Cambridge IGCSE Mathematics 0580 — 2021 Feb/March Paper 1 · Variant 2
0580/12/F/M/21 · 21 questions · 56 marks · ≈63 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 scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Question 1
1 (a) Complete this statement. The diagram has rotational symmetry of order ................... [1] (b) On the diagram, draw all the lines of symmetry. [2]
Mark scheme: Question Answer Marks Partial Marks 1(a) 2 1 1(b) 2 correct lines 2 B1 for each
Q2 · On the grid, draw a kite
2 (a) On the grid, draw a kite. [1] (b) Write down two geometrical properties of a rhombus. 1. ................................................................................................................................................. 2. ................................................................................................................................................. [2]
Mark scheme: 2(a) Any kite drawn 1 2(b) Two correct geometrical properties 2 B1 for 1 correct property
Q3 · Calculate the value of .729
3 Calculate the value of .729 . ................................................. [1]
Mark scheme: 3 2.7[0] 1
Q4 · Write down a multiple of 9 between 100 and 110
4 Write down a multiple of 9 between 100 and 110. ................................................. [1]
Mark scheme: 4 108 1
Q5 · Tanvi rounds the number 4896
5 (a) Tanvi rounds the number 4896. She writes down 4900. Rahul says Tanvi rounded 4896 correct to the nearest 100. Explain why Rahul cannot be certain that Tanvi rounded 4896 correct to the nearest 100. ..................................................................................................................................................... ..................................................................................................................................................... [1] (b) Calculate. 6.4 # 42 17.9 - 6.1 Give your answer correct to 3 decimal places. ................................................. [2]
Mark scheme: 5(a) A correct alternative rounding 1 e.g. Tanvi rounded to nearest 10 5(b) 8.678 2 512 40 M1 for or 859 or 8.68 or 8.67 or 59 8.677…
Q6 · These are the heights of four sisters
6 These are the heights of four sisters. 1.61 m 1.65 m 1.53 m 1.58 m (a) Work out the range of these heights. Give your answer in centimetres. ............................................ cm [2] (b) The four sisters have a brother. The range of the five heights is 18 cm. Work out the two possible heights of the brother. .................... m or .................... m [2]
Mark scheme: 6(a) 12 2 M1 for 1.65−1.53 soi by figs 12 or B1 for a clear subtraction seen of any 2 heights correctly converted to cm 6(b) 1.47 1.71 2 B1 for each or M1 for 1.65 − 0.18 or 1.53 + 0.18
Question 7
7 Work out. - 3 (a) 2 e 7o [1] f p 8 - 5 (b) + e- 6o e 2o [1] f p
Mark scheme: 7(a) − 6 1 14 7(b) 3 1 −4
Q8 · Sahil and Anika share $78 in the ratio 5 : 8
8 Sahil and Anika share $78 in the ratio 5 : 8. Calculate the amount each receives. Sahil $ ................................................. Anika $ ................................................. [2]
Mark scheme: 8 30 2 78 M1 for × k oe where k = 1, 5 or 8 48 5 + 8
Q9 · NOT TO SCALE 3 cm 4 cm The diagram shows a prism
9 NOT TO SCALE 3 cm 4 cm The diagram shows a prism. The cross-section of the prism is an equilateral triangle. Draw a net of the prism on the 1cm2 grid. [3]
Mark scheme: 9 Correct net 3 B1 for one correct face drawn B1 for 3 rectangles and 2 triangles drawn in correct places, but not the correct size
Q10 · The number of passengers on a bus is recorded each day for 14 days
10 The number of passengers on a bus is recorded each day for 14 days. 15 18 22 17 35 38 24 19 19 24 25 31 36 29 Complete the stem-and-leaf diagram. 1 2 3 Key: 1q5 represents 15 passengers [2]
Mark scheme: 10 2 B1 for two rows correct or for a fully correct 1 5 7 8 9 9 unordered stem-and-leaf diagram or for a correct diagram with one leaf incorrect or 2 2 4 4 5 9 omitted 3 1 5 6 8
Q11 · The mean of nine numbers is 17
11 The mean of nine numbers is 17. Seven of these numbers add to 132. The other two numbers have a difference of 5. Find the two numbers with a difference of 5. ...................... , ....................... [3]
Mark scheme: 11 8 13 3 9 × 17 − 132 M2 for 2 or M1 for 9 × 17
Question 12
12 Factorise completely. 9t 2 w - 3t ................................................. [2]
Mark scheme: 12 3 t ( 3 tw − 1 ) final answer 2 B1 for 3 ( 3t 2 w − t ) or for t ( 9 tw − 3 )
Q13 · Saanvi makes some biscuits
13 Saanvi makes some biscuits. 5 She sells of the biscuits. 13 She now has 96 biscuits left. Work out the total number of biscuits Saanvi makes. ................................................. [3]
Mark scheme: 13 156 3 8 M1 for 96 = x 13 M1 for 96 × 13 = 8x or better
Q14 · These are the first four terms of a sequence
14 These are the first four terms of a sequence. 29 22 15 8 (a) Write down the next two terms. ....................... , ....................... [2] (b) Find the nth term. ................................................. [2]
Mark scheme: 14(a) 1 −6 2 B1 for each If 0 scored, SC1 for two terms with a difference of −7 14(b) 36 − 7n oe final answer 2 B1 for 36 + jn , j ≠ 0 or k − 7n or for correct answer shown in working and then spoilt
Q15 · Find the lowest common multiple (LCM) of 18 and 21
15 Find the lowest common multiple (LCM) of 18 and 21. ................................................. [2]
Mark scheme: 15 126 2 B1 for 126k as final answer k ≠ 1 or M1 for [18 = ] 2 × 3 × 3 and [ 21 = ] 3 × 7 or 2 correct factor trees or 18, 36, 54, … and 21, 42, 63,.. or 2 × 3 × 3 × 7 or better
Q16 · Write 567 000 000 in standard form
16 (a) Write 567 000 000 in standard form. ................................................. [1] (b) .65 # 10 -2 .61 # 10 -1 .62 # 102 .679 # 101 .618 # 102 .635 # 10 -2 Calculate the product of the largest number and the smallest number from this list. Give your answer in standard form. ................................................. [2]
Mark scheme: 16(a) 5.67 × 10 8 1 16(b) 3.937 × 101 2 M1 for 6.35 × 10 − 2 × k or j × 6 .2 × 1 0 2 where j and k are another number from the list or B1 for 6.35 × 10 − 2 and 6.2 × 10 2 selected or for figs 3937
Q17 · P NOT TO A SCALE x cm 1.61 cm R 3.2 cm Q C 2.8 cm B Triangle ABC is mathematically…
17 P NOT TO A SCALE x cm 1.61 cm R 3.2 cm Q C 2.8 cm B Triangle ABC is mathematically similar to triangle PQR. Find the value of x. x = ................................................. [2]
Mark scheme: 17 1.84 2 1.61 2.8 M1 for = oe x 3.2
Question 18
18 (a) Simplify. (i) x 12 ' x 3 ................................................. [1] 5 (ii) ( y2 ) ................................................. [1] p 1 (b) 3 = 81 Find the value of p. p = ................................................. [1]
Mark scheme: 18(a)(i) 𝑥ଽ cao 1 18(a)(ii) 𝑦ଵ cao 1 18(b) −4 1
Q19 · 219 Without using a calculator, work out 2 # 3
1 219 Without using a calculator, work out 2 # 3 . 4 3 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 19 9 11 M1 and oe improper fractions 4 3 99 A1 oe improper fraction 12 1 A1 dep on 1st A1 84cao final answer 9 11 If M0 scored, SC1 for or oe improper 4 3 fraction
Q20 · Solve the simultaneous equations
20 Solve the simultaneous equations. You must show all your working. 5x + 6y = 14 2x + 8y = 7 x = ................................................. y = ................................................. [4]
Mark scheme: 20 Correctly equating one set of M1 or making x or y the subject of one equation coefficients correctly Correct method to eliminate one M1 or substitution for x or y for their rearranged variable formula x = 2.5 A2 A1 for one correct value If M0 scored, SC1 for 2 values satisfying one y = 0.25 of the original equations
Q21 · C NOT TO 6 cm SCALE O B 5 cm A The diagram shows a shape made from a quarter-circle, OAB…
21 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]
Mark scheme: 21 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×
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.
2Types of number2Algebraic manipulation1Area and perimeter1Compound shapes and parts of shapes1Equations1Fractions, decimals and percentages1Geometrical terms1Indices I1Introduction to algebra1Percentages1Powers and roots1Ratio and proportion1Sequences1Similarity1Standard form1Statistical charts and diagrams1Symmetry1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2021 Feb/March, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.