Cambridge IGCSE Mathematics 0580 — 2020 May/June Paper 2 · Variant 3
0580/23/M/J/20 · 21 questions · 70 marks · ≈79 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper12 pages
Mark scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · 32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8…
1 32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8, ................................................. [1] (b) a square number, ................................................. [1] (c) a prime number. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 32 1 1(b) 36 1 1(c) 37 1
Q2 · 6.5 cm NOT TO SCALE 4 cm 8 cm The diagram shows a cuboid
2 6.5 cm NOT TO SCALE 4 cm 8 cm The diagram shows a cuboid. Calculate the volume of the cuboid. .......................................... cm3 [1]
Mark scheme: 2 208 1
Q3 · A NOT TO SCALE 32° B C Triangle ABC is isosceles
3 A NOT TO SCALE 32° B C Triangle ABC is isosceles. Angle ABC = 32° and AB = AC. Find angle BAC. Angle BAC = ................................................. [2]
Mark scheme: 3 116 2 M1 for angle ACB = 32 soi
Q4 · A train journey takes 5 hours 54 minutes
4 A train journey takes 5 hours 54 minutes. (a) The journey starts at 09 15. Find the time that the journey ends. ................................................. [1] (b) The average speed of the train for this journey is 80 km/h. Calculate the distance travelled. ........................................... km [2]
Mark scheme: 4(a) 15 09 1 Accept 3 09 pm 4(b) 472 2 M1 for 80 × their time oe or B1 for time = 5.9
Q5 · Sofia has a bag containing 8 blue beads and 7 red beads only
5 Sofia has a bag containing 8 blue beads and 7 red beads only. She takes one bead out of the bag at random and replaces it. She does this 90 times. Find the number of times she expects to take a red bead. ................................................. [2]
Mark scheme: 5 42 2 7 M1 for [× 90] 15
Question 6
6 Simplify. (a) p 2 # p 4 ................................................. [1] (b) m 15 ' m 5 ................................................. [1] (c) ( k3 ) 5 ................................................. [1]
Mark scheme: 6(a) p 6 1 6(b) m10 1 6(c) k 15 1
Q7 · 27 Without using a calculator, work out 3 - 2
1 27 Without using a calculator, work out 3 - 2 . 4 3 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 7 Correct common denominator M1 Correct method M1 3 − 8 12 + 3 − 8 e.g. 1 or or 12 12 ((3 × 4) + 1) × 3 − ( ( 2 × 3 ) + 2 ) × 4 39 − 32 or 12 12 7 A1 cao 12
Q8 · The bearing of X from Y is 274°
8 The bearing of X from Y is 274°. Calculate the bearing of Y from X. ................................................. [2]
Mark scheme: 8 [0]94 2 M1 for 86 or 274 – 180 or for sketch with 274 marked correctly
Q9 · Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°
9 Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°. Give your answer in square centimetres. .......................................... cm2 [3]
Mark scheme: 9 15.5 or 15.48 to 15.49 3 B2 for 1550 or 1548 to 1549 42 2 or M2 for × π × 6.5 360 42 2 or M1 for × π × 65 360
Q10 · A solid cylinder has radius 3 cm and height 4.5 cm
10 A solid cylinder has radius 3 cm and height 4.5 cm. Calculate the total surface area of the cylinder. .......................................... cm2 [4]
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]
Q11 · Y is directly proportional to the cube root of ( x + 3 )
11 y is directly proportional to the cube root of ( x + 3 ) . When x = 5, y = 2. 3 Find y when x = 24. y = ................................................. [3]
Mark scheme: 11 [y =] 1 3 M1 for y = k × 3 x + 3 M1 for y = their k × 3 24 + 3 OR y 2 1 M2 for = × oe 3 24 + 3 3 3 5 + 3
Q12 · The total perimeter of a semicircle is 19.02 cm
12 The total perimeter of a semicircle is 19.02 cm. Calculate the radius of the semicircle. ............................................ cm [3]
Mark scheme: 12 3.7[0] or 3.689 to 3.699… 3 19.02 M2 for 2 + π or M1 for 2 r + π r [ = 19.02] oe
Q13 · Y 4 3 2 R 1 x 0 1 2 3 4 Write down the three inequalities that define the region R
13 y 4 3 2 R 1 x 0 1 2 3 4 Write down the three inequalities that define the region R. ................................................. ................................................. ................................................. [4]
Mark scheme: 13 x + y < 4 4 B3 for any two correct or B1 for y ⩾ 1.5 y ⩾ 1.5 B2 for x + y < 4 or y ⩽ 2x + 1 or x + y = 4 and y = 2x + 1 or with incorrect y ⩽ 2x + 1 inequality signs or B1 for x + y = 4 or y = 2x + 1 or SC3 for > instead of ⩾ etc.
Q14 · The diagram shows the speed–time graph of a train journey between two stations
14 The diagram shows the speed–time graph of a train journey between two stations. 12 NOT TO SCALE Speed (m/s) 0 0 40 250 300 Time (s) (a) Find the acceleration of the train during the first 40 seconds. ......................................... m/s2 [1] (b) Calculate the distance between the two stations. ............................................. m [3]
Mark scheme: 14(a) 0.3 oe 1 14(b) 3060 3 1 M2 for ( 300 + 210 ) × 12 oe 2 or M1 for one correct part area
Q15 · The table shows the amount of money, $x, given to a charity by each of 60 people
15 The table shows the amount of money, $x, given to a charity by each of 60 people. Amount ($x) 0 1 x G 20 20 1 x G 25 25 1 x G 35 35 1 x G 50 50 1 x G 100 Frequency 21 16 6 10 7 Calculate an estimate of the mean. $ ................................................. [4]
Mark scheme: 15 28.33 or 28.3 or 28.33… 4 M1 for midpoints soi M1 for use of ∑fx M1 dep for ∑fx ÷ 60
Q16 · Paddy and Anna each invest $2000 for 5 years
16 Paddy and Anna each invest $2000 for 5 years. Paddy earns simple interest at a rate of 1.25% per year. Anna earns compound interest at a rate of r % per year. At the end of 5 years, Paddy’s investment is worth the same as Anna’s investment. Calculate the value of r. r = ................................................. [5]
Mark scheme: 16 1.22 or 1.219 to 1.22 5 2000 × 5 × 1.25 M1 for SI = 100 2000 + their125 M3 for 5 2000 or M2 for 2000 k 5 = 2000 + their SI or M1 for CI = 2000k 5
Q17 · NOT TO SCALE m cm 8 cm The diagram shows two shapes that are mathematically similar
17 NOT TO SCALE m cm 8 cm The diagram shows two shapes that are mathematically similar. The smaller shape has area 52.5 cm2 and the larger shape has area 134.4 cm2. Calculate the value of m. m = ................................................. [3]
Mark scheme: 17 5 3 52.5 M2 for 8 × oe 134.4 52.5 134.4 or M1 for or oe 134.4 52.5
Q18 · Write x 2 - 18 x - 27 in the form ( x + k) 2 + h
18 (a) Write x 2 - 18 x - 27 in the form ( x + k) 2 + h . ................................................. [2] (b) Use your answer to part (a) to solve the equation x 2 - 18x - 27 = 0 . x = .................... or x = .................... [2]
Mark scheme: 18(a) ( x − 9 )2 − 108 2 B1 for ( x + h ) 2 − 108 or ( x − 9 ) 2 + h or k = − 9 18(b) 19.4 or 19.39… 2 M1FT x − their 9 = ± their108 −1.39 or −1.392… A1 for 9 ± 108 or 9 ± 6 3
Q19 · In a class of 40 students: • 28 wear glasses (G ) • 13 have driving lessons (D) • 4 do…
19 (a) In a class of 40 students: • 28 wear glasses (G ) • 13 have driving lessons (D) • 4 do not wear glasses and do not have driving lessons. G D ....... ....... ....... ....... (i) Complete the Venn diagram. [2] (ii) Use set notation to describe the region that contains a total of 32 students. ................................................. [1] (b) This Venn diagram shows information about the number of students who play basketball (B), football (F ) and hockey (H ). B F 7 2 6 5 3 4 12 8 H Find n (( B , F ) + H l) . ................................................. [1] (c) P Q R Shade the region P , ( Q + R ) l. [1]
Mark scheme: 19(a)(i) 2 B1 for two correct G D 23 5 8 4 19(a)(ii) G ∪ D ′ oe 1 19(b) 15 1 19(c) 1 Shade whole rectangle except for region containing x x
Q20 · V NOT TO SCALE 18.6 cm D C M A 11 cm B The diagram shows a pyramid with a square base ABCD
20 V NOT TO SCALE 18.6 cm D C M A 11 cm B The diagram shows a pyramid with a square base ABCD. The diagonals AC and BD intersect at M. The vertex V is vertically above M. AB = 11 cm and AV = 18.6 cm. Calculate the angle that AV makes with the base. ................................................. [4] Question 21 is printed on the next page.
Mark scheme: 20 65.3 or 65.28.. 4 1 2 2 11 + 11 2 M3 for cos = or better 186. 1 2 2 or M2 for AM = 11 + 11 oe 2 or M1 for AC2 = 112 + 112 If 0 scored, SC1 for identifying angle VAM
Q21 · P Q b NOT TO SCALE O R a V S T O is the origin and OPQR is a parallelogram
21 P Q b NOT TO SCALE O R a V S T O is the origin and OPQR is a parallelogram. SOP is a straight line with SO = OP. TRQ is a straight line with TR = RQ. STV is a straight line and ST : TV = 2 : 1. OR = a and OP = b . (a) Find, in terms of a and b, in its simplest form, (i) the position vector of T, ................................................. [2] (ii) RV . RV = ................................................. [1] (b) Show that PT is parallel to RV. [2]
Mark scheme: 21(a)(i) a − b or –b + a 2 B1 for a correct route or identifying OT 21(a)(ii) 1 1 a− b or – b + a 1 2 2 21(b) PT = a − 2b oe M1 PT = 2 RV oe A1 Dep on correct vector RV Accept in words
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Circles, arcs and sectors2Ratio and proportion2Algebraic manipulation1Angles1Area and perimeter1Averages and measures of spread1Fractions, decimals and percentages1Indices I1Inequalities1Introduction to probability1Right-angled triangles1Sets1Surface area and volume1Time1Types of number1Vectors in two dimensions1