Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/15 · 23 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 · Write down the difference in temperature between 8°C and −9°C
1 Write down the difference in temperature between 8°C and −9°C. Answer .............................................°C [1]
Mark scheme: Question Answer Mark Part Marks 1 17 1
Q2 · Parallelogram Trapezium Rhombus Write down which one of these shapes has • rotational…
2 Parallelogram Trapezium Rhombus Write down which one of these shapes has • rotational symmetry of order 2 and • no line symmetry. Answer ................................................... [1] __________________________________________________________________________________________
Mark scheme: 2 Parallelogram 1
Q3 · Carlos changed $950 into euros (€) when the exchange rate was €1 = $1.368
3 Carlos changed $950 into euros (€) when the exchange rate was €1 = $1.368 . Calculate how many euros Carlos received. Answer € ................................................... [2] __________________________________________________________________________________________
Mark scheme: 3 694 or 694.4[4...] 2 M1 for 950 ÷ 1.368
Q4 · - 3 4 AB = e 5 o Find AB
- 3 4 AB = e 5 o Find AB . Answer .................................................. [2]
Mark scheme: 4 5.83 or 5.830 to 5.831 2 2 2 M1 for (− 3) + 5 1 4 3
Q5 · Calculate the volume of a hemisphere with radius 5 cm
5 Calculate the volume of a hemisphere with radius 5 cm. 4 3 [The volume, V, of a sphere with radius r is V = 3 r r .] Answer .......................................... cm3 [2]
Mark scheme: 1 4 3 5 262 or 261.7 to 261.83… 2 M1 for × π × 5 2 3 If zero scored SC1 for final answer 524 or 523.5 to 523.7
Q6 · The Venn diagram shows the number of students who study French (F), Spanish (S) and…
6 The Venn diagram shows the number of students who study French (F), Spanish (S) and Arabic (A). F S 7 4 5 1 2 3 8 0 A (a) Find n(A (F S )). Answer(a) .................................................. [1] (b) On the Venn diagram, shade the region Fl S. [1]
Mark scheme: 6 (a) 18 1 (b) 1
Q7 · 3 - 4 5 0 M = N = e - 2 4 o e 1 2 o Calculate MN
7 3 - 4 5 0 M = N = e - 2 4 o e 1 2 o Calculate MN. Answer [2] f p
Mark scheme: 7 11 − 8 2 B1 for two correct elements − 6 8 7
Q8 · Robert buys a car for $8000
8 Robert buys a car for $8000. At the end of each year the value of the car has decreased by 10% of its value at the beginning of that year. Calculate the value of the car at the end of 7 years. Answer $ ................................................. [2]
Mark scheme: 8 3826 or 3826.38 2 M1 for 8000 × −1 10 7 oe 100 k × 50 000 × 50 000
Q9 · The scale on a map is 1 : 50 000
9 The scale on a map is 1 : 50 000. The area of a field on the map is 1.2 square centimetres. Calculate the actual area of the field in square kilometres. Answer .......................................... km2 [2]
Mark scheme: k × 50 000 × 50 000 9 0.3 2 M1 for oe 100 000 × 100 000 If zero scored SC1 for figs 3 15 2 f
Q10 · Jason receives some money for his birthday
10 Jason receives some money for his birthday. 11 He spends 15 of the money and has $14.40 left. Calculate how much money he received for his birthday. Answer $ .................................................. [3]
Mark scheme: 15 10 54 3 M2 for 14 4. × oe 4 4 or M1 for 14.4 ÷ 4 or associated with 14.4 15 If zero scored SC1 for final answer 19.6[4] 2 2
Q11 · NOT TO 8 cm SCALE 5 cm x cm Calculate the value of x
11 NOT TO 8 cm SCALE 5 cm x cm Calculate the value of x. Answer x = ................................................. [3]
Mark scheme: 11 6.24 or 6.244 to 6.245 3 M2 for 8 2 − 5 2 or M1 for 8 2 = 5 2 + x 2 or better 3 15 27 9× 3
Q12 · 11 12 Without using your calculator, work out 2 4 - 12
1 11 12 Without using your calculator, work out 2 4 - 12 . You must show all your working and give your answer as a fraction in its lowest terms. Answer .................................................. [3]
Mark scheme: 3 15 27 9 × 3 12 2 or 1 or or M1 Accept any correct conversion with common 12 12 12 4 × 3 denominator 12k 27 11 16 their ( − = ) oe M1 Correct resolving of their subtraction with 12 12 12 denominator 12k showing full working 1 4 1 or cao 3 3 A1 Working and then simplified answer must both be seen 12 4
Q13 · 74° NOT TO SCALE y cm 39° 12.4 cm Calculate the value of y
13 74° NOT TO SCALE y cm 39° 12.4 cm Calculate the value of y. Answer y = .................................................. [3]
Mark scheme: 124. 13 8.12 or 8.118… 3 M2 for × sin 39 sin 74 sin 39 sin 74 or M1 for implicit version = oe y 124.
Q14 · Jasjeet and her brother collect stamps
14 Jasjeet and her brother collect stamps. When Jasjeet gives her brother 1% of her stamps, she has 2475 stamps left. Calculate how many stamps Jasjeet had originally. Answer ................................................. [3]
Mark scheme: 1 oe14 2500 nfww 3 M2 for 2475 ÷ 1 −100 or M1 for 2475 associated with 99% ( )( )
Q15 · Factorise (a) 9w 2 - 100 , Answer(a) ................................................
15 Factorise (a) 9w 2 - 100 , Answer(a) ................................................. [1] (b) mp + np - 6mq - 6nq . Answer(b) ................................................. [2]
Mark scheme: 15 (a) (3 w + 10 )(3 w − 10 ) final answer 1 (b) (m + n )( p − 6 q ) oe final answer 2 B1 for p (m + n ) − 6 q (m + n ) oe or m ( p − 6 q ) + n ( p − 6 q ) oe 26
Q16 · NOT TO SCALE 26° 15 cm The diagram shows a sector of a circle with radius 15 cm
16 NOT TO SCALE 26° 15 cm The diagram shows a sector of a circle with radius 15 cm. Calculate the perimeter of this sector. Answer ............................................ cm [3]
Mark scheme: 26 16 36.8 or 36.80 to 36.81 3 M1 for × 2 × π × 15 360 M1 for 2 × 15 + a term involving π ( ) 2
Q17 · Y is directly proportional to the square of (x − 1)
17 y is directly proportional to the square of (x − 1). y = 63 when x = 4. Find the value of y when x = 6. Answer y = .................................................. [3]
Mark scheme: 17 175 3 M1 for y = k ( x − 1) 2 oe A1 for k = 7 63 y or M2 for 2 = 2 oe (4 − 1) (6 − 1)
Q18 · A rectangle has length 5.8 cm and width 2.4 cm, both correct to 1 decimal place
18 A rectangle has length 5.8 cm and width 2.4 cm, both correct to 1 decimal place. Calculate the lower bound and the upper bound of the perimeter of this rectangle. Answer Lower bound ............................................ cm Upper bound ............................................ cm [3]
Mark scheme: 18 16.2 3 M1 for two of 2.35, 5.75, 2.45, 5.85 seen or 2 × (5.8 – 0.05 + 2.4 0.05) 16.6 nfww or 2 × (5.8 + 0.05 + 2.4 + 0.05) A1 16.2 or 16.6 in either answer space If zero scored SC2 for both correct reversed answers provided 16.6 nfww ( ) 2
Q19 · Solve the equation 5x 2 - 6x - 3 = 0
19 Solve the equation 5x 2 - 6x - 3 = 0 . Show all your working and give your answers correct to 2 decimal places. Answer x = ............................. or x = ............................. [4]
Mark scheme: 19 (− 6 ) 2 − 4 ( 5)( −3) or better seen B1 If completing the square 2 B1 for − x 3 oe 5 p + q p − q if or seen then B1 r r 3 3 3 2 3 3 3 2 B1 for + + or − + oe p = − (− 6) and r = 2 × 5 5 5 5 5 5 5 B1 If B0, SC1 for B1 −0.38 − 0.4 and 1.6 1.58 cao final answers or − 0.379[795..] and 1.579[795..] or − 1.58 and 0.38 as final answers or − 0.38 and 1.58 seen in working
Q20 · A car passes through a checkpoint at time t = 0 seconds, travelling at 8 m/s
20 A car passes through a checkpoint at time t = 0 seconds, travelling at 8 m/s. It travels at this speed for 10 seconds. The car then decelerates at a constant rate until it stops when t = 55 seconds. (a) On the grid, draw the speed-time graph. 10 8 6 Speed (m/s) 4 2 t 0 10 20 30 40 50 60 Time (seconds) [2] (b) Calculate the total distance travelled by the car after passing through the checkpoint. Answer(b) ............................................. m [3]
Mark scheme: 20 (a) B1 line from (0, 8) to (10, 8) 8 B1 line from their (10, 8) to (55, 0) 10 55 (b) 260 3FT M2FT for 8 × 10 + 0.5 × 8 × 45 oe or for a fully correct area calculation for their graph or M1FT for 8 × 10 or 0.5 × 8 × 45 or for one correct area calculation for their graph 7 2 15 25
Q21 · NOT TO SCALE 25 cm 15 cm 7.2 cm x cm The diagram shows two jugs that are mathematically…
21 (a) NOT TO SCALE 25 cm 15 cm 7.2 cm x cm The diagram shows two jugs that are mathematically similar. Find the value of x. Answer(a) x = ................................................. [2] (b) NOT TO 16 cm SCALE y cm The diagram shows two glasses that are mathematically similar. The height of the larger glass is 16 cm and its volume is 375 cm3. The height of the smaller glass is y cm and its volume is 192 cm3. Find the value of y. Answer(b) y = .................................................. [3]
Mark scheme: 2.7 15 25 21 (a) 12 2 M1 for = oe or better eg 2.7 × x 25 15 192 3 oe (b) 12.8 3 M2 for 16× 375 or 3 192 375 16 375 M1 for 3 or 3 oe or oe = 375 192 y 192
Q22 · The table shows information about the numbers of pets owned by 24 students
22 The table shows information about the numbers of pets owned by 24 students. Number of pets 0 1 2 3 4 5 6 Frequency 1 2 3 5 7 3 3 (a) Calculate the mean number of pets. Answer(a) .................................................. [3] (b) Jennifer joins the group of 24 students. When the information for Jennifer is added to the table, the new mean is 3.44 . Calculate the number of pets that Jennifer has. Answer(b) ................................................. [3]
Mark scheme: 22 (a) 3.5 nfww 3 M1 for Σfx soi M1 (dep) for ÷ 24 their 84 + x (b) 2 nfww 3 M2FT for = .344 or better 25 or M1 for 25 × 3.44 8 5
Q23 · A box contains 6 red pencils and 8 blue pencils
23 A box contains 6 red pencils and 8 blue pencils. A pencil is chosen at random and not replaced. A second pencil is then chosen at random. (a) Complete the tree diagram. First pencil Second pencil Red ....... Red 6 14 8 13 Blue Red ....... ....... Blue ....... Blue [2] (b) Calculate the probability that (i) both pencils are red, Answer(b)(i) ................................................. [2] (ii) at least one of the pencils is red. Answer(b)(ii) ................................................. [3]
Mark scheme: 8 523 (a) and 1 14 13 6 7 1 and 13 13 30 (b) (i) oe 2 M1FT for 6 × 5 182 14 their13 126 (ii) oe 3 M2FT for 182 8 7 1 − × 14 13 6 5 6 8 8 6 or × + + × 14 13 14 ×13 14 13 6 8 6 or + × oe 14 14 13 or M1FT for sum of any two of 6 5 6 8 8 6 × or × or 14 13 14 13 14 ×13
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Circles, arcs and sectors2Vectors in two dimensions2Algebraic manipulation1Area and perimeter1Averages and measures of spread1Equations1Fractions, decimals and percentages1Limits of accuracy1Non-right-angled triangles1Probability of combined events1Proportion1Pythagoras’ theorem1Ratio and proportion1Scale drawings1Sets1Similarity1Symmetry1The four operations1What you needed in this session
Cambridge’s own grade thresholds for 2015 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.