Cambridge IGCSE Mathematics (9-1) 0980 — 2021 May/June Paper 2 · Variant 2
0980/22/M/J/21 · 24 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 paper16 pages
Mark scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The probability that Jane wins a game is
1 The probability that Jane wins a game is . 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]
Mark scheme: Question Answer Marks Partial Marks 1(a) 3 1 oe 10 1(b) 35 1
Question 2
2 Calculate 4 .00256 . ................................................. [1]
Mark scheme: 2 2 1 0.4 or 5
Q3 · Emma has 15 mathematics questions to complete
3 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
Q4 · Write down an expression for the range of k consecutive integers
4 Write down an expression for the range of k consecutive integers. ................................................. [1]
Mark scheme: 4 k – 1 1
Q5 · Henrik draws this scatter diagram
5 (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
Q6 · A rhombus has side length 6.5 cm
6 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 7
7 (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]
Mark scheme: 7(a) 5 2 B1 for each 97 7(b) 7 1
Q8 · A = 5c Find b when a = 5.625 and c = 2
8 a = 5c Find b when a = 5.625 and c = 2 . b = ................................................. [2]
Mark scheme: 8 [±] 7.5 oe 2 b 2 M1 for 5.625 = or better 2 × 5
Q9 · Without using a calculator, work out ' 1
9 Without using a calculator, work out ' 1 . 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
Q10 · Write 0.006 54 in standard form
10 (a) Write 0.006 54 in standard form. ................................................. [1] (b) The number .1467 # 10102 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
Q11 · Write .004o o as a fraction in its simplest form
11 Write .004o o as a fraction in its simplest form. ................................................. [1]
Mark scheme: 11 4 1 cao 99
Q12 · = {integers greater than 2} A = {prime numbers} B = {odd numbers} C = {square numbers}…
12 (a) = {integers greater than 2} A = {prime numbers} B = {odd numbers} C = {square numbers} (i) Describe the type of numbers in the set B l + 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) 1 B C A 12(b) 1 D E F
Q13 · A B x° NOT TO SCALE O D 44° C A, B and C are points on a circle, centre O
13 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
Q14 · 15.4 cm NOT TO SCALE 18.2 cm 62° The diagram shows a trapezium
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]
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
Q15 · Complete the table showing information about the congruence of pairs of triangles
15 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
Q16 · A is the point (5, 7) and B is the point (9, - 1)
16 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 2 2 M2 for ( 9 − 5 ) + ( −−1 7 ) oe 2 2 or M1 for ( 9 − 5 ) + ( −−1 7 ) oe 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
Q17 · Find the gradient of the line that is perpendicular to the line 3y = 4x - 5
17 Find the gradient of the line that is perpendicular to the line 3y = 4x - 5 . ................................................. [2]
Mark scheme: 17 3 2 4 x − 5 – or – 0.75 M1 for y = or better 4 3 −1 or for their gradient
Q18 · F ( x) = x 2 - 25 g ( x) = x + 4 Solve fg (x + 1 ) = gf (x)
18 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
Q19 · NOT TO A SCALE B C The diagram shows a shape made from an equilateral triangle ABC and a…
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]
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
Question 20
20 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
Q21 · The force of attraction, F Newtons, between two magnets is inversely proportional to the…
21 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 = 2 oe or better d d 21(b) 1 [ n = ]1 or 0.25 4
Question 22
22 Simplify. 2x 2 - 5x - 12 3x 2 - 12x ................................................. [4]
Mark scheme: 22 2 x + 3 4 B2 for ( x − 4 )( 2 x + 3 ) final answer 3 x 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 3 x ( x − 4 )
Q23 · Find all the solutions of 4 sinx = 3 for 0° G x G 360 °
23 Find all the solutions of 4 sinx = 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 24
24 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
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Algebraic manipulation1Averages and measures of spread1Averages and range1Circle theorems I1Circles, arcs and sectors1Equations1Fractions, decimals and percentages1Functions1Geometrical constructions1Geometrical terms1Introduction to probability1Length and midpoint1Perpendicular lines1Powers and roots1Proportion1Right-angled triangles1Scatter diagrams1Sets1Standard form1The four operations1Trigonometric functions1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2021 May/June, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.