Question 1
Question
32 33 34 35 36 37 38 39 From this list of numbers, write down (a) a multiple of 8, (b) a square number, (c) a prime number�
Mark scheme
1(a) 32 1 1(b) 36 1 1(c) 37 1
Mathematics 0580/23 May/June 2020: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2020. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s20_qp_230580_s20_ms_230580/23/M/J/20
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/23/M/J/20
0580/23 mark scheme, question by question
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question 2
Question
6.5 cm NOT TO SCALE 4 cm 8 cm The diagram shows a cuboid� Calculate the volume of the cuboid�
Mark scheme
2 208 1
Question 3
Question
A NOT TO SCALE 32° B C Triangle ABC is isosceles� Angle ABC = 32° and AB = AC� Find angle BAC�
Mark scheme
3 116 2 M1 for angle ACB = 32 soi
Question 4
Question
A train journey takes 5 hours 54 minutes� (a) The journey starts at 09 15� Find the time that the journey ends� (b) The average speed of the train for this journey is 80 km/h� Calculate the distance travelled�
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
Question 5
Question
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�
Mark scheme
5 42 2 7 M1 for [× 90] 15
Question 6
Question
Simplify� (a) p2 # p4 (b) m 15 ' m 5 (c) (k 3) 5 1 2
Mark scheme
6(a) p6 1 6(b) m10 1 6(c) k 15 1
Question 7
Question
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�
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
Question 8
Question
The bearing of X from Y is 274°� Calculate the bearing of Y from X�
Mark scheme
8 [0]94 2 M1 for 86 or 274 – 180 or for sketch with 274 marked correctly
Question 9
Question
Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°� Give your answer in square centimetres�
Mark scheme
9 15.5 or 15.48 to 15.49 3 B2 for 1550 or 1548 to 1549 42 or M2 for × π × 6.52 360 42 or M1 for × π × 652 360
Question 10
Question
A solid cylinder has radius 3 cm and height 4�5 cm� Calculate the total surface area of the cylinder�
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]
Question 11
Question
y is directly proportional to the cube root of (x + 3) � 2 When x = 5, y = � 3 Find y when x = 24�
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 3 = ×3 oe 24 + 3 3 5+3
Question 12
Question
The total perimeter of a semicircle is 19�02 cm� Calculate the radius of the semicircle�
Mark scheme
12 3.7[0] or 3.689 to 3.699… 3 19.02 M2 for 2+ π or M1 for 2r + π r [ = 19.02] oe
Question 13
Question
y 4 3 2 R 1 0 1 2 3 4 x Write down the three inequalities that define the region R�
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.
Question 14
Question
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� (b) Calculate the distance between the two stations�
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
Question 15
Question
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�
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
Question 16
Question
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�
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 2000k 5 = 2000 + their SI or M1 for CI = 2000k 5
Question 17
Question
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�
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
Question 18
Question
(a) Write x 2 - 18x - 27 in the form (x + k) 2 + h � (b) Use your answer to part (a) to solve the equation x 2 - 18x - 27 = 0 �
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
Question 193 marks
Question
(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� (b) This Venn diagram shows information about the number of students who play basketball (B), football (F ) and hockey (H )� B F 2 7 6 5 3 4 12 8 H Find n ((B , F ) + H l) � (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
Question 20
Question
V NOT TO SCALE 18.6 cm D C M A B 11 cm 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� Question 21 is printed on the next page.
Mark scheme
20 65.3 or 65.28.. 4 1 112 + 112 M3 for cos = 2 or better 18.6 1 or M2 for AM = 112 + 112 oe 2 or M1 for AC2 = 112 + 112 If 0 scored, SC1 for identifying angle VAM ρ
Question 212 marks
Question
P Q b NOT TO SCALE O R a S V 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, (ii) RV � (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 ρ 21(b) PT = a − 2b oe M1 ρ ρ PT = 2 RV oe A1 Dep on correct vector RV Accept in words
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Where can I find the 0580/23 May/June 2020 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/23, May/June 2020 (0580_s20_ms_23), and the question paper (0580_s20_qp_23), to read or download, with each question's marking points written out underneath.
How many marks is 0580/23 out of?
Mathematics 0580/23 for May/June 2020 is out of 70 marks, with 1 hour 30 minutes to answer it.
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