Cambridge IGCSE Mathematics 0580 — 2013 May/June Paper 1 · Variant 2
0580/12/M/J/13 · 24 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · For Examiner's Use 0 0.5 1.0 Write down the number the arrow points to on the scale
1 For Examiner's Use 0 0.5 1.0 Write down the number the arrow points to on the scale. Answer ............................................... [1] _____________________________________________________________________________________
Mark scheme: Qu Answers Mark Part Marks 1 0.65 cao 1
Q2 · 100 164 200 343 999 Write down the cube number from this list
2 100 164 200 343 999 Write down the cube number from this list. Answer ............................................... [1] _____________________________________________________________________________________
Mark scheme: 2 343 1
Q3 · Write down the next prime number after 23
3 Write down the next prime number after 23. Answer ............................................... [1] _____________________________________________________________________________________
Mark scheme: 3 29 1
Q4 · Calculate the number of seconds in 3 hours
4 Calculate the number of seconds in 3 hours. Answer ............................................ s [1] _____________________________________________________________________________________
Mark scheme: 4 10800 1
Q5 · For Examiner′s Use The diagram shows the net of a solid
5 For Examiner′s Use The diagram shows the net of a solid. Write down the mathematical name of this solid. Answer ............................................... [1] _____________________________________________________________________________________
Mark scheme: 5 cuboid 1 Accept [rectangular] prism.
Q6 · Bryony asks her friends how many pets they have
6 Bryony asks her friends how many pets they have. She is going to use this table to record her results. Number of pets Frequency 0 – 1 1 – 2 2 – 3 3 or more Explain what is wrong with this frequency table. Answer ..................................................................................................................................................... ........................................................................................................................................................... [1] _____________________________________________________________________________________
Mark scheme: 6 Overlapping class intervals oe 1
Q7 · Draw an acute angle
7 (a) Draw an acute angle. Label the acute angle with the letter a. [1] (b) Write down the mathematical name of angle b. b Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 7 (a) Any acute angle with angle indicated 1 (b) Obtuse 1
Q8 · For Examiner's Use 1 row 2 rows 3 rows Complete the table for 4 rows and 5 rows
8 For Examiner's Use 1 row 2 rows 3 rows Complete the table for 4 rows and 5 rows. Number of rows 1 2 3 4 5 Number of cans 1 3 6 [2] _____________________________________________________________________________________
Mark scheme: 8 10, 15 1, 1 If 10 not correct allow SC1 for x, x + 5
Q9 · The probability that the school hockey team will win its next match is 0.45
9 The probability that the school hockey team will win its next match is 0.45 . The probability that it will lose its next match is 0.3 . Work out the probability that the school hockey team will draw its next match. Answer ............................................... [2] _____________________________________________________________________________________
Mark scheme: 9 0.25 oe 2 M1 for 1– (0.45 + 0.3) or better or SC1 for 0.52 as final answer 24
Q10 · 4 -5 a = b = e 7 o e 2 o Write each of the following as a single vector
10 4 -5 a = b = e 7 o e 2 o Write each of the following as a single vector. (a) 6a Answer(a) [1] e o (b) a + b Answer(b) [1] e o _____________________________________________________________________________________
Mark scheme: 10 (a) 1 42 − 1 (b) 1 9
Q11 · For Examiner′s A Use NOT TO SCALE 8 cm B C Triangle ABC has a height of 8 cm and an area…
11 For Examiner′s A Use NOT TO SCALE 8 cm B C Triangle ABC has a height of 8 cm and an area of 42 cm². Calculate the length of BC. Answer BC = ......................................... cm [2] _____________________________________________________________________________________
Mark scheme: 11 10.5 www 2 M1 for 42 = 1 2 × BC × 8 or better
Q12 · Use your calculator to work out 65 – 1.72
12 (a) Use your calculator to work out 65 – 1.72 . Write down all the numbers displayed on your calculator. Answer(a) ............................................... [1] (b) Write your answer to part (a) correct to 2 signifi cant fi gures. Answer(b) ............................................... [1] _____________________________________________________________________________________
Mark scheme: 12 (a) 5.17225... 1 (b) 5.2 1FT FT their (a)
Q13 · The exterior angle of a regular pentagon is 72°
13 The exterior angle of a regular pentagon is 72°. For Examiner's Use (a) Write down the interior angle of a regular pentagon. Answer(a) ............................................... [1] (b) The diagram shows three pentagons which fi t together. Uta thinks that three regular pentagons will fi t together in the same way. Explain how you know she is wrong. Answer(b) ........................................................................................................................................ ................................................................................................................................................... [1] _____________________________________________________________________________________
Mark scheme: 13 (a) 108° 1 (b) 3 × 108 ≠ 360 oe 1
Q14 · Y 11 10 9 B 8 7 6 A 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Describe fully the single…
14 y 11 10 9 B 8 7 6 A 5 4 3 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Describe fully the single transformation that maps shape A onto shape B. Answer .............................................................................................................................................. [3] _____________________________________________________________________________________
Mark scheme: 14 Enlargement 1 [Centre] (5,4) 1 [Scale factor] 3 1 IGCSE – May/June 2013 0580 12
Q15 · For Examiner′s Use 128° NOT TO SCALE x° A straight line intersects two parallel lines as…
15 (a) For Examiner′s Use 128° NOT TO SCALE x° A straight line intersects two parallel lines as shown. Find the value of x. Answer(a) x = ................................................ [2] (b) NOT TO 30° SCALE 128° y° Calculate the value of y. Answer(b) y = ............................................... [1] _____________________________________________________________________________________
Mark scheme: 15 (a) 52 2 M1 for 180 – 128 or 128 or 52 marked on diagram in a correct position. (b) 22 1 5
Q16 · The average distance of the Moon from the Earth is 384 400 km
16 (a) The average distance of the Moon from the Earth is 384 400 km. Write this distance in standard form. Answer(a) ......................................... km [1] (b) Calculate (4.3 × 108 ) + (2.5 × 107 ) . Give your answer in standard form. Answer(b) ............................................... [2] _____________________________________________________________________________________
Mark scheme: 16 (a) 3.844 × 105 1 (b) 4.55 × 108 2 B1 for figs 455 seen
Q17 · For Examiner's = < > Use Write one of the three symbols between each pair of numbers
17 For Examiner's = < > Use Write one of the three symbols between each pair of numbers. Each symbol can be used more than once. 1 (a) 30% ............ [1] 3 (b) –2 ............ –3 [1] (c) π ............ 10 [1] _____________________________________________________________________________________
Mark scheme: 17 (a) < 1 (b) > 1 (c) < 1
Q18 · –3 – 4 –7 2 5 Choose three different numbers from the list to complete this calculation
18 (a) –3 – 4 –7 2 5 Choose three different numbers from the list to complete this calculation. .............. + .............. + .............. = – 6 [1] (b) Find the value of 5x – 3y when x = –2 and y = 4. Answer(b) ............................................... [2] _____________________________________________________________________________________
Mark scheme: 18 (a) –4, –7, [+]5 in any order 1 (b) –22 2 M1 for –10 and –12 seen SC1 for –10 +12 seen 5 k B1 f
Q19 · 2 Examiner′s19 Without using a calculator, work out ÷ 1
6 2 Examiner′s19 Without using a calculator, work out ÷ 1 . 7 3 Use Write down all the steps in your working. Answer ............................................... [3] _____________________________________________________________________________________
Mark scheme: 5 k 19 with 2 correct steps seen 3 B1 for 3k 18k 6 3 35k and M1 for × their 7 5
Q20 · B C NOT TO O SCALE A A, B and C are points on the circumference of a circle centre O
20 B C NOT TO O SCALE A A, B and C are points on the circumference of a circle centre O. AC is a straight line. (a) Explain why angle ABC is 90°. Answer(a) ................................................................................................................................. [1] (b) The diameter of the circle is 3 cm. Calculate the area of this circle. Answer(b) ........................................ cm2 [2] _____________________________________________________________________________________
Mark scheme: 20 (a) Angle or triangle [in a] semi-circle 1 (b) 7.068 to 7.07 2 M1 for π × 1.52 seen 2 3
Q21 · Carol invests $6250 at a rate of 2% per year compound interest
21 Carol invests $6250 at a rate of 2% per year compound interest. For Examiner's Use Calculate the total amount Carol has after 3 years. Answer $ ............................................... [3] _____________________________________________________________________________________
Mark scheme: 2 21 6632.55 cao final answer 3 M2 for 6250 × + 1 oe 100 2 2 or M1 for 6250 × + 1 oe 100 SC2 for answer 382.55 final answer
Question 22
22 Solve the equation. 5(2y – 17) = 60 Answer y = ............................................... [3] _____________________________________________________________________________________
Mark scheme: 22 14.5 oe 3 M2 for complete correct method or M1 for one correct step
Question 23
23 (a) Simplify y 0. Answer(a) ............................................... [1] 1 (b) Make v the subject of E = 2 mv 2. Answer(b) v = ............................................... [3] _____________________________________________________________________________________
Mark scheme: 23 (a) 1 1 2 E E E 2 E or or (b) [v =] 1 3 M2 for v2 = m 5.0 m m m 2 E or M1 for mv2 = 2E or ½ v2 = m IGCSE – May/June 2013 0580 12
Q24 · For Examiner′s y Use 8 7 6 5 4 3 2 S 1 x –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9…
24 For Examiner′s y Use 8 7 6 5 4 3 2 S 1 x –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 –6 –7 –8 (a) On the grid (i) plot the point (–5 , –2) and label it P, [1] (ii) draw the line y = 2x. [1] (b) (i) Write down the order of rotational symmetry of shape S. Answer(b)(i) ............................................... [1] (ii) Draw the image of shape S after a rotation through 90° clockwise about (0, 0). [2] _____________________________________________________________________________________
Mark scheme: 24 (a) (i) P in correct position at (– 5, – 2) 1 (ii) y = 2x drawn 1 (b) (i) 2 1 (ii) S rotated correctly 2 SC1 if rotated 90acw or 90cw about wrong centre.
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.
3Angles2Equations2Fractions, decimals and percentages2Area and perimeter1Circles, arcs and sectors1Classifying statistical data1Compound shapes and parts of shapes1Drawing linear graphs1Introduction to probability1Percentages1Powers and roots1Sequences1Standard form1The four operations1Time1Transformations1Using a calculator1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2013 May/June, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.