Cambridge IGCSE Mathematics 0580 — 2023 Feb/March Paper 2 · Variant 2

1 12 15 27 29 91 93 From the list of numbers, write down (a) a cube number ................................................. [1] (b) a prime number. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1(a) 27 1 1(b) 29 1

More questions on Types of number

- 1 2 2 v = y = e 3o e5o Find (a) v - y [1] f p (b) 2 v . [1] f p

Mark scheme: 2(a)  −3  1    −2  2(b)  −2  1    6 

More questions on Vectors in two dimensions

3 A B On the Venn diagram, shade the region A k B . [1]

Mark scheme: 3 Correct shading 1

More questions on Sets

4 23, 17, 11, 5, .... (a) Write down the next number in this sequence. ................................................. [1] (b) Find the nth term of this sequence. ................................................. [2]

Mark scheme: 4(a) –1 1 4(b) 29 – 6n oe final answer 2 B1 for k – 6n or 29 – kn or 29 – 6n seen then spoiled

More questions on Sequences

5 Factorise completely. 8g - 2g 2 ................................................. [2]

Mark scheme: 5 2g(4 – g) final answer 2 B1 for 2(4g – g2) or for g(8 – 2g) or for 2g(4 – g) seen then spoiled

More questions on Algebraic manipulation

46 Without using a calculator, work out ' 8 . 7 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [2]

Mark scheme: 6 4 1 4 56 M1  oe or  oe 7 8 7 7 1 A1 cao 14

More questions on The four operations

7 Solve. (a) 15t + 8 = 4 - t t = ................................................ [2] 25 - 2 u (b) = 2 3 u = ................................................ [2]

Mark scheme: 7(a) 1 2 M1 for 15t + t = 4 – 8 oe − oe 4 7(b) 9.5 oe 2 M1 for 25 – 2u = 3 × 2 oe 25 2u or for − 2 = 3 3

More questions on Equations

8 Calculate .032 . Give your answer in standard form. ................................................. [2]

Mark scheme: 8 9  10−2 2 B1 for 0.09 oe or M1 for their decimal correctly converted to standard form if negative power

More questions on Standard form

9 Solve the simultaneous equations. You must show all your working. 3x - 2y = 19 x + y = 3 x = ................................................ y = ................................................ [3]

Mark scheme: 9 Correctly eliminating one variable M1 [x =] 5 A1 [y = ] –2 A1 If M0 scored SC1 for 2 values satisfying one of the original equations.

More questions on Equations

10 3.0 cm A B 2.0 cm 2.7 cm X NOT TO SCALE C D 7.5 cm In the diagram, AB and CD are parallel. The lines CB and AD intersect at X. AB = 3. 0 cm, AX = 2. 0 cm, BX = 2. 7 cm and CD = 7. 5 cm . Find the length of BC. BC = ........................................... cm [3]

Mark scheme: 10 9.45 3 2.7  7.5 M2 for + 2.7 oe 3 OR B2 for 6.75 oe 3 2.7 or M1 for = oe 7.5 XC If 0 scored SC1 for answer 7.7

More questions on Similarity

11 Find the highest common factor (HCF) of 12x 12 and 16x 16. ................................................. [2]

Mark scheme: 11 4x12 final answer 2 B1 for 4xk or kx12 or for 4x12 seen then spoiled

More questions on Powers and roots

12 In a regular polygon, the interior angle and the exterior angle are in the ratio interior : exterior = 11 : 1. Find the number of sides of this regular polygon. ................................................. [3]

Mark scheme: 12 24 3 M2 for 180 ( n − 2 ) = 11  360 oe OR 180 M1 for [× 11] oe 11 + 1 360 M1 for their 15 ( n − 2 ) 180 or for = (180 − their 15 ) n

More questions on Ratio and proportion

13 10 NOT TO SCALE Speed (m/s) 0 0 8 10 Time (s) The diagram shows the speed–time graph for part of a car journey. Calculate the total distance travelled during the 10 seconds. ............................................. m [2]

Mark scheme: 13 90 2 M1 for a correct area calculation e.g. 8 × 10 or 0.5 × 2 × 10 or better

More questions on Rates

14 P 9 cm NOT TO SCALE 6 cm O Q The diagram shows a sector of a circle with centre O and radius 9 cm. The length of the chord PQ is 6 cm. Calculate the length of the arc PQ. ............................................ cm [3]

Mark scheme: 14 6.12 or 6.116… to 6.118 3 3 9 2 + 9 2 − 6 2 M1 for sin = oe or cos = oe 9 2 9 9 their angle M1 dep for  2 9 dependent 360 on use of trig for their angle

More questions on Circles, arcs and sectors

1 15 Simplify 3125 w 3125 5 . ` j ................................................. [2]

Mark scheme: 15 5w625 final answer 2 B1 for kw625 or 5wk final answer or for 5w625 then spoiled

More questions on Powers and roots

16 y is inversely proportional to x2. When x = 3, y = 2 . Find y when x = 2 . y = ................................................ [3]

Mark scheme: 16 4.5 oe 3 M2 for 2 2  y = 3 2  2 OR k M1 for y = x 2 theirk M1 for y = 2 2

More questions on Ratio and proportion

17 C X 85° B D NOT TO SCALE 42° 55° P Q A ABCD is a cyclic quadrilateral, ABX is a straight line and PQ is a tangent to the circle at A. Angle CBX = 85° , angle BAQ = 55° and angle CAD = 42° . Find (a) angle CBD Angle CBD = ................................................ [1] (b) angle ACB Angle ACB = ................................................ [1] (c) angle ADC Angle ADC = ................................................ [1] (d) angle BCD Angle BCD = ................................................ [2] (e) angle PAD. Angle PAD = ................................................ [1]

Mark scheme: 17(a) 42 1 17(b) 55 1 17(c) 85 1 17(d) 108 2 M1 for [angle ACD = ] 53 or [angle BAC = ] 30 17(e) 53 1

More questions on Circle theorems I

18 Two solids are mathematically similar and have volumes 81 cm 3 and 24 cm 3. The surface area of the smaller solid is 44 cm 2. Calculate the surface area of the larger solid. ......................................... cm2 [3]

Mark scheme: 18 99 3 2  81  3 M2 for 44   oe  24  1 1  81  3  24  3 or M1 for   oe or   oe  24   81   44 3  24  2 or = oe      Area   81 

More questions on Compound shapes and parts of shapes

19 Find the values of x when 6x + y = 10 and y = x 2 - 3x + 10 . x = .............................. or x = .............................. [3]

Mark scheme: 19 0 and –3 3 B2 for x2 + 3x [= 0] or better or M1 for 10 – 6x = x2 – 3x + 10 oe or for correct simplification of their quadratic to the form ax2 + bx + c [= 0] or better or finding y = 28 and y = 10

More questions on Equations

20 Find the nth term of each sequence. (a) –1, 0, 7, 26, 63, f ................................................. [2] (b) 24, 12, 6, 3, 1.5, f ................................................. [2]

Mark scheme: 20(a) ( n − 1)3 − 1 oe 2 M1 for any cubic or third differences = 6 20(b) n−1 2 an + b  1   1  24   oe M1 for c   oe where a, b and c are  2   2  constants and a > 0

More questions on Sequences

21 A car travels 14 km, correct to the nearest kilometre. This takes 12 minutes, correct to the nearest minute. Calculate the lower bound of the speed of the car. Give your answer in kilometres per minute. .................................... km/min [3]

Mark scheme: 21 1.08 3 13 to14 14 − 0.5 M2 for oe or oe 12 + 0.5 12 to 13 or M1 for 14 + 0.5 oe or 14 – 0.5 oe or 12 + 0.5 oe or 12 – 0.5 oe

More questions on Limits of accuracy

22 Q NOT TO SCALE P D C 4 cm 7 cm A B 5 cm The diagram shows a triangular prism ABCDQP of length 7 cm. The cross-section is triangle PAB with PA = 4 cm , AB = 5 cm and angle PAB = 90° . Calculate the angle between the line PC and the base ABCD. ................................................. [4]

Mark scheme: 22 24.9 or 24.93 to 24.94 4 4 M3 for tan = oe 5 2 + 7 2 or M2 for 52 + 72 oe or 52 + 72 + 42 oe or M1 for recognition of angle PCA.

More questions on Pythagoras’ theorem and trigonometry

23 Simplify. 5x 2 - 19x + 12 x 2 - 9 ................................................. [4]

Mark scheme: 23 5 x − 4 4 B2 for ( 5 x − 4 )( x − 3 ) final answer x + 3 or B1 for ( 5x + a )( x + b ) with ab = 12 or a + 5b = –19 or for 5 x ( x − 3 ) − 4 ( x − 3 ) or x ( 5 x − 4 ) − 3 ( 5 x − 4 ) B1 for ( x + 3 )( x − 3 )

More questions on Algebraic fractions

24 The probability of Jamie hitting a target is 1. 3 64 The probability that he hits the target for the first time on his nth attempt is . 2187 Find the value of n. n = ................................................ [2] Question 25 is printed on the next page.

Mark scheme: 24 7 2 B1 for answer 6  2 k 1 or M1 for   shown with k > 1  3 3 an + b  2  1 64 or = oe     3  3 2187 or for 3n = 2187 soi or 2n – 1 = 64 or 3n – 1 = 729 or better

More questions on Probability of combined events

25 f ( x) = x 3 + 1 Find f -1 ( x) . f -1 ( x) = ................................................ [2]

Mark scheme: 25 1 2 M1 for x = y 3 + 1 or for y −=1 x 3 3 3 x − 1 or ( x − 1) or better

More questions on Functions