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Mathematics 0580/22 May/June 2019: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), May/June 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_s19_qp_220580_s19_ms_220580/22/M/J/19

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Paper
Paper 2 (Extended)
Total marks
70
Time
1 hour 30 minutes
Code on the paper
0580/22/M/J/19
0580_s19_ms_22.pdf

0580/22 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 11 mark

Question

Write down a prime number between 50 and 60. …… [1] 1 - `sin 33°j . 2

Mark scheme

1 53 or 59 1

Question 21 mark

Question

Use your calculator to work out …… [1]

Mark scheme

2 0.839 or 0.8386 to 0.8387 1

Question 31 mark

Question

Write the recurring decimal 0.7o as a fraction. …… [1]

Mark scheme

3 7 1 9

Question 42 marks

Question

Complete each statement. (a) A quadrilateral with only one pair of parallel sides is called a …… . [1] (b) An angle greater than 90° but less than 180° is called …… . [1]

Mark scheme

4(a) Trapezium 1 4(b) Obtuse 1

Question 52 marks

Question

The distance between Prague and Vienna is 254 kilometres. The local time in Prague is the same as the local time in Vienna. A train leaves Prague at 15 20 and arrives in Vienna at 19 50 the same day. Calculate the average speed of the train. …… km/h [2]

Mark scheme

5 56.4 or 56.44… 2 254 254 M1 for or [×60] their 4.5 their 270

Question 62 marks

Question

Solve the equation. 9f + 11 = 3f + 23 f = …… [2]

Mark scheme

6 2 2 M1 for 9f – 3f oe or 23 − 11 oe

Question 72 marks

Question

NOT TO SCALE 3.5 cm 8.4 cm Calculate the area of this triangle. …… cm2 [2]

Mark scheme

7 14.7 2 1 M1 for × 8.4 × 3.5 oe 2

Question 82 marks

Question

(a) Write 0.047 883 correct to 2 significant figures. …… [1] (b) Write 0.005 27 in standard form. …… [1]

Mark scheme

8(a) 0.048 cao 1 8(b) 5.27 × 10−3 1

Question 92 marks

Question

Find the highest common factor (HCF) of 90 and 48. …… [2]

Mark scheme

9 6 2 M1 for 2 × 32 × 5 or 24 × 3 or for 2 × 3 as final answer or B1 for 2 or 3 as final answer

Question 102 marks

Question

On a map with scale 1 : 25 000, the area of a lake is 33.6 square centimetres. Calculate the actual area of the lake, giving your answer in square kilometres. …… km2 [2]

Mark scheme

10 2.1 2 33.6 × 25000 2 M1 for oe 1000002 or answer figs 21

Question 112 marks

Question

Write down the matrix that represents an enlargement, scale factor 3, centre (0, 0). f p [2]

Mark scheme

11  3 0 2 B1 for one row or one column correct in a   2 by 2 matrix in the final answer  0 3  0 3 or SC1 for    3 0

Question 123 marks

Question

Simplify. (a) 5m 2 # 2m 3 …… [2] (b) `x 8j 3 …… [1]

Mark scheme

12(a) 10m5 final answer 2 B1 for 10mk or km5 as final answer 12(b) x 24 final answer 1

Question 133 marks

Question

Without using a calculator, work out 2 14 ' 37 . You must show all your working and give your answer as a mixed number in its simplest form. …… [3]

Mark scheme

13 9 7 63 12 M2 9 × or ÷ oe with common B1 for oe seen 4 3 28 28 4 denominator 9 7 or M1 for their × 4 3 1 A1 5 cao 4

Question 143 marks

Question

Solve the simultaneous equations. You must show all your working. 5x + 8y = 4 1 2 x + 3y = 7 x = …… y = …… [3]

Mark scheme

14 Correctly eliminating one variable M1 [x =] − 4 A2 A1 for one correct [y =] 3 If M0 scored, SC1 for 2 values satisfying one of the original equations

Question 153 marks

Question

Shona buys a chair in a sale for $435.60 . This is a reduction of 12% on the original price. Calculate the original price of the chair. $ …… [3]

Mark scheme

15 495 3 100 − 12 M2 for 435.6 ÷ oe 100 or B1 for recognising 435.6 as 88[%]

Question 163 marks

Question

y 10 8 6 4 2 –4 –2 0 2 4 6 8 10 12 14 x –2 –4 –6 y G- 12 x + 6 y H 3x - 4 x+y H 5 (a) By shading the unwanted regions of the grid, find and label the region R that satisfies the three inequalities. [2] (b) Find the largest value of x + y in the region R, where x and y are integers. …… [1]

Mark scheme

16(a) R identified correctly 2 B marks 0 1 1 2 0 1 1 0 1 1 0 1 0 1 0 16(b) 7 1

Question 173 marks

Question

Write as a single fraction in its simplest form. 2x x+3 + x+3 x-5 …… [3]

Mark scheme

17 3x 2 − 4 x + 9 3 B1 for common denominator final answer ( x + 3)( x − 5) oe isw ( x + 3)( x − 5) M1 for 2 x ( x − 5 ) + ( x + 3)( x + 3) or better

Question 183 marks

Question

The table shows the number of people in different age groups at a cinema. Age ( y years) 15 1 y G 25 25 1 y G 30 30 1 y G 50 50 1 y G 80 Number of people 35 32 44 12 Dexter draws a histogram to show this information. The height of the bar he draws for the group 15 1 y G 25 is 7 cm. Calculate the height of each of the remaining bars. 25 1 y G 30 …… cm 30 1 y G 50 …… cm 50 1 y G 80 …… cm [3]

Mark scheme

18 12.8 3 B2 for 2 correct heights or 3 correct freq 4.4 densities 0.8 or B1 for 1 correct height or 2 correct freq densities

Question 194 marks

Question

Rearrange this formula to make m the subject. k+m P= m …… [4]

Mark scheme

19 k 4 k m= final answer B3 for final answer P −1 P −1 OR M1 for multiplying or dividing by m correctly M1 for term(s) in m on one side correctly and terms not in m on the other side correctly M1 for correctly factorising m with a 2-term bracket oe M1 for correct division by their 2-term bracket with m as the subject To a maximum of M3 for an incorrect answer

Question 204 marks

Question

Solve the equation 3x 2 - 2x - 10 = 0 . Show all your working and give your answers correct to 2 decimal places. x = …… or x = …… [4]

Mark scheme

20 B2 − ( −2 ) ± ( −2 ) − 4 ( 3)( −10 ) ( −2 ) − 4 ( 3)( −10 ) or better 2 2 B1 for 2×3 p+ q p− q and if in form or then r r B1 for p = −(− 2) and r = 2(3) −1.52 and 2.19 final ans cao B1B1 If B0B0, SC1 for −1.5 and 2.2 or −1.523 to −1.522... and 2.189.... or 1.52 and −2.19 or −1.52 and 2.19 seen in working

Question 214 marks

Question

(a) In the Venn diagram, shade X l k Y . X Y [1] (b) The Venn diagram below shows information about the number of gardeners who grow melons (M ), potatoes (P ) and carrots (C ). M P 3 6 12 2 5 10 7 23 C (i) A gardener is chosen at random from the gardeners who grow melons. Find the probability that this gardener does not grow carrots. …… [2] (ii) Find n ((M k P) j C l) . …… [1] 2 7 3 4

Mark scheme

21(a) X 1 Y 21(b)(i) 9 2 9 k oe B1 for or provided fraction is less 16 k 16 than 1 21(b)(ii) 46 1

Question 224 marks

Question

A =e o B =e o 1 3 0 1 (a) Calculate AB. f p [2] (b) Find A -1 , the inverse of A. f p [2]

Mark scheme

22(a)  6 15  2 B1 for 2 correct elements   3 7  22(b)  −3 7 2  3 −7    oe isw B1 for k   soi or det = − 1 soi  1 −2  −1 2

Question 234 marks

Question

N NOT TO D C SCALE p X A q B M ABCD is a parallelogram with AB = q and AD = p . ABM is a straight line with AB : BM = 1 : 1. ADN is a straight line with AD : DN = 3 : 2 . (a) Write MN , in terms of p and q, in its simplest form. MN = …… [2] (b) The straight line NM cuts BC at X. X is the midpoint of MN. BX = kp Find the value of k. k = …… [2]

Mark scheme

23(a) 5 2 M1 for correct unsimplified answer p− 2q oe simplified 3 5 or cp− 2q or p + cq c ≠ 0 3 or for a correct route 23(b) 5 their c 2 B2FT for 2 if their (a) is cp− 2q oe 6 JJJJG 5 M1 for MX = p− q 6 JJJJG 1 or MX = their (a) 2 JJJG 1 JJJG or BX = AN 2 1 JJJJG or q + their (a) or q + MX − kp = 0 oe 2

Question 244 marks

Question

H G E F 12 cm NOT TO SCALE D C 7 cm A 18 cm B ABCDEFGH is a cuboid. AB = 18 cm, BC = 7 cm and CG = 12 cm. Calculate the angle that the diagonal AG makes with the base ABCD. …… [4] Question 25 is printed on the next page.

Mark scheme

24 31.9 or 31.85... 4 12 M3 for tan = oe 182 + 7 2 or M2 for 182 + 7 2 or M1 for 182 + 7 2 or B1 for identifying correct angle CAG

Question 256 marks

Question

y 7 6 5 A 4 3 2 1 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x –1 –2 –3 B C –4 –5 –6 –7 Describe fully the single transformation that maps (a) triangle A onto triangle B, …… [3] (b) triangle A onto triangle C. …… [3]

Mark scheme

25(a) Rotation 3 B1 for each 90° clockwise oe (1, 0) 25(b) Enlargement 3 B1 for each −2 (0, 2)

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How this paper is marked

Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.

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Where can I find the 0580/22 May/June 2019 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/22, May/June 2019 (0580_s19_ms_22), and the question paper (0580_s19_qp_22), to read or download, with each question's marking points written out underneath.

How many marks is 0580/22 out of?

Mathematics 0580/22 for May/June 2019 is out of 70 marks, with 1 hour 30 minutes to answer it.

Can I get my 0580/22 answers marked?

Yes. Upload your answers to 0580/22/M/J/19 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.