Cambridge IGCSE Mathematics 0580 — 2022 May/June Paper 2 · Variant 1

1 Write down a prime number between 30 and 40. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1 31 or 37 1

More questions on Types of number

2 Calculate 4 5 - 5 4 . ................................................. [1]

Mark scheme: 2 399 1

More questions on Powers and roots

3 Jason starts a run at 10.05 am and finishes at 1.02 pm. Work out the time Jason takes to complete the run. ................... h ................... min [1]

Mark scheme: 3 2h 57 min 1

More questions on Time

1 - 0.74 Calculate , giving your answer correct to 4 significant figures. 0.45 - 0.38 ................................................. [2]

Mark scheme: 4 4.286 cao 2 30 2 B1 for 4.285[7...] or 4.29 or or 4 7 7 or for correctly rounding their more accurate decimal to 4sf

More questions on The four operations

5 Kirsty changes $380.80 into pounds (£) when £1 = $1.19 . Calculate the amount Kirsty receives. £ ................................................ [2]

Mark scheme: 5 320 2 M1 for 380.8 ÷ 1.19 oe

More questions on Ratio and proportion

6 Write 180 as a product of its prime factors. ................................................. [2]

Mark scheme: 6 2 × 2 × 3 × 3 × 5 oe 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree/diagram/table.

More questions on Types of number

3 27 Without using a calculator, work out - . 7 21 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [2]

Mark scheme: 7 9 and 212 oe M1 Allow any correct denominator 21k 21 1 A1 cao and correct working 3

More questions on Fractions, decimals and percentages

1 28 s = at 2 (a) Work out the value of s when a = 0.9 and t = 4. s = ................................................ [1] (b) Rearrange the formula to find t in terms of s and a. t = ................................................ [2]

Mark scheme: 8(a) 7.2 oe 1 8(b) 2s 2 s 1 2 [±] final answer M1 for  t or 2s = at2 or better a a 2 2 xy  y 2 or y 14 x  7 y  9 7 y  2 x  y  final answer 2 B1 for 7   or 7 y  2 x  y  seen then spoilt

More questions on Algebraic manipulation

10 22, 17, 12, 7, 2, … (a) Find the next term of the sequence. ................................................. [1] (b) Find the nth term of the sequence. ................................................. [2]

Mark scheme: 10(a) –3 1 10(b) 27 – 5n oe final answer 2 B1 for j – 5n or 27 – kn, k ≠0 or for 27 – 5n seen then spoilt

More questions on Sequences

11 C R NOT TO 6 cm SCALE A B P Q 8 cm 6 cm Triangle ABC is mathematically similar to triangle PQR. (a) Calculate QR. QR = ........................................... cm [2] (b) The two triangles are the cross-sections of two mathematically similar prisms. The volume of the larger prism is 320 cm 3 . Calculate the volume of the smaller prism. .......................................... cm3 [2]

Mark scheme: 11(a) 4.5 oe 2 8 6 M1 for oe or better 6 QR 11(b) 135 2 3 3 3  6   8   their 4.5  M1 for   or   or   oe  8   6   6 

More questions on Similarity

12 The interior angles of a pentagon are in the ratio 4 | 5 | 5 | 7 | 9. Find the size of the largest angle. ................................................. [3]

Mark scheme: 12 162 3  (5  2)  180  M2 for   × k where k = 1, 4, 5,  4  5  5  7  9  7, 9 or M1 for 180n ÷ (4 + 5 + 5 + 7 + 9) where n ⩾ 2 or for (5 – 2) × 180 oe

More questions on Ratio and proportion

13 Work out 2 # 10 100 - 2 # 10 98 , giving your answer in standard form. ................................................. [2]

Mark scheme: 13 1.98 × 10100 2 B1 for 200  10 98 or 0.02  10100 or answer with figs 198

More questions on Standard form

14 A train passes through a station at a speed of 108 km/h. The length of the station is 120 m. The train takes 7 seconds to completely pass through the station. Work out the length of the train. .............................................. m [3]

Mark scheme: 14 90 3 B2 for 210 or 0.09 km OR M1 for speed × time seen M1 for correct conversion of both km to m and between h and s

More questions on Rates

x 115 4 = 64 Find the value of x. x = ................................................ [1]

Mark scheme: 15 –3 1

More questions on Indices I

16 y 9 8 T 7 6 5 4 3 P 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 Describe fully the single transformation that maps triangle T onto triangle P. ............................................................................................................................................................. ............................................................................................................................................................. [3]

Mark scheme: 16 Enlargement 3 B1 for each 1 [sf]  2 [centre] (4, 4)

More questions on Transformations

17 Find the radius of a hemisphere of volume 80 cm 3 . 4 3 [The volume, V, of a sphere with radius r is V = rr . ] 3 ........................................... cm [3]

Mark scheme: 17 3.37 or 3.367 to 3.368 3 3 120 M2 for isolating 3r , e.g. r   1 4 3 or M1 for   r  80 oe 2 3 If 0 scored SC1 for answer 2.67 or 2.672 to 2.673...

More questions on Surface area and volume

18 U D 38° 60° NOT TO T SCALE C B x° y° A A, B, C and D are points on a circle. TU is a tangent to the circle at D. DA is parallel to CB. Find the value of x and the value of y. x = ................................................ y = ................................................ [3]

Mark scheme: 18 [x = ] 38 3 B1 for [x = ] 38 and [y = ] 22 B2 for [y = ] 22 or M1 for angle ACB = their x or angle BAD = 60 or angle CBA = 120

More questions on Circle theorems I

19 A B NOT TO SCALE X P Q In the diagram, AB is parallel to PQ. AQ and PB intersect at X with AX = XQ . Complete the following statements. In triangles ABX and QPX, AX = XQ is given information. Angle BAX = Angle ......................... because ......................................................................................... Angle AXB = Angle ......................... because ......................................................................................... Triangle ABX is congruent to triangle QPX because of the congruency criterion .................................... PX = .............................. because the triangles are congruent. [4]

Mark scheme: 19 PQX and alternate 4 B2 for lines 1 and 2 correct PXQ and [vertically] opposite oe or B1 for line 1 or 2 correct, or both angles correct ASA XB B1 for line 3 correct B1 for line 4 correct

More questions on Geometrical terms

20 12 NOT TO Speed (m/s) SCALE 0 0 16 24 Time (s) The diagram shows the speed–time graph for 24 seconds of a car journey. Calculate (a) the deceleration of the car in the final 8 seconds, .......................................... m/s2 [1] (b) the total distance travelled during the 24 seconds. .............................................. m [2]

Mark scheme: 20(a) 1 1 1.5 or 12 20(b) 240 2 M1 for one correct area

More questions on Area and perimeter

21 Factorise completely. 1 – q – a + aq .................................................. [2]

Mark scheme: 21 (1 – q)(1 – a) or (a – 1)( q – 1) 2 B1 for 1 – q – a(1 – q) or 1 – a – q(1 – a) or final answer better or correct answer seen and spoilt

More questions on Algebraic manipulation

322 Simplify fully ( 216y 216 ) 2 . ................................................. [2]

Mark scheme: 22 36y144 final answer 2 B1 for ky144 or 36 ky final answer k ≠ 0 or correct answer seen and spoilt

More questions on Powers and roots

23 x 2 + 8x + 10 = ( x + p) 2 + q (a) Find the value of p and the value of q. p = ................................................ q = ................................................ [2] (b) Solve. x 2 + 8x + 10 = 30 x = .................... or x = .................... [2]

Mark scheme: 23(a) [p = ] 4 2 B1 for one correct [q = ] –6 2 or  x  4   6 or x2 + px + px + p2 [+ q] 23(b) –10 and 2 2 2 M1 for  x  4   36 or  x  their 4  2  30  their  6  or for correct method to solve quadratic e.g.  x  10  x  2 

More questions on Algebraic manipulation

24 A cuboid measures 24 cm by 12 cm by 8 cm. Calculate the length of a diagonal of the cuboid. ............................................ cm [3]

Mark scheme: 24 28 3 M2 for 242 + 122 + 82 or M1 for 242 + 122 or 242 + 82 or 122 + 82

More questions on Pythagoras’ theorem

25 w is proportional to the square root of y. y is inversely proportional to x. When x = 4, y = 16 and w = 8. Find w in terms of x. w = ............................................... [3]

Mark scheme: 25 16 3 oe final answer M2 for w k oe x x OR M1 for w  j y M1 for y c x

More questions on Proportion

26 B NOT TO SCALE b K L O a A The diagram shows a triangle OAB and a parallelogram OALK. The position vector of A is a and the position vector of B is b. K is a point on AB so that AK | KB = 1 | 2 . Find the position vector of L, in terms of a and b. Give your answer in its simplest form. ................................................. [4]

Mark scheme: 26 5 1 4  1 1  2 2 a + b final answer M1 for AK =  a + b or BK  a  b 3 3 3 3 3 3    M1 for AL (or OK ) = a + their AK oe soi   or OK (or AL ) = b + their ሬሬሬሬሬ⃗AK oe soi  or BL = a + their ሬሬሬሬሬ⃗AK oe soi   M1 for a correct route e.g. OL , a + AL , b +  BL

More questions on Vectors in two dimensions

27 The line y = x + 1 intersects the graph of y = x 2 - 3x - 11 at the points A and B. Find the coordinates of A and the coordinates of B. You must show all your working. A ( ..................... , ...................... ) B ( ..................... , ...................... ) [4]

Mark scheme: 27 (–2, –1) and (6, 7) 4 B3 for x = – 2 and 6 OR M1 for x 2  3 x  11  x  1 or better M1 for correct method to solve their quadratic e.g.  x  2  x  6  If 0 scored, SC1 for one correct pair of coordinates

More questions on Equations