Cambridge IGCSE Mathematics 0580 — 2016 Feb/March Paper 2 · Variant 2
0580/22/F/M/16 · 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Solve (x – 7)(x + 4) = 0
1 Solve (x – 7)(x + 4) = 0. x = ................................. or x = .................................[1]
Mark scheme: Qu. Answers Mark Part Marks 1 7, − 4 1
Q2 · Factorise 2x – 4xy
2 Factorise 2x – 4xy. ................................................... [2]
Mark scheme: 2 2x(1 – 2y) final answer 2 M1 for 2(x – 2xy) or x(2 – 4y) or for correct answer then spoilt 0 9
Q3 · C NOT TO SCALE 3.5 m B A 0.9 m Calculate angle BAC
3 C NOT TO SCALE 3.5 m B A 0.9 m Calculate angle BAC. Angle BAC = .................................................. [2]
Mark scheme: 0.9 3 75.1 or 75.09 to 75.10 2 M1 for cos […= ] 3.5
Question 4
4 Solve the inequality. 6n + 3 8n ................................................... [2]
Mark scheme: 4 n < 1.5 oe final answer 2 B1 for 1.5 oe in answer or M1 for 3 > 8n − 6n oe 5 2 12 4
Q5 · Triangle ABC is similar to triangle PQR
5 Triangle ABC is similar to triangle PQR. Q B NOT TO SCALE 5.2 cm A C P R 12.4 cm 21.7 cm Find PQ. PQ = ............................................ cm [2]
Mark scheme: 5.2 12.4 5 9.1 oe 2 M1 for = oe PQ 21.7 4
Q6 · Write the recurring decimal .04o as a fraction
6 Write the recurring decimal .04o as a fraction. [ .04o means 0.444…] ................................................... [2]
Mark scheme: 4 6 oe, must be fraction 2 M1 for 10 × 0.4 − 0.4 oe 9
Q7 · 22.3 cm NOT TO SCALE 25° 27.6 cm Calculate the area of this triangle
7 22.3 cm NOT TO SCALE 25° 27.6 cm Calculate the area of this triangle. ............................................cm2 [2]
Mark scheme: 7 130 or 130.0 to 130.1 2 M1 for ½ × 22.3 × 27.6 × sin25 1 7 2 1 a b 7 2
Q8 · - 2 8 Find the inverse of the matrix c- 8 7m
3 - 2 8 Find the inverse of the matrix c- 8 7m. [2] f p
Mark scheme: 1 7 2 1 a b 7 2 8 oe isw 2 M1 for soi or k k ≠ 0 5 8 3 5 c d 8 3 or det = 5 soi 35( or 95) 39 35k ( or 95k ) 39 k
Q9 · Without using your calculator, work out 1 7 + 13
9 Without using your calculator, work out 1 7 + 13 . 12 20 You must show all your working and give your answer as a mixed number in its simplest form. ................................................... [3]
Mark scheme: 35( or 95) 39 35k ( or 95k ) 39 k 9 + M1 accept + 60 60 60 k 60 k 7 67 134 k 74 k 14 k 230 A2 or A1 for 30 or 60 k or 160 k or 2 60 k 1 6 × 20000 2
Q10 · The scale on a map is 1 : 20 000
10 The scale on a map is 1 : 20 000. The area of a lake on the map is 1.6 square centimetres. Calculate the actual area of the lake. Give your answer in square metres. ..............................................m2 [3]
Mark scheme: 1.6 × 20000 10 64 000 3 M2 for 2 oe 100 or M1 for figs 64 in answer or 1 cm2 = 40 000 m2
Q11 · A NOT TO SCALE O 38° 25 cm B The diagram shows a sector of a circle, centre O, radius 25…
11 A NOT TO SCALE O 38° 25 cm B The diagram shows a sector of a circle, centre O, radius 25 cm. The sector angle is 38°. Calculate the length of the arc AB. Give your answer correct to 4 significant figures. AB = ............................................ cm [3]
Mark scheme: 11 16.58 cao 3 B2 for 16.6 or 16.580 to 16.583 final answer or 16.58 not as final answer or 38 M1 for ×2×π×25 360 and B1 for rounding their more accurate answer correctly to 4sf
Q12 · A metal pole is 500 cm long, correct to the nearest centimetre
12 A metal pole is 500 cm long, correct to the nearest centimetre. The pole is cut into rods each of length 5.8 cm, correct to the nearest millimetre. Calculate the largest number of rods that the pole can be cut into. ................................................... [3]
Mark scheme: 12 87 cao nfww 3 B2 for 87.04…. or 87.0 nfww or M1 for 500.5 or 5.75 seen or for (500 + 0.5) ÷ (5.8 – 0.05) and B1 for truncating their decimal answer to an integer 5 2 5 2
Q13 · Write 2016 as the product of prime factors
13 (a) Write 2016 as the product of prime factors. ................................................... [3] (b) Write 2016 in standard form. ................................................... [1]
Mark scheme: 13 (a) 2 5 × 32 × 7 oe final answer 3 B2 for product of two of 2 5 , 3 2 , 7 or B1 for 2, 3 and 7 seen or M1 for 2 × 1008 or 3 × 672 or 7 × 288 soi (b) 2.016 × 10 3 1 8 7 8 k k 7
Question 14
14 Simplify. (a) x 3 y 4 # x 5 y 3 ................................................... [2] (b) ^3p 2 m 5h3 ................................................... [2]
Mark scheme: 14 (a) x 8 y 7 final answer 2 B1 for answer x 8 y k or kx y 7 (k ≠ 0) (b) 27p 6 m15 final answer 2 B1 for 2 correct of 27, p 6 , m15 in a product as answer 2.8 2 + 3.6 2 − 5.32
Q15 · P° 2.8 cm 3.6 cm NOT TO SCALE 5.3 cm Find the value of p
15 p° 2.8 cm 3.6 cm NOT TO SCALE 5.3 cm Find the value of p. p = .................................................. [4]
Mark scheme: 2.8 + 3.6 5.3 15 111.2 or 111.1 to 111.2 4 M2 for [cos =] 2 × 2.8 × 3.6 or M1 for implicit form A1 for [cos =] −0.362 to −0.361
Q16 · Raj measures the height, h cm, of 70 plants
16 Raj measures the height, h cm, of 70 plants. The table shows the information. Height (h cm) 10 h 20 20 h 40 40 h 50 50 h 60 60 h 90 Frequency 7 15 27 13 8 Calculate an estimate of the mean height of the plants. ............................................................ cm [4]
Mark scheme: 16 44.1 or 44.07... 4 M1 for 4 of mid-values 15 30 45 55 75 soi M1 for ∑fx for any x in intervals including boundaries M1 dep for ∑fx ÷ 70 Dep on 2nd M mark earned
Q17 · Solve the equation 3x 2 - 11x + 4 = 0
17 Solve the equation 3x 2 - 11x + 4 = 0 . Show all your working and give your answers correct to 2 decimal places. x = ............................ or x = ............................[4]
Mark scheme: ( ) ( ) ( )( ) 2 17 2 B1 for ( −11) − 4(3)(4) or better 2 × 3 p + q p − q and, if in form or , r r B1 for p = −(−11) and r = 2(3) 0.41 and 3.26 final ans cao B1B1 SC1 for 0.4 and 3.3 or 0.409... and 3.257... or − 0.41 and −3.26 or 0.41 and 3.26 seen in working
Q18 · X° NOT TO SCALE 47° Find the value of x
18 (a) x° NOT TO SCALE 47° Find the value of x. x = .................................................. [1] (b) 85° 115° NOT TO SCALE 97° y° Find the value of y. y = .................................................. [2] (c) 58° NOT TO z° SCALE O The diagram shows a circle, centre O. Find the value of z. z = .................................................. [2]
Mark scheme: 18 (a) 47 1 (b) 117 2 M1 for 360 − (115 + 85 + 97) (c) 244 2 B1 for 116 seen at centre or 122 seen at circumference
Q19 · Y 4 3 2 1 x –3 –2 –1 0 1 2 3 4 –1 Find the four inequalities that define the region that…
19 y 4 3 2 1 x –3 –2 –1 0 1 2 3 4 –1 Find the four inequalities that define the region that is not shaded. ................................................... ................................................... ................................................... ................................................... [5]
Mark scheme: 19 y < 2 oe and x ⩾ –2 oe 2 B1 for either correct 1 1 y ⩾ x + 1 oe and y ⩽ – x + 3 oe 3 B2 for either y ⩾ x + 1 oe or y ⩽ – x + 3 oe 2 2 1 or SC2 for y = x + 1 oe and y = – x + 3 oe 2 1 or SC1 for y = x + 1 oe or y = – x + 3 oe 2 1 or SC4 for y ⩽ 2 oe , x > –2 oe, y > x + 1 oe 2 and y < – x + 3 oe
Q20 · The nth term of a sequence is an 2 + bn
20 The nth term of a sequence is an 2 + bn . (a) Write down an expression, in terms of a and b, for the 3rd term. ................................................... [1] (b) The 3rd term of this sequence is 21 and the 6th term is 96. Find the value of a and the value of b. You must show all your working. a = .................................................. b = .................................................. [4] Question 21 is printed on the next page.
Mark scheme: 20 (a) 9a + 3b 1 (b) 36a + 6b = 96 or 9a + 3b = 21 B1 for correct method to eliminate M1 one variable a = 3 A1 If M0 A0 A0 scored SC1 for b = −2 A1 2 values satisfying 36a + 6b = 96 or 9a + 3b = 21 or if no working shown, but 2 correct answers given
Q21 · Dan either walks or cycles to school
21 Dan either walks or cycles to school. The probability that he cycles to school is 1 . 3 (a) Write down the probability that Dan walks to school. ................................................... [1] (b) When Dan cycles to school the probability that he is late is 1 . 8 When Dan walks to school the probability that he is late is 3 . 8 Complete the tree diagram. 1 Late 8 Cycles 1 3 Not late .......... Late 3 8 .......... Walks Not late .......... [2] (c) Calculate the probability that (i) Dan cycles to school and is late, ................................................... [2] (ii) Dan is not late. ................................................... [3]
Mark scheme: 2 21 (a) oe 1 3 2 7 5 7 5 (b) their , , oe 2 B1 for either or 3 8 8 8 8 1 1 1 (c) (i) oe 2 M1 for × seen 24 3 8 17 1 7 2 5 (ii) oe 3 M2FT for × + × 24 3 8 3 8 1 7 2 5 or M1FT for × or × 3 8 3 8
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.
3Fractions, decimals and percentages2Inequalities2Algebraic manipulation1Angles1Area and perimeter1Averages and measures of spread1Circles, arcs and sectors1Indices I1Introduction to algebra1Limits of accuracy1Non-right-angled triangles1Probability of combined events1Ratio and proportion1Right-angled triangles1Similarity1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2016 Feb/March, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.