Area and perimeter — Paper 2 · IGCSE Mathematics 0580

19 For Examiner's Use NOT TO SCALE 35 m 35 m The diagram shows an athletics track with six lanes. The distance around the inside of the inner lane is 400 metres. The radius of each semicircular section of the inside of the inner lane is 35 metres. (a) Calculate the total length of the two straight sections at the inside of the inner lane. Answer(a) m [3] (b) Each lane is one metre wide. Calculate the difference in the distances around the outside of the outer lane and the inside of the inner lane. Answer(b) m [2]

5 marks

Mark scheme: 19 (a) 180 3* M1 for 2 x π x 35 oe M1 dep for 400 - π x 70 (b) 37.7 2* M1 for 2 π (41 – 35) or 2 π 41 + (a) – 400 IGCSE EXAMINATIONS – NOVEMBER 2004 0580/0581 2 * indicates that it is necessary to look in the working following a wrong answer

This question in 0580/21 Oct/Nov 2004

21 For Examiner's Use 40 30 Speed car 20 (m / s) truck 10 0 10 20 30 40 50 60 Time (seconds) The graph shows the speed of a truck and a car over 60 seconds. (a) Calculate the acceleration of the car over the first 45 seconds. Answer(a) m/s2 [2] (b) Calculate the distance travelled by the car while it was travelling faster than the truck. Answer(b) m [3] Question 22 is printed on the next page.

5 marks

Mark scheme: 21 (a) 0.8 or 4/5 cao 2 M1 speed/time (b) 960 www 3 M1 30 × (12 + 36)/2 M1 12 × 40 M1 10 × (12 + 36)/2 M1 ½ × 40 × 24 IGCSE – October/November 2009 0580 21

This question in 0580/21 Oct/Nov 2009

21 For Examiner's Use 40 30 Speed car 20 (m / s) truck 10 0 10 20 30 40 50 60 Time (seconds) The graph shows the speed of a truck and a car over 60 seconds. (a) Calculate the acceleration of the car over the first 45 seconds. Answer(a) m/s2 [2] (b) Calculate the distance travelled by the car while it was travelling faster than the truck. Answer(b) m [3] Question 22 is printed on the next page.

5 marks

Mark scheme: 21 (a) 0.8 or 4/5 cao 2 M1 speed/time (b) 960 www 3 M1 30 × (12 + 36)/2 M1 12 × 40 M1 10 × (12 + 36)/2 M1 ½ × 40 × 24 IGCSE – October/November 2009 0580 22

This question in 0580/22 Oct/Nov 2009

7 NOT TO 0.8 m SCALE 1.4 m The top of a desk is made from a rectangle and a quarter circle. The rectangle measures 0.8m by 1.4m. Calculate the surface area of the top of the desk. Answer m2 [3]

3 marks

Mark scheme: 1 7 1.62 3 M1 π 0.82 4 M1 adding (0.8 × 1.4) to their k π 8 (a) (i) or 1 (ii) 1 (b) 2 1

This question in 0580/21 May/June 2010

10 NOT TO 1.5 m SCALE 3.5 m The diagram represents a rectangular gate measuring 1.5m by 3.5m. It is made from eight lengths of wood. Calculate the total length of wood needed to make the gate. Answer m [3]

3 marks

Mark scheme: 10 24.3(0788…) 3 M1 5 × 3.5 + 2 × 1.5 M1 (√) 1.52 + 3.52 2cw − 4 w

This question in 0580/21 May/June 2010

17 Examiner's Use NOT TO Q R SCALE P 8 m S O W T V U The diagram shows the junction of four paths. In the junction there is a circular area covered in grass. This circle has centre O and radius 8 m. (a) Calculate the area of grass. Answer(a) m2 [2] (b) Q NOT TO SCALE 12 m 45° P O The arc PQ and the other three identical arcs, RS, TU and VW are each part of a circle, centre O, radius 12m. The angle POQ is 45°. The arcs PQ, RS, TU, VW and the circumference of the circle in part(a) are painted white. Calculate the total length painted white. Answer(b) m [4]

6 marks

Mark scheme: 17 (a) 201 2 M1 π × 82 45 (b) 87.9 or 88.0 4 M1 × 2 × π × 12 ….. d 360 M1 2 × π × 8 ……………..e M1 ft for their (4d + e) which must come from multiples of π SC2 43.9 or 44.0

This question in 0580/22 May/June 2010

15 8 cm NOT TO SCALE 6 cm 6 cm A semicircle of diameter 6 cm is cut from a rectangle with sides 6 cm and 8 cm. Calculate the perimeter of the shaded shape, correct to 1 decimal place. Answer cm [3]

3 marks

Mark scheme: 1 15 31.4 cao 3 M1 × 2 × π × 3 oe 2 M1 6 + 8 + 6 + 1 + 1 + k π 3

This question in 0580/21 Oct/Nov 2010

13 For Examiner's NOT TO Use SCALE The diagram shows a circle of radius 5cm in a square of side 18cm. Calculate the shaded area. Answer cm2 [3]

3 marks

Mark scheme: 13 245 or 246 3 M1 π × 52 M1 182 – their kπ

This question in 0580/22 Oct/Nov 2010

21 An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for Examiner's 9 seconds and then slows to a stop in a further 4 seconds. Use The graph shows this information. 14 12 10 Speed 8 (m / s) 6 4 2 0 2 4 6 8 10 12 14 16 18 20 Time (seconds) (a) Calculate its acceleration during the first seven seconds. Answer(a) m/s2 [1] (b) Write down its speed 18 seconds after the start. Answer(b) m/s [1] (c) Calculate the total distance that the animal travelled. Answer(c) m [3] Question 22 is printed on the next page.

5 marks

Mark scheme: 21 (a) 2 1 (b) 6.7 to 7.3 1 (c) 203 3 M1 intention to find area under the graph 1 1 M1 × 7 × 14 + 9 × 14 + × 4 × 14 oe 2 2

This question in 0580/22 Oct/Nov 2010

21 For 20 Examiner's Use 18 16 14 12 Speed 10 (m / s) 8 6 4 2 0 10 20 30 40 Time (seconds) The graph shows 40 seconds of a car journey. The car travelled at a constant speed of 20 m/s, decelerated to 8 m/s then accelerated back to 20 m/s. Calculate (a) the deceleration of the car, Answer(a) m/s2 [1] (b) the total distance travelled by the car during the 40 seconds. Answer(b) m [3]

4 marks

Mark scheme: 21 (a) 2.4 oe 1 (b) 680 3 M1 an area found 1 M1 40 × 20 – × 20 × 12 oe 2

This question in 0580/23 Oct/Nov 2010

16 ForFor Examiner'sExaminer's UseUse k cm The diagram shows a square of side k cm. The circle inside the square touches all four sides of the square. (a) The shaded area is A cm2. Show that 4A = 4k2 – πk2. Answer (a) [2] (b) Make k the subject of the formula 4A = 4k2 – πk2. Answer(b) k = [3]

5 marks

Mark scheme: k 16 (a) Answer given 2 M1 (A =)k2 – π    2  πk 2 E1 A = k2 – 4 correctly completed to 4A = 4k2 – πk2 4 A A (b) k = (±) or 2 3 M1 factorising (must contain a π) (4 − π ) (4 − π ) M1 division (by coefficient of k2) M1 square root

This question in 0580/21 May/June 2011

15 A container ship travelled at 14 km/h for 8 hours and then slowed down to 9 km/h over a period of For 30 minutes. Examiner's Use It travelled at this speed for another 4 hours and then slowed to a stop over 30 minutes. The speed-time graph shows this voyage. 16 14 12 10 Speed 8 (km / h) 6 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Time (hours) (a) Calculate the total distance travelled by the ship. Answer(a) km [4] (b) Calculate the average speed of the ship for the whole voyage. Answer(b) km/h [1]

5 marks

Mark scheme: 15 (a) 156 4 M1 intention to find area under graph B2 completely correct area statement or B1 two areas found correctly (or one trapezium area) (b) 12 1ft Their (a)/13

This question in 0580/21 Oct/Nov 2011

19 For y Examiner's Use 6 5 C 4 A 3 2 1 B x 0 1 2 3 4 5 6 7 A(1, 3), B(4, 1) and C(6, 4) are shown on the diagram. (a) Using a straight edge and compasses only, construct the angle bisector of angle ABC. [2] (b) Work out the equation of the line BC. Answer(b) [3] (c) ABC forms a right-angled isosceles triangle of area 6.5 cm2. Calculate the length of AB. Answer(c) AB = cm [2]

7 marks

Mark scheme: 19 (a) correct bisector (through 3½, 3½) 2 B1 correct line B1 correct arcs 1 1 (b) y = 1 x – 5 oe 3 B2 y = 1 x + k or y = kx – 5 k any number 2 2 1 or B1 1 x + k or kx – 5 2 1 If O scored allow one each for m = 1 or c = –5 2 clearly identified in working 1 2 2 (c) 3.61 2 M1 × L × L = 6.5 or M1 (3 + 2 ) 2

This question in 0580/22 Oct/Nov 2011

15 The scale of a map is 1 : 500 000 . (a) The actual distance between two towns is 172 km. Calculate the distance, in centimetres, between the towns on the map. Answer(a) cm [2] (b) The area of a lake on the map is 12 cm2. Calculate the actual area of the lake in km2. Answer(b) km2 [2]

4 marks

Mark scheme: 15 (a) 34.4 2 SC1 figs 344 seen (b) 300 2 SC1 figs 3 seen − 1 2 

This question in 0580/21 May/June 2012

18 For 20 Examiner's Use 15 Speed 10 (m / s) 5 0 10 20 30 40 50 60 70 80 90 100 110 120 Time (s) The diagram shows the speed-time graph for the first 120 seconds of a car journey. (a) Calculate the acceleration of the car during the first 25 seconds. Answer(a) m/s2 [1] (b) Calculate the distance travelled by the car in the first 120 seconds. Answer(b) m [4]

5 marks

Mark scheme: 18 (a) 0.8 1 (b) 1850 4 M1 for area = distance travelled M1 for two correct area statements M1 for complete correct area statement IGCSE – May/June 2012 0580 21

This question in 0580/21 May/June 2012

7 8 cm NOT TO r SCALE 6 cm The perimeter of the rectangle is the same length as the circumference of the circle. Calculate the radius, r, of the circle. Answer r = cm [3]

3 marks

Mark scheme: 7 4.46 or 4.456 to 4.459 cao 3 B1 for 28 seen their 28 M1ft for oe or better. 2π 2 3

This question in 0580/22 May/June 2012

10 For Examiner's 500 Use 400 300 Speed (m / min) 200 100 0 10 20 30 40 50 60 Time (min) The diagram shows the speed-time graph for a boat journey. (a) Work out the acceleration of the boat in metres / minute2. Answer(a) m / min 2 [1] (b) Calculate the total distance travelled by the boat. Give your answer in kilometres. Answer(b) km [2]

3 marks

Mark scheme: 10 (a) 50 1 (b) 15 2 M1 finding area under graph SC1 15000 2

This question in 0580/22 May/June 2012

12 NOT TO 6 cm SCALE The diagram shows a circular disc with radius 6 cm. In the centre of the disc there is a circular hole with radius 0.5 cm. Calculate the area of the shaded section. Answer cm2 [3]

3 marks

Mark scheme: 12 112 or 112.3 to 112.33 3 M2 for π × 62 – π × 0.52 or M1 for π × 62 or π × 0.52 seen IGCSE – October/November 2012 0580 21

This question in 0580/21 Oct/Nov 2012

15 For Examiner's 25 Use 20 15 Speed (metres per second) 10 5 0 5 10 15 20 25 30 35 Time (seconds) The diagram shows the speed-time graph for the last 35 seconds of a car journey. (a) Find the deceleration of the car as it came to a stop. Answer(a) m/s2 [1] (b) Calculate the total distance travelled by the car in the 35 seconds. Answer(b) m [3]

4 marks

Mark scheme: 15 (a) 3 1 (b) 637.5 3 M1 finding area under graph M1dep all correct area statements

This question in 0580/22 Oct/Nov 2012

19 For Examiner's 5 Use 4 Speed 3 (metres per second) 2 1 0 2 4 6 8 10 12 14 16 18 Time (seconds) The diagram shows the speed-time graph for the last 18 seconds of Roman’s cycle journey. (a) Calculate the deceleration. Answer(a) m/s2 [1] (b) Calculate the total distance Roman travels during the 18 seconds. Answer(b) m [3]

4 marks

Mark scheme: 19 (a) 0.625 or 5/8 1 (b) 62 3 M1 for area under graph implied M1 for correct, complete, area statement

This question in 0580/23 Oct/Nov 2012

25 For Examiner′s Use 28 NOT TO SCALE Speed (m/s) 0 20 30 Time (seconds) The diagram shows the speed-time graph of a car. It travels at 28 m/s for 20 seconds and then decelerates until it stops after a further 10 seconds. (a) Calculate the deceleration of the car. Answer(a) … m/s2 [1] (b) Calculate the distance travelled during the 30 seconds. Answer(b) … m [3] _____________________________________________________________________________________ Question 26 is printed on the next page.

4 marks

Mark scheme: 25 (a) 1 2.8 oe (b) 3 M2 for ½(20 + 30) × 28 oe 700 or M1 for a correct area statement 2 2

This question in 0580/21 May/June 2013

7 For Examiner′s 4 cm Use NOT TO SCALE 5 cm 10 cm 18 cm The shaded shape has rotational symmetry of order 2. Work out the shaded area. Answer … cm2 [3] _____________________________________________________________________________________

3 marks

Mark scheme: 7 260 3 M2 for [2 × ](4 × 10 + 18 × 5) oe or M1 for a correct area statement 2500 3

This question in 0580/23 May/June 2013

21 For Examiner′s C Use NOT TO SCALE D B X A ABCD is a kite. The diagonals AC and BD intersect at X. AC = 12 cm, BD = 20 cm and DX : XB = 3 : 2 . (a) Calculate angle ABC. Answer(a) Angle ABC = … [3] (b) Calculate the area of the kite. Answer(b) … cm2 [2] _____________________________________________________________________________________

5 marks

Mark scheme: 20 21 (a) 73.7 or 73.73 to 73.74 3 M1 for × 2 or B1 for BX = 8 3 + 2 6 M1 for tan [ ] = or better their 8 (b) 120 2 M1 for 12 × 20 × 12 oe 5

This question in 0580/21 Oct/Nov 2013

7 Find the interior angle of a regular polygon with 18 sides. Answer … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 360 180 × (18 − 2 ) 7 160 3 M2 for 180 − or oe 18 18 360 or M1 for 180 × (18 – 2) or 18

This question in 0580/23 Oct/Nov 2014

12 D C E A B (a) Draw the locus of the points which are 3 cm from E. [1] (b) Using a straight edge and compasses only, construct the bisector of angle DCB. [2] (c) Shade the region which is ● less than 3 cm from E and ● nearer to CB than to CD. [1] __________________________________________________________________________________________

4 marks

Mark scheme: 12 (a) Complete circle centre E radius 1 3cm (b) Correct ruled bisector with two 2 B1 for correct bisector with no/wrong arcs pairs of correct arcs (c) 1 dep on attempt at bisector of C and enclosed region 16 x 2 + 18 x + 9

This question in 0580/23 Oct/Nov 2014

13 E (x – 4) cm A B NOT TO (x – 1) cm SCALE 7 cm D C F G (a) ABCD is a square. Find the value of x. Answer(a) x = … [1] (b) Square ABCD and isosceles triangle EFG have the same perimeter. Work out the length of FG. Answer(b) FG = … cm [2] __________________________________________________________________________________________

3 marks

Mark scheme: 13 (a) 11 1 (b) 8 2FT FT 30 – 2 × their (a) or M1 for 4 × 7 = 2(x – 1) + FG oe or 4(x – 4) = 2(x – 1) + FG oe or 2 × 7 + 2(x – 4) = 2(x – 1) + FG oe Allow x to be their (a) in each

This question in 0580/22 May/June 2015

23 20 18 16 14 12 Speed 10 (m/s) 8 6 4 2 0 10 20 30 40 50 60 70 80 90 100 110 120 Time (s) The diagram shows the speed-time graph for 120 seconds of a car journey. (a) Calculate the deceleration of the car during the first 20 seconds. Answer(a) … m/s2 [1] (b) Calculate the total distance travelled by the car during the 120 seconds. Answer(b) … m [3] (c) Calculate the average speed for this 120 second journey. Answer(c) … m/s [1] __________________________________________________________________________________________

5 marks

Mark scheme: 2 23 (a) 0.4 or 1 5 (b) 1430 3 M2 for correct, complete, area statement 1 1 e.g. 120 × 10 + × 20 × 8 + × 30 × 10 oe 2 2 or M1 for one area calculation 1 1 e.g. 10 × 120 or × 20 × 8 or × 30 × 10 2 2 (c) 11.9 or 11.91 to 11.92 1FT their (b) ÷ 120

This question in 0580/22 May/June 2015

18 P NOT TO SCALE 8 cm D C 20 cm M A 20 cm B The diagram shows a solid pyramid on a square horizontal base ABCD. The diagonals AC and BD intersect at M. P is vertically above M. AB = 20 cm and PM = 8 cm. Calculate the total surface area of the pyramid. Answer … cm2 [5]

5 marks

Mark scheme: 18 912 or 912.2… 5 M4 for 4 × 0.5 × 20 × 8 2 + 10 2 + 20 × 20 or better or M3 for 4 × 0.5 × 20 × 8 2 + 10 2 or better or M1 for 8 2 + 10 2 and M1 for 0.5 × 20 × 8 2 + 10 2 and M1 for 20 × 20

This question in 0580/23 May/June 2015

20 R NOT TO SCALE 9 cm P Q 10 cm The area of triangle PQR is 38.5 cm2. Calculate the length QR. Answer QR = … cm [6]

6 marks

Mark scheme: 385. 20 9.37 or 9.370 to 9.371 6 M2 for sin[P] = 5.0 × 9 × 10 or M1 for 0.5 × 10 × 9 × sin = 38.5 M3 for √(92 + 102 – 2×9×10 × cos (their P)) or M2 for 92 + 102 – 2×9×10 × cos (their P) or M1 for a correct implicit expression 9 2 + 10 2 − RQ 2 e.g. cos(their P)= 2 × 9 × 10 Note: 87.8, 87.81[…] or 87.7[55…] score 4 marks or M is foot of perpendicular from R to PQ M2 for perp.ht = 38.5 ÷ 1 × 10 or 7.7 2 or M1 for 1 × 10 × […] = 38.5 2 M1 for PM = √(92 – 7.72)[ = 4.659… or 4.66] M1 for QM = 10 – their 4.659…[ = 5.34…] M1 for QR = √((their QM)2 + 7.72)

This question in 0580/23 May/June 2015

19 25° 5 cm NOT TO SCALE 15 cm The diagram shows a wooden prism of height 5 cm. The cross section of the prism is a sector of a circle with sector angle 25°. The radius of the sector is 15 cm. Calculate the total surface area of the prism. Answer … cm2 [5] __________________________________________________________________________________________

5 marks

Mark scheme: 14 19 nfww 4 B3 19.3 or 19.28 to 19.29 or 300 × 60 2 M2 for oe 56 × 1000 or M1 for distance divided by speed 56× 1000 e.g. their 300 ÷ their 56 or 60 2 If B0 then B1 for seeing their answer in decimal form correctly written to the nearest integer x + 4

This question in 0580/21 Oct/Nov 2015

20 A car passes through a checkpoint at time t = 0 seconds, travelling at 8 m/s. It travels at this speed for 10 seconds. The car then decelerates at a constant rate until it stops when t = 55 seconds. (a) On the grid, draw the speed-time graph. 10 8 6 Speed (m/s) 4 2 t 0 10 20 30 40 50 60 Time (seconds) [2] (b) Calculate the total distance travelled by the car after passing through the checkpoint. Answer(b) … m [3]

5 marks

Mark scheme: 20 (a) B1 line from (0, 8) to (10, 8) 8 B1 line from their (10, 8) to (55, 0) 10 55 (b) 260 3FT M2FT for 8 × 10 + 0.5 × 8 × 45 oe or for a fully correct area calculation for their graph or M1FT for 8 × 10 or 0.5 × 8 × 45 or for one correct area calculation for their graph 7 2 15 25

This question in 0580/22 Oct/Nov 2015

7 22.3 cm NOT TO SCALE 25° 27.6 cm Calculate the area of this triangle. … cm2 [2]

2 marks

Mark scheme: 7 130 or 130.0 to 130.1 2 M1 for ½ × 22.3 × 27.6 × sin25 1  7 2  1 a b   7 2 

This question in 0580/22 Feb/March 2016

23 8 cm D C 8 cm NOT TO SCALE A B 12 cm Calculate the area of this trapezium. … cm2 [4]

4 marks

Mark scheme: 2 − 4 223 69.3 or 69.28… 4 M2 for height = 8 or M1 for 42 + h2 = 82 oe 1 and M1 for (8 + 12) × their perp height oe 2

This question in 0580/21 May/June 2016

3 NOT TO SCALE 6 cm 5 cm x cm The area of this parallelogram is 51.5 cm2. Work out the value of x. x = … [2]

2 marks

Mark scheme: 3 10.3 oe 2 M1 for 5x = 51.5 oe 1

This question in 0580/23 May/June 2016

4 13 cm NOT TO 5 cm SCALE 4 cm 16 cm Calculate the area of this trapezium. … cm2 [2]

2 marks

Mark scheme: (13 + 16 ) × 4 14 58 2 M1 for or 4 × 13 + 2 × 4 × 3 oe 2

This question in 0580/22 Oct/Nov 2016

14 The shaded shape is made by joining a square and a rhombus. NOT TO SCALE 4.5 cm 5 cm Work out (a) the perimeter of the shaded shape, … cm [1] (b) the area of the shaded shape. … cm2 [2]

3 marks

Mark scheme: 14 (a) 30 1 (b) 47.5 2 M1 for 4.5 × 5 oe

This question in 0580/23 Oct/Nov 2016

21 (a) B 6.2 cm 82° A NOT TO SCALE 4.7 cm C Calculate the area of triangle ABC. … cm2 [2] (b) E 107 mm NOT TO SCALE x° D 75 mm F The area of triangle DEF is 2050 mm2. Work out the value of x. x = … [2]

4 marks

Mark scheme: 1 21 (a) 14.4 or 14.42 to 14.43 2 M1 for × 6.2 × 4.7 × sin 82 oe 2 2050 (b) 30.7 or 30.72… 2 M1 for sin = 1 × 1 07 × 75 2

This question in 0580/23 Oct/Nov 2016

16 The speed-time graph shows the first 60 seconds of a train journey. 15 10 Speed (m/s) 5 0 0 20 40 60 Time (s) (a) Find the acceleration of the train. … m/s2 [1] (b) Calculate the distance the train has travelled in this time. Give your answer in kilometres. … km [3]

4 marks

Mark scheme: 16 (a) 1 1 0.25 or 4 (b) 0.45 3 B2 for 4550 or 1 M2 for × 60 × 15 ÷÷ 1000 22 1 or M1 foor × 60 × 115 2 If 0 scoreed SC1 for ccorrect conveersion of their disttance in metrres to kilomeetres

This question in 0580/22 Feb/March 2017

19 P NOT TO SCALE 2.8 cm 79° Q 8.3 cm R (a) Calculate the area of triangle PQR. … cm2 [2] (b) Triangle PQR is enlarged by scale factor 4.5 . Calculate the area of the enlarged triangle. … cm2 [2]

4 marks

Mark scheme: 1 19 (a) 11.4 or 111.40 to 11.441 2 M1 for × 2.8 × 8.3 ×× sin79 oe 22 (b) 231 or 2230.8 to 231.1 2FT FT their (a) × 4.52 M1 for 4.524 or 20.25 seen

This question in 0580/22 Feb/March 2017

20 (a) 20 cm NOT TO SCALE A cylinder has height 20 cm. The area of the circular cross section is 74 cm2. Work out the volume of this cylinder. … cm3 [1] (b) Cylinder A is mathematically similar to cylinder B. NOT TO 10 cm A B SCALE The height of cylinder A is 10 cm and its surface area is 440 cm2. The surface area of cylinder B is 3960 cm2. Calculate the height of cylinder B. … cm [3]

4 marks

Mark scheme: 20(a) 1480 1 20(b) 30 3 3960 440 M2 for 10 × or 10 ÷ 440 3960 3960 440 or M1 for or or 440 3960  h 2 3960 oe  =  10  440

This question in 0580/21 Oct/Nov 2017

7 The area of a triangle is 528 cm2. The length of its base is 33 cm. Calculate the perpendicular height of the triangle. … cm [2]

2 marks

Mark scheme: 7 32 2 1 M1 for × 33 × h = 528 oe 2

This question in 0580/22 Oct/Nov 2017

17 20 NOT TO Speed SCALE (m/s) 0 0 10 100 130 Time (seconds) The speed-time graph shows information about the journey of a tram between two stations. (a) Calculate the distance between the two stations. … m [3] (b) Calculate the average speed of the tram for the whole journey. … m/s [1]

4 marks

Mark scheme: 17(a) 2200 3 M2 for 12 ( 90 + 130 ) × 20 or 1 2 (10 × 20) + (90 × 20) + 12 (30 × 20) or M1 for one area 17(b) 16.9 or 16.92… 1 FT their (a) ÷ 130

This question in 0580/21 May/June 2018

10 7.5 cm NOT TO SCALE 5 cm 12 cm Calculate the total surface area of the cuboid. … cm2 [3]

3 marks

Mark scheme: 10 375 3 M2 for 2 (12 × 5 + 12 × 7.5 + 5 × 7.5 ) oe or M1 for 12 × 5 or 12 × 7.5 or 5 × 7.5

This question in 0580/22 Feb/March 2019

12 A cone with height 14.8 cm has volume 275 cm3. Calculate the radius of the cone. 1 2 [The volume, V, of a cone with radius r and height h is V = r r h .] 3 … cm [3]

3 marks

Mark scheme: 12 4.21 or 4.212 … 3 275 × 3 M2 for oe 14.8 × π 1 2 or M1 for 275 = × π × r × 14.8 oe 3

This question in 0580/22 Feb/March 2019

24 20 NOT TO Speed SCALE (m/s) 0 0 60 70 Time (seconds) The diagram shows information about the final 70 seconds of a car journey. (a) Find the deceleration of the car between 60 and 70 seconds. … m/s2 [1] (b) Find the distance travelled by the car during the 70 seconds. … m [3]

4 marks

Mark scheme: 24(a) 2 1 24(b) 1300 3 20 M2 for × (60 + 70) oe 2 or M1 for any relevant area

This question in 0580/21 May/June 2019

7 NOT TO SCALE 3.5 cm 8.4 cm Calculate the area of this triangle. … cm2 [2]

2 marks

Mark scheme: 7 14.7 2 1 M1 for × 8.4 × 3.5 oe 2

This question in 0580/22 May/June 2019

13 11 cm NOT TO 39° SCALE 13 cm Calculate the area of the triangle. … cm2 [2]

2 marks

Mark scheme: 13 45[.0] or 44.99 to 45.00 2 1 M1 for × 13 × 11 × sin 39 oe 2

This question in 0580/21 Oct/Nov 2019

23 4 3 Speed 2 (km/min) 1 0 0 5 10 15 20 25 30 t Time (minutes) The speed–time graph shows information about a train journey. (a) By drawing a suitable tangent to the graph, estimate the gradient of the curve at t = 24 . … [3] (b) What does this gradient represent? … [1] (c) Work out the distance travelled by the train when it is travelling at constant speed. … km [2]

6 marks

Mark scheme: 23(a) Tangent ruled at t = 24 B1 – 0.7 to – 0.3 B2 B2 dep on correct tangent or close attempt at tangent M1 for rise/run also dep on correct tangent drawn or close attempt at tangent. Must see correct or implied calculation from a drawn tangent. 23(b) acceleration or deceleration oe 1 23(c) 68 2 M1 for (22 – 5) × 4

This question in 0580/22 Oct/Nov 2019

19 18 16 14 12 10 Speed (m/s) 8 6 4 2 0 0 10 20 30 40 50 60 70 Time (s) The diagram shows the speed–time graph for 70 seconds of a car journey. (a) Calculate the deceleration of the car during the first 20 seconds. … m/s2 [1] (b) Calculate the total distance travelled by the car during the 70 seconds. … m [3]

4 marks

Mark scheme: 19(a) 3 1 0.3 or 10 19(b) 760 3 M2 for correct complete area statement 1 e.g. 70 × 10 + × 20 × 6 oe 2 or M1 for one of these area calculations 1 70 × 10, × 20 × 6, 50 × 10 or 2 1 × (16 + 10) × 20 2

This question in 0580/23 Oct/Nov 2019

7 NOT TO 8.5 cm SCALE 10.8 cm The diagram shows a right-angled triangle. (a) Calculate the area. … cm2 [2] (b) Calculate the perimeter. … cm [3]

5 marks

Mark scheme: 7(a) 45.9 2 M1 for 0.5 × 8.5 × 10.8 oe 7(b) 33[.0] or 33.04… 3 2 2 M2 for 8.5 + 10.8 + 8.5 + 10.8 oe or M1 for 8.5 2 + 10.8 2 oe

This question in 0580/22 Feb/March 2020

1 Rectangle A measures 3 cm by 8 cm. 8 cm NOT TO 3 cm A SCALE Five rectangles congruent to A are joined to make a shape. NOT TO SCALE Work out the perimeter of this shape. … cm [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 86 2 M1 for correct method to find the perimeter e.g. (8 + 3) × 2 × 5 – 3 × 8 If 0 scored, SC1 for answer 98

This question in 0580/21 May/June 2020

22 Find the area of a regular hexagon with side length 7.4 cm. … cm2 [3]

3 marks

Mark scheme: 22 142 or 142.2 to 142.3 3 1 M2 for × 7.4 × 7.4 × sin60 × 6 2 7.4 7.4 or tan60 × × × 6 2 2 1 7.4 or M1 for × 7.4 × 7.4 × sin60 or tan60 × 2 2

This question in 0580/21 May/June 2020

6 11 cm NOT TO SCALE 5 cm 7 cm Calculate the area of the trapezium. … cm2 [2]

2 marks

Mark scheme: 6 45 2 11 + 7 M1 for × 5 oe 2

This question in 0580/22 May/June 2020

10 A solid cylinder has radius 3 cm and height 4.5 cm. Calculate the total surface area of the cylinder. … cm2 [4]

4 marks

Mark scheme: 10 141 or 141.3 to 141.4 4 M1 for[2 ×] π × 32 M2 for 2 × π × 3 × 4.5 or M1 for 2 × π × 3 [× 4.5]

This question in 0580/23 May/June 2020

15 20 Car 18 16 14 Motorbike 12 Speed 10 (m/s) 8 6 4 2 0 0 10 20 30 40 50 60 70 80 90 100 Time (s) The diagram shows the speed–time graph for 100 seconds of the journey of a car and of a motorbike. (a) Find the deceleration of the car between 60 and 100 seconds. … m/s2 [1] (b) Calculate how much further the car travelled than the motorbike during the 100 seconds. … m [3]

4 marks

Mark scheme: 15(a) 0.3 1 15(b) 360 3 M2 for correct complete area statement e.g. 1 18 × 60 + × 40 × (18 + 6) – 12 × 100 2 1 1 or × 6 × (60 + 80) – × 6 × 20 2 2 or for answer 420 or M1 for one area calculation

This question in 0580/21 Oct/Nov 2020

7 C NOT TO SCALE h cm A 6 cm B The area of triangle ABC is 27 cm2 and AB = 6 cm. Calculate the value of h. h = … [2]

2 marks

Mark scheme: 7 9 2 1 M1 for × 6 × h = 27 oe 2

This question in 0580/22 Oct/Nov 2020

17 4 3 Speed 2 (m/s) 1 0 0 10 20 30 40 Time (seconds) The diagram shows the speed–time graph for the first 40 seconds of a cycle ride. (a) Find the acceleration between 20 and 40 seconds. … m/s2 [1] (b) Find the total distance travelled. … m [3]

4 marks

Mark scheme: 17(a) 1 1 0.1 or 10 17(b) 90 3 M2 for 1 1 × 10 × 2 + 10 × 2 + ( 2 + 4 ) × 20 oe 2 2 or M1 for one area calculation or indicated on diagram

This question in 0580/22 Oct/Nov 2020

19 v + 10 NOT TO SCALE Speed v (m/s) 0 0 24 40 Time (seconds) The diagram shows the speed–time graph for the final 40 seconds of a car journey. At the start of the 40 seconds the speed is v m/s. (a) Find the acceleration of the car during the first 24 seconds. … m/s2 [1] (b) The total distance travelled during the 40 seconds is 1.24 kilometres. Find the value of v. v = … [4]

5 marks

Mark scheme: 19(a) 5 1 or 0.417 or 0.4166 to 0.4167 12 19(b) 32.5 4 M3 for 1 1 ( v + v + 10 ) × 24 + × 16 ( v + 10 ) = 1240 2 2 oe OR 1 M2 for ( v + v + 10 ) × 24 oe and 2 1 × 16 ( v + 10 ) oe 2 or M1 for one area expression M1 for correctly solving their (av + b = 1240) oe (a ≠ 0, b ≠ 0)

This question in 0580/23 Oct/Nov 2020

12 C NOT TO 6 cm SCALE O B 5 cm A The diagram shows a shape made from a quarter-circle, OAB, and a right-angled triangle OBC. The radius of the circle is 5 cm and OC = 6 cm. Calculate the area of the shape. … cm2 [3]

3 marks

Mark scheme: 12 34.6 or 34.63 to 34.64 3 1 2 1 M2 for × π × 5 + × 5 × 6 oe 4 2 1 2 1 or M1 for × π × 5 oe or × 5 × 6 oe 4 2

This question in 0580/22 Feb/March 2021

14 15.4 cm NOT TO SCALE 18.2 cm 62° The diagram shows a trapezium. The trapezium has one line of symmetry. Work out the area of the trapezium. … cm2 [4]

4 marks

Mark scheme: 14 456 or 456.4… 4 18.2 M2 for oe tan62 18.2 or M1 for tan62 = oe x M1 for 1 ( ( theirtrapeziumbase ) + 15.4 ) × 18.2 oe 2

This question in 0580/22 May/June 2021

19 (a) NOT TO A SCALE B C The diagram shows a shape made from an equilateral triangle ABC and a sector of a circle. Points B and C lie on the circle, centre A. The side length of the equilateral triangle is 12.4 cm. Work out the perimeter of the shape. … cm [3] (b) NOT TO SCALE 41° The diagram shows two sectors of a circle. The major sector is shaded. The area of the major sector is 74.5 cm2. Calculate the radius of the circle. … cm [3]

6 marks

Mark scheme: 19(a) 77.3 or 77.32 to 77.33… 3 360 − 60 M2 for × π× 12.4 × 2 oe 360 [± n × 12.4] or M1 for angle 60° or 300° soi k or for × π× 12.4 × 2 oe [± n × 12.4] 360 19(b) 5.17 or 5.172 to 5.173… 3 74.5 360 2 M2 for × = r oe or better π 360 − 41 360 − 41 2 or M1 for 74.5 = × πr oe 360 74.5 360 or for × oe π k

This question in 0580/22 May/June 2021

18 A car starts from rest and accelerates at a rate of 3 m/s 2 for 4 seconds. The car then travels at a constant speed for 10 seconds. V Speed NOT TO (m/s) SCALE 00 4 14 Time (seconds) The diagram shows the speed–time graph for this journey. (a) Find the value of V. V = … [1] (b) Calculate the total distance travelled by the car during the 14 seconds. … m [2]

3 marks

Mark scheme: 18(a) 12 1 18(b) 144 2 FT 12 × their V M1 for any relevant area FT their V

This question in 0580/23 May/June 2021

18 B NOT TO 800 m SCALE 30° A C 2300 m The diagram shows some land in the shape of a triangle ABC. Houses are built on this land. Each house requires 400 m 2 of land. Find the greatest number of houses that can be built on this land. … [3]

3 marks

Mark scheme: 18 1150 3  1  M2 for  × 800 × 2300 × sin30  ÷ 400 oe  2  1 or M1 for × 800 × 2300 × sin30 oe 2

This question in 0580/21 Oct/Nov 2021

4 NOT TO SCALE 5 cm 4 cm 7 cm Calculate the total surface area of this cuboid. … cm2 [3]

3 marks

Mark scheme: 4 166 3 M2 for [2 ×] (7×4 + 4×5 + 5×7) or M1 for 7×4 or 4×5 or 5×7

This question in 0580/22 Feb/March 2022

17 O R X NOT TO 4 cm SCALE P Q 11 cm The diagram shows a rectangle OPQR with length 11 cm and width 4 cm. OQ is a diagonal and OPX is a sector of a circle, centre O. Calculate the percentage of the rectangle that is shaded. … % [5]

5 marks

Mark scheme: 17 77.8 or 77.77 to 77.80 5 B4 for answer 22.2[%] or 22.20[%] to 22.23[%] OR − 111 − 1 4 M1 for tan oe or tan oe 4 11 their acuteangle 2 M2 for 4 × 11 − × π × 4 oe 360 their acuteangle 2 or M1 for π × 4 oe 360 their shaded area M1 for [×100] oe 4 ×1 1 their sector area or ×100 oe 4 ×1 1

This question in 0580/22 Feb/March 2022

20 12 NOT TO Speed (m/s) SCALE 0 0 16 24 Time (s) The diagram shows the speed–time graph for 24 seconds of a car journey. Calculate (a) the deceleration of the car in the final 8 seconds, … m/s2 [1] (b) the total distance travelled during the 24 seconds. … m [2]

3 marks

Mark scheme: 20(a) 1 1 1.5 or 12 20(b) 240 2 M1 for one correct area

This question in 0580/21 May/June 2022

5 Find the total surface area of a cuboid with length 8 cm, width 6 cm and height 3 cm. … cm2 [3]

3 marks

Mark scheme: 5 180 3 M2 for  2   8  6 8 3 3 6  oe or M1 for 8  6 or 8  3 or 3  6

This question in 0580/22 May/June 2022

23 6.2 cm NOT TO SCALE l The diagram shows a solid metal shape made from a cone and a hemisphere, both with radius 6.2 cm. The total surface area of the solid shape is 600 cm2. Calculate the slant height, l, of the cone. [The surface area, A, of a sphere with radius r is A = 4rr 2 .] [The curved surface area, A, of a cone with radius r and slant height l is A = rrl .] l = … cm [4]

4 marks

Mark scheme: 23 18.4 or 18.40… 4 1 2 600  4  6.2 2 M3 for oe 6.2  or M2 for 1 2 4  6.2   6.2 l 600 oe 2 600  4  6.2 2 or or better 6.2  1 2 or M1 for 4  6.2 or  6.2  l  2

This question in 0580/22 May/June 2022

20 k cm B C NOT TO SCALE E A M D The diagram shows a square ABCD with side length k cm. MDE is a sector of a circle, centre D. E lies on the diagonal, BD, of the square. M is the midpoint of AD. Find the percentage of the square that is shaded. … % [4]

4 marks

Mark scheme: 20 90.2 or 90.18… 4 B3 for 9.82[%] OR  2 45  k  2  2  k M3 for 100   k        360  2     oe 45  k  2 2  k oe or M2 for 100      360  2  2 45  k  2 or k     360  2  or 100× (k2 – mπk2 ) ÷ k2 c  k  2 or M1 for    oe 360  2  or for (k2 – mπk2 ) ÷ k2 or for 100× (k2 – mk2 ) ÷ k2

This question in 0580/23 May/June 2022

13 14 Speed (m/s) NOT TO SCALE 0 0 5 15 Time (seconds) The diagram shows the speed–time graph of the first 15 seconds of a car journey. (a) Find the acceleration of the car during the first 5 seconds. … m/s2 [1] (b) Find the distance travelled during the 15 seconds. … m [2]

3 marks

Mark scheme: 13(a) 2.8 oe 1 13(b) 175 2 M1 for a correct relevant area calculation e.g. 1 (15 – 5) 14 or 5  14 oe or better 2

This question in 0580/21 Oct/Nov 2022

10 NOT TO 14 cm SCALE h cm 10 cm The diagram shows a right-angled triangle. (a) Calculate the value of h. h = … [3] (b) Find the perimeter of this triangle. … cm [1]

4 marks

Mark scheme: 10(a) 9.8[0] or 9.797 to 9.798 3 M2 for 142 –102 oe or better or M1 for 102 + h2 = 142 oe or better 10(b) 33.8 or 33.79 to 33.80 1 FT 24 + their (a)

This question in 0580/23 Oct/Nov 2022

12 10 Speed NOT TO (m/s) SCALE 00 12 16 Time (seconds) The diagram shows a speed–time graph for 16 seconds of a car journey. (a) Find the deceleration of the car in the final 4 seconds. … m/s2 [1] (b) Find the total distance travelled during the 16 seconds. … m [2]

3 marks

Mark scheme: 12(a) 2.5 oe 1 12(b) 140 2 M1 for a correct area 1 e.g. 10 × 12, 4 10 , 0.5 × (16 + 12) × 10 2

This question in 0580/22 Oct/Nov 2023

18 A solid cylinder has radius 5 cm and height 8 cm. Calculate the total surface area of the cylinder. … cm2 [4]

4 marks

Mark scheme: 18 408 or 408.4 to 408.5 4 M3 for 2 5 8 + 2   5 2 oe OR M1 for 2 5 8 M1 for 2  52

This question in 0580/22 Oct/Nov 2023

10 5.3 cm S R NOT TO 4.4 cm 3.83.8 cmcm SCALE P Q 8.7 cm The diagram shows a trapezium PQRS. Calculate the area of the trapezium. … cm2 [2]

2 marks

Mark scheme: 10 26.6 2 1 M1 for  ( 5.3 + 8.7 )  3.8 oe 2

This question in 0580/22 Feb/March 2024

20 C NOT TO SCALE 5.6 cm 23° A B 4.9 cm Calculate the area of triangle ABC. … cm2 [2]

2 marks

Mark scheme: 20 5.36 or 5.360 to 5.361 2 1 M1 for  5.6  4.9  sin23 oe 2

This question in 0580/22 Feb/March 2024

7 12.8 cm J L NOT TO SCALE 12.8 cm K The diagram shows a shape made from a triangle JKL and a semicircle with diameter JL. JKL is an isosceles right-angled triangle with JK = JL = 12.8 cm. (a) Calculate the area of this shape. … cm2 [3] (b) Calculate the perimeter of this shape. … cm [4]

7 marks

Mark scheme: 7(a) 146 or 146.2 to 146.3 3 1 M1 for  12.8  12.8 2  1   12.8  2 M1 for       2   2  7(b) 51[.0] or 51.00 to 51.01… 4 1 M1 for  12.8 2 2 2 12.8 M2 for 12.8  12.8 or oe sin 45 or M1 for 12.8 2  12.8 2 oe 12.8 or sin 45  oe KL

This question in 0580/21 May/June 2024

16 The speed–time graph shows information about a car journey. 16 NOT TO Speed SCALE (m/s) 0 0 30 240 320 Time (s) (a) Find the deceleration of the car between 240 and 320 seconds. … m / s2 [1] (b) Calculate the total distance the car travels during the 320 seconds. … m [3]

4 marks

Mark scheme: 16(a) 0.2 oe 1 16(b) 4240 3 1 M2 for   210  320   16 oe 2 or M1 for one area correct

This question in 0580/22 May/June 2024

4 The base of a cuboid measures 10 cm by 7 cm. The volume of the cuboid is 280 cm3. Calculate the height of the cuboid. … cm [2]

2 marks

Mark scheme: 4 4 2 M1 for 10 × 7 × [...] = 280 oe or better

This question in 0580/23 May/June 2024

6 The diagram shows a trapezium. NOT TO 9.5 cm SCALE x cm 6 cm The area of the trapezium is 42 cm 2. Calculate the value of x. x = … [2]

2 marks

Mark scheme: 6 4.5 oe 2 1 M1 for 6 ( x + 9.5 ) = 42 oe 2 2 or 42  −9.5 oe 6

This question in 0580/22 Oct/Nov 2024

14 20 NOT TO SCALE Speed (m/s) 00 10 17 Time (seconds) The diagram shows the speed–time graph for 17 seconds of a car journey. (a) Find the acceleration of the car during the first 10 seconds. … m/s2 [1] (b) Calculate the total distance travelled by the car during the 17 seconds. … m [3]

4 marks

Mark scheme: 14(a) 2 1 14(b) 240 3 M2 for correct complete area statement 1 e.g. × 20 × 10 + 7 × 20 oe 2 or M1 for one correct area

This question in 0580/22 Oct/Nov 2024

19 4.3 cm NOT TO SCALE 11.9 cm A solid is made from a cylinder and a hemisphere, both of radius 4.3 cm. The cylinder has length 11.9 cm. (a) Calculate the volume of the solid. 4 3 [The volume, V, of a sphere with radius r is V = r r .] 3 … cm3 [3] (b) Calculate the total surface area of the solid. [The surface area, A, of a sphere with radius r is A = 4 rr 2 .] … cm2 [4]

7 marks

Mark scheme: 19(a) 858 or 857.7 to 857.9 3  1  4 3 M2 for   π  4.3 + π × 4.32 × 11.9 oe    2  3  1  4 3 or M1 for   π  4.3    2  3 or π × 4.32 × 11.9 19(b) 496 or 495.7 to 495.8… 4 M3 for 1 2 2 4  4.3 +  4.3 + 2  4.3 11.9 2 oe OR M1 for π × 4.32 × k where k is a whole number M1 for 2 × π × 4.3 × 11.9

This question in 0580/22 Oct/Nov 2024

6 10 cm NOT TO SCALE 15 cm 9 cm 8 cm Work out the area of the trapezium. … cm2 [2]

2 marks

Mark scheme: 6 96 2 15 + 9 M1 for  8 oe 2

This question in 0580/22 Feb/March 2025

4 The area of a triangle is 12 cm 2. The length of the base of the triangle is 8 cm. Work out the height of the triangle. … cm [2]

2 marks

Mark scheme: 4 3 2 1 M1 for 8 h = 12 oe 2

This question in 0580/21 Oct/Nov 2025

4 A rectangle measures 5 cm by 19 cm. 19 cm NOT TO 5 cm SCALE Two of these rectangles are joined to make a shape. NOT TO SCALE Work out the perimeter of the shape. … cm [2]

2 marks

Mark scheme: 4 86 2 M1 for 5 × 3 + 19 × 3 + 19 – 5 oe

This question in 0580/23 Oct/Nov 2025

24 (a) Simplify. 125 - 20 … [2] (b) NOT TO 2 2 cm SCALE 3 8 cm The area of this rectangle is k cm 2. Work out the value of k. k = … [2] (c) Rationalise the denominator. 1 7 + 2 … [2]

6 marks

Mark scheme: 24(a) 2 3 5 B1 for 5 5 or 2 5 24(b) 24 2 M1 for 6 16 oe or 6 2  2 2 or 3 8  8 24(c) 2 7 − 2 1 2 1 7 − 2 or 7 ‒ M1 for  oe 3 3 3 7 + 2 7 − 2

This question in 0580/23 Oct/Nov 2025

29 In this question all measurements are in centimetres. R 2R NOT TO SCALE 5R x Solid A Solid B Solid A is made from a cylinder and a hemisphere, both of radius 2R. The cylinder has height 5R. Solid B is a cone of radius R and sloping edge x. The total surface area of solid A is equal to the total surface area of solid B. Find R in terms of x. R = … [5]

5 marks

Mark scheme: 29 x 5 M1 for π (2R)2 oe [R =] M1 for 2 × π × 2R × 5R oe 31 2 4π ( 2 R ) M1 for oe 2 M1 for π × R × x + π × R2 oe

This question in 0580/23 Oct/Nov 2025