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Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s21_qp_220580_s21_ms_220580/22/M/J/21
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
The probability that Jane wins a game is 7 . 10 (a) Find the probability that Jane does not win the game. …… [1] (b) Jane plays this game 50 times. Find the number of times she is expected to win the game. …… [1] 4
Mark scheme
1(a) 3 1 oe 10 1(b) 35 1
Question
Calculate 0.0256 . …… [1]
Mark scheme
2 2 1 0.4 or 5
Question
Emma has 15 mathematics questions to complete. The stem‑and‑leaf diagram shows the time, in minutes, it takes her to complete each question. 0 3 5 6 7 7 8 8 1 1 2 2 3 6 6 6 2 0 Key: 2 | 0 = 20 minutes Complete the table. Mode …… min Median …… min Range …… min [3]
Mark scheme
3 3 B1 for each Mode 16 Median 11 Range 17
Question
Write down an expression for the range of k consecutive integers. …… [1]
Mark scheme
4 k–1 1
Question
(a) Henrik draws this scatter diagram. Put a ring around the one correct statement about this scatter diagram. It shows It is not possible to tell if It shows negative It shows positive no correlation. there is correlation as there correlation. correlation. are not enough points. [1] (b) Each of the four scatter diagrams shows the same set of data. A line has been drawn on each diagram. Diagram A Diagram B Diagram C Diagram D Complete the statement. The line in Diagram …… is the most appropriate line of best fit. [1]
Mark scheme
5(a) It is not possible to tell if there is 1 correlation as there are not enough points. 5(b) C 1
Question
A rhombus has side length 6.5 cm. The rhombus can be constructed by drawing two triangles. Using a ruler and compasses only, construct the rhombus. Leave in your construction arcs. One diagonal of the rhombus has been drawn for you. [2]
Mark scheme
6 Accurate construction of rhombus with 2 B1 for accurate diagram with no/wrong sides 6.5 cm and correct construction arcs. arcs or for one triangle (6.5 cm, 6.5 cm, 8 cm) correctly constructed with correct arcs or for four correct arcs
Question
(a) Complete these statements. The reciprocal of 0.2 is …… A prime number between 90 and 100 is …… [2] (b) 7 0.6 7 8 9 5 From this list, write down an irrational number. …… [1] b2
Mark scheme
7(a) 5 2 B1 for each 97 7(b) 7 1
Question
a= 5c Find b when a = 5.625 and c = 2 . b = …… [2]
Mark scheme
8 [±] 7.5 oe 2 b2 M1 for 5.625 = or better 2×5
Question
Without using a calculator, work out 2 ' 1 3 . 3 7 You must show all your working and give your answer as a fraction in its simplest form. …… [3]
Mark scheme
9 2 7 M2 10 × or B1 for oe 3 10 7 14 30 2 7 ÷ oe with common denominator or M1 for × their 21 21 3 10 7 A1 cao 15
Question
(a) Write 0.006 54 in standard form. …… [1] (b) The number 1.467 # 10 102 is written as an ordinary number. Write down the number of zeros that follow the digit 7. …… [1]
Mark scheme
10(a) 6.54 × 10 –3 1 10(b) 99 1
Question
o o as a fraction in its simplest form. Write 0.04 …… [1]
Mark scheme
11 4 1 cao 99
Question
(a) = {integers greater than 2} A = {prime numbers} B = {odd numbers} C = {square numbers} (i) Describe the type of numbers in the set Bl + C . …… [1] (ii) Complete the set labels on the Venn diagram. [1] (b) D E F Shade the region D l , (E + F)l . [1]
Mark scheme
12(a)(i) Even square numbers oe 1 12(a)(ii) B 1 C A 12(b) D E 1 F
Question
A B x° NOT TO SCALE O D 44° C A, B and C are points on a circle, centre O. DA and DC are tangents. Angle ADC = 44° . Work out the value of x. x = …… [3]
Mark scheme
13 68 3 M1 for correctly identifying 90° angle soi or DAC / DCA = 68 M1 for [obtuse angle] AOC identified as 2x soi or x = their DAC / DCA
Question
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. …… cm 2 [4]
Mark scheme
14 456 or 456.4… 4 18.2 M2 for oe tan 62 18.2 or M1 for tan 62 = oe x M1 for 1 2 ( ( their trapeziumbase ) + 15.4 ) × 18.2 oe
Question
Complete the table showing information about the congruence of pairs of triangles. The first two rows have been completed for you. All diagrams are not to scale. Congruent or Congruence Pair of triangles not congruent criterion Congruent ASA 60° 25° 25° 60° 6 cm 6 cm 3.4 cm 4.8 cm 3 cm Not congruent None 4 cm 3 cm 3.4 cm 7 cm 35° 6.5 cm 6.5 cm 35° 7 cm 4.5 cm 5 cm 5 cm 4 cm 4.5 cm 4 cm 5.2 cm 5.2 cm 35° 65° [3]
Mark scheme
15 Congruent SAS 3 B1 for each correct row Congruent SSS Not congruent None
Question
A is the point (5, 7) and B is the point (9, -1). (a) Find the length AB. …… [3] (b) Find the equation of the line AB. …… [3]
Mark scheme
16(a) 8.94 or 8.944… 3 M2 for ( 9 − 5 )2 + ( −1 − 7 )2 oe or M1 for ( 9 − 5 ) + ( −1 − 7 ) oe 2 2 16(b) y = –2x + 17 oe final answer 3 B2 for answer –2x + 17 OR −1 − 7 M1 for oe 9−5 M1 for correct substitution of (5, 7) or (9, –1) into y = their mx + c oe
Question
Find the gradient of the line that is perpendicular to the line 3y = 4x - 5. …… [2]
Mark scheme
17 3 2 4x − 5 – or – 0.75 M1 for y = or better 4 3 −1 or for their gradient
Question
f (x) = x 2 - 25 g (x) = x + 4 Solve fg (x + 1) = gf (x) . x = …… [4]
Mark scheme
18 [x =] –2.1 oe 4 M3 for x2 + 10x = x2 – 21 or better OR M1 for (x + 1 + 4)2 – 25 or better M1 for x2 – 25 + 4 or better 11 If 0 scored SC1 for answer − oe 6
Question
(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 cm 2 . Calculate the radius of the circle. …… cm [3]
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 M2 for × = r 2 oe or better π 360 − 41 360 − 41 or M1 for 74.5 = × π r 2 oe 360 74.5 360 or for × oe π k
Question
Expand and simplify. (x - 2) (2x + 5) (x + 3) …… [3]
Mark scheme
20 2 x 3 + 7 x 2 − 7 x − 30 final answer 3 B2 for unsimplified expansion with at most one error or for simplified four-term expression of correct form with three terms correct or B1 for correct expansion of two brackets with at least three terms out of four correct
Question
The force of attraction, F Newtons, between two magnets is inversely proportional to the square of the distance, d cm, between the magnets. When d = 1.5, F = 48 . (a) Find an expression for F in terms of d. F = …… [2] (b) When the distance between the two magnets is doubled the new force is n times the original force. Work out the value of n. n = …… [1]
Mark scheme
21(a) 108 2 k [ F =] 2 final answer M1 for F = oe or better d d2 21(b) 1 1 [ n =] or 0.25 4
Question
Simplify. 2x 2 - 5x - 12 3x 2 - 12x …… [4]
Mark scheme
22 2x + 3 4 B2 for ( x − 4 )( 2 x + 3) final answer 3x or B1 for (x + a) (2x + b) where ab = –12 or 2a + b = – 5 or x ( 2 x + 3) − 4 ( 2 x + 3) or 2 x ( x − 4 ) + 3 ( x − 4 ) B1 for 3x( x − 4 )
Question
Find all the solutions of 4 sin x = 3 for 0° G x G 360° . …… [2]
Mark scheme
23 48.6 or 48.59… 2 B1 for each and If 0 scored SC1 for two answers with a sum of 180° 131.4 or 131.4…
Question
Solve. 1 9 + =1 x+1 x+9 x = …… or x = …… [5]
Mark scheme
24 x = 3, x = –3 5 M2 for x + 9 + 9(x + 1) = (x + 1)(x + 9) oe nfww or better or M1 for x + 9 + 9(x + 1) or (x + 1)(x + 9) oe or better B1 for x 2 + x + 9 x + 9 seen M1 dep for [ 0 = ] x 2 − 9 oe simplified or better
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Mathematics 0580/22 for May/June 2021 is out of 70 marks, with 1 hour 30 minutes to answer it.
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