i. 5.25kg ii. 5.35kg c. i. 11.35m ii. 11.45m d. i. 2.245 litres ii. 2.255 litres e. i. 4500m ii. 5500m f. i. 31.5mm ii. 32.5mm g. i. 1.525kg ii. 1.535kg

7.2 – Units and Accuracy a. 14.5cm, 15.5cm, 27.5cm, 28.5cm Page 651 a. 14.5cm, 15.5cm, 27.5cm, 28.5cm Lower bound 84cm, upper bound 88cm Upper bound 80.798m2, lower bound 79.008 m2 a. Height 6.15cm, 6.25cm; area 23.5cm2, 24.5cm2 i. 3.92 ii. 3.98 (2 d.p.) 3.98cm (2 d.p.)

7.3 – Prisms 72cm3 a. b = 8 b. h = 4 a. Students’ own sketch Page 651 72cm3 a. b = 8 b. h = 4 a. Students’ own sketch c. Areas are 20cm2, 28cm2 and 35cm2.The identical pairs are (top,bottom) (front,back) and (left side,right side) Surface area is 166cm2 72cm

7.3 – Prisms Page 651 a. Yes, because it has the same cross section all along its length, 12 cm2 72cm3, same value as for volume calculated in Q1. a. 80 cm3 b. 204 cm3 a. 4cm b. 108cm2 4cm

7.3 – Prisms a. Suitable sketch of cube 1 cm3 = 1,000mm3 Page 651 a. Suitable sketch of cube 1 cm3 = 1,000mm3 Divide by 1,000 a. 1m3 and 1,000,000cm3 Multiply by 1,000,000 a. 4,500,000cm3 b. 52,000mm3 9.5 m3 d. 3.421cm3 5.2 litres f. 1700cm3 75cm3 h. 3000 litres a. 9.44 m2 b. 3

7.3 – Prisms Page 651 9.2cm a. 0.05 m3 Estimated volume of leaf mould in wood is 20000 x 0.2 = 4000 m3 4000 0.05 = 80,000,12 x 80,000 = 960,000 worms Volume = 1 2 x 4x x 2x x 5x = 20x3 Upper bound: 5.5 x 3.5 x 8.5 = 163.63 cm3, Lower bound: 4.5 x 2.5 x 7.5 = 84.38cm3

7.4 – Circles a. r = 5 b. r = ± 5 a. x = y m b. x = ±t c. x = ± 𝑝 Page 651 a. r = 5 b. r = ± 5 a. x = y m b. x = ±t c. x = ± 𝑝 a. All ratios are 3.14 to 2 d.p. b. 3.14159265 a. 28.3 cm b. 14.8 m c. 75.4 mm a. 50.3 cm2 b. 4.5 m2 c. 38.5 m2 5 boxes a. 38.5 mm b. 1164 mm2 Circumference = 201cm, 1000 2.01 = 497

7.4 – Circles Page 652 a. 10πcm, 25πcm2 b. 14πcm, 49πcm2 c. 20πcm, 100πcm2 d. 24πcm, 144πcm2 a. i. area 36πcm, circumference 12πcm ii. 110cm2 (2 s.f.), 38cm The answers in terms of π because they have not been rounded a. 104 = πd b. d = 33.1cm 3.8 cm (1 d.p.)

7.4 – Circles a. 12.87 m b. 28.3 cm a. A π = r2 b. A π = r Page 652 a. 12.87 m b. 28.3 cm a. A π = r2 b. A π = r X: 3.6cm Y: 2.8 cm Z: 4.7 cm 8 x 66 circles = 528 Total area of circles = 528 x 9π = 14,929cm2 (to nearest cm2) Area thrown away = 20,000 – 14,929 = 5071cm2 Percentage thrown away = 5071 20000 = 0.25 or 25%

7.5 – Sector of Circles a. 16πcm, 64πcm2 b. 50.3 cm, 201 cm2 Page 652 a. 16πcm, 64πcm2 b. 50.3 cm, 201 cm2 a. 4π b. 2π + 10.2 c. 3π + 7 a. i. 18πcm2 ii. 56.5 cm2 b. i. 25πcm2 ii. 78.5 cm2 a. i. (3π + 6) cm ii. 15.4 cm b. i. (5π + 10)cm ii. 25.7 cm a. (16π +16)cm b. 66.3 cm a. 4.4m2 b. 8.8m 21.5 cm2 a. 3.090193616cm b. 3.1cm 58.9 cm

7.5 – Sector of Circles Arc length = 7.85cm, perimeter = 37.9cm Page 652 Arc length = 7.85cm, perimeter = 37.9cm a. 24.4 cm, 85.5cm2 b. 73.7 cm2 ≤ area < 98.2 cm2 a. 10 = x 360 x π x 32 b. 127° (to the nearest degree) 74° 8.56 m 5.0 cm (1 d.p.) (16π - 32) cm2

7.6 – Cylinders & Spheres Students’ sketches Page 652 Students’ sketches a. ±6 b. 4.3 c. ±1.6 d. 2.2 a. πr2 b. V = πr2h a. 197cm3 b. 167,283.5 mm3 0.267 m3 3.2 cm a. 188.5cm2 b. 16,889.2mm2 c. 41.3m2 26 mm 300cm3

7.6 – Cylinders & Spheres Page 652 a. SA = 324πmm2, V = 972πmm3 b. SA = 100πcm2, V = 500π 3 cm3 191 mm3 ≤ volume ≤ 348mm3 a. Total volume = - 1088 3 π = 1140mm3 (3 s.f.) b. Total SA = 208π = 653mm2 17mm 6.31m 3.1cm

7.7 – Spheres & Composite Solids Page 652 a. 20 cm2 b. 21cm2 9.4 cm a. Net of square-based pyramid, square 4cm side, height of each triangle 6cm Triangular face 12cm2, square 16cm2 64cm2 213 cm3 a. i. = 8.7 cm (1 d.p.) b. Total volume = 950 cm3

7.7 – Spheres & Composite Solids Page 652 a. 96πcm3 b. 302cm3 a. 257πcm2 b. 657πcm2 c. 907πcm2 l = 97 = 9.85cm (2 d.p.), area = 123.8cm2 Volume = 63,363mm3 (to nearest mm3) Surface area = 9,694 mm2 (to nearest mm2) 10.6cm

7.7 – Spheres & Composite Solids Page 652 Radius of sphere = 5.2322... cm, height of cone = 20.9cm Volume of whole cone = 144π, volume of smaller cone = 128 3 π Volume of frustum = 304 3 π a. 10πx3 b. 20πx2 c. 10πx3 + 20πx2 = 10πx2(x + 2) 51π = 160cm3 (3 s.f.)

7 – Problem-Solving Page 652 6.6cm 8.6cm 72.2% £935.03 864 cm3

7 – Problem-Solving Page 652 a. 9.5 cm3 b. 25cm 7cm a. 50.3cm b. 64π = 201.1cm2 25.7cm a. 15,7cm2 b. 5.2cm a. 40,000cm2 b. 0.56m2 c. 9.5m3 d. 3000ml – 3000cm3

7 – Problem-Solving 9.5 cm3 ≤ volume < 105cm3 Page 652 9.5 cm3 ≤ volume < 105cm3 a. 35.5 m ≤ 36m < 36.5m b. 9.15cm ≤ 9.2cm < 9.25cm c. 23.55 km ≤ 23.6km < 23.65km 36cm3 492.9 cm2 36πcm3 301.6cm3 Students‘ own answers

7 – Strengthen 2D Shapes a. 2cm b. 10.3cm Page 652 2D Shapes a. 2cm b. 10.3cm a. 55 = 1 2 (7 + b) x 10 b. 55 = 35 + 5b c. b = 4cm a. i. 4πcm ii. 12.6cm b. i. 12πcm ii. 37.7cm a. 2πr = 19.5cm, πr2 = 342 b. A = πr2 c. C = 2πr a. i. 4πcm2 ii. 12.6cm2 b. i. 36πcm2 ii. 113.1cm2

7 – Strengthen Page 652 a. 153.9cm2 b. 77.0cm2 c. 44.0cm d. 50.3cm e. 14.0cm f. 36.0cm a. 1 4 b. 1 8 c. 100 360 = 5 8 a. 1 8 b. 201.1cm2 c. 25.1cm2 d. 50.3cm e. 6.3cm f. 16cm g. 22.3cm

7 – Strengthen Accuracy and Measures Page 652 Accuracy and Measures a. 10,000cm2, 20,000cm2 b. cm2 10,000 cm2 x10,000 ÷10,000 m2 1 2 3 4 5 m2 a. 1,000,000cm3, 2,000,000cm2 b. cm2 10,000 cm2 x1,000,000 ÷1,000,000 m3 1 2 3 4 5 m2 a. 2.5 b. 27.5 and 22.5 c. 22.5 ≤ 25 ≤ 27.5 a. 22.5 ≤ l < 23.5 b. 31.5 ≤ l ≤ 32.5

7 – Strengthen Page 653 3D Solids a. 60cm3 b. 63cm3 c. 240π = 754cm3 a. Students’ sketches b. i. 113.1 cm2 ii. 37.7cm iii. 301.6cm2 iv. 527.8cm2

7 – Strengthen Page 653 a. Volume = 340 cm3 = 4 3 πr3, surface area = 746 cm2 = 4πr2 b. Surface area = 4πr2 c. Volume = 4 3 πr2 d. i. 452.39cm2 ii. 904.78cm3 a. 4cm b. 5cm c. 37.7 cm3 d. 75.4cm2

7 – Extend Page 653 a. 82.5 cm2 a. 50xy b. 500xyz a. Split the garden with a line parallel to the wall to form a rectangle and a right- angled triangle. The hypotenuse of the triangle is 5 m. The right hand side of the triangle is 11 - 8 = 3m. These are two sides of a Pythagorean triple, so the third side is 4m. This side is the same length as the wall, so the wall is 4 m long, Area of lawn = 38 m2; 2 bottles 201m

7 – Extend Page 653 Capacity of tank = 942,477.8 cm3 = 942,477.8 ml Time to fill = 3,142 seconds = 52 minutes a. Shade rectangle a by x b. Shade rectangle a by x and rectangle b by x c. Shade one of the end triangles a. 3.5cm b. 28 cm2 Area of trapezium = 1 2 (a + b)h So 144 = 1 2 ((x - 6) + (x + 2)) x 3x 144 = 1 2 (2x - 4) x 3x 144 = (x - 2) x 3x Therefore 3x2 - 6x = 144

7 – Extend Page 653 6 litres 3x a. 19.9 b. 24.8625 c. 389.098125 d. 3.7710... a. 528.75 b. 265 225 c. 37.184... 3.85 x 1013m2

7 – Unit Test Page 653 Sample student answer The question asks for the answer correct to 3 s.f. The student has rounded to 4 s.f. Although all the maths is correct they must make sure they write the answer in the requested way