Mathematics 0580/22 February/March 2023: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), February/March 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_m23_qp_220580_m23_ms_220580/22/F/M/23

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Paper: Paper 2 (Extended)
Total marks: 70
Time: 1 hour 30 minutes
Code on the paper: 0580/22/F/M/23

0580_m23_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 1

Question

12 15 27 29 91 93 From the list of numbers, write down (a) a cube number (b) a prime number� -1 2

Mark scheme

1(a) 27 1 1(b) 29 1

Question 22 marks

Question

v=e o y=e o 3 5 Find (a) v - y f p [1] (b) 2 v � f p [1]

Mark scheme

2(a) −3 1 −2 2(b) −2 1 6

Question 31 mark

Question

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

Mark scheme

3 Correct shading 1

Question 4

Question

23, 17, 11, 5, �� (a) Write down the next number in this sequence� (b) Find the nth term of this sequence�

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

Question 5

Question

Factorise completely� 8g - 2g 2 4

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

Question 6

Question

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�

Mark scheme

6 4 1 4 56 M1 × oe or ÷ oe 7 8 7 7 1 A1 cao 14

Question 7

Question

Solve� (a) 15t + 8 = 4 - t 25 - 2u (b) =2 3

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

Question 8

Question

Calculate 0.3 2 � Give your answer in standard form�

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

Question 9

Question

Solve the simultaneous equations� You must show all your working� 3x - 2y = 19 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.

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�

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

Question 11

Question

Find the highest common factor (HCF) of 12x 12 and 16x 16 �

Mark scheme

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

Question 12

Question

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�

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 or for ( n − 2 ) ×180 = (180 − their 15 ) n

Question 13

Question

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�

Mark scheme

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

Question 14

Question

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�

Mark scheme

14 6.12 or 6.116… to 6.118 3 3 92 + 92 − 6 2 M1 for sin = oe or cos = oe 9 2× 9× 9 their angle M1 dep for × π × 2 × 9 dependent 360 on use of trig for their angle

Question 15

Question

Simplify `3125w 3125j5 � 1 16 y is inversely proportional to x 2 � When x = 3, y = 2 � Find y when x = 2 �

Mark scheme

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

Question 16

Question

In the question paper above.

Mark scheme

16 4.5 oe 3 M2 for 22 × y = 32 × 2 OR k M1 for y = x2 theirk M1 for y = 22

Question 17

Question

C X 85° B D NOT TO SCALE 42° 55° P A Q 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 (b) angle ACB (c) angle ADC (d) angle BCD (e) angle PAD�

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

Question 18

Question

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�

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 3 2 44 24 or = oe Area 81

Question 19

Question

Find the values of x when 6x + y = 10 and y = x 2 - 3x + 10 �

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

Question 20

Question

Find the nth term of each sequence� (a) –1, 0, 7, 26, 63, f (b) 24, 12, 6, 3, 1�5, f

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

Question 21

Question

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�

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

Question 22

Question

Q NOT TO SCALE P D C 4 cm 7 cm A 5 cm B 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�

Mark scheme

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

Question 23

Question

Simplify� 5x 2 - 19x + 12 x2 - 9 1

Mark scheme

23 5x − 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)

Question 24

Question

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

Mark scheme

24 7 2 B1 for answer 6 k 2 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

Question 25

Question

f (x) = x 3 + 1 Find f -1 (x) �

Mark scheme

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

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Where can I find the 0580/22 February/March 2023 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/22, February/March 2023 (0580_m23_ms_22), and the question paper (0580_m23_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 February/March 2023 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/F/M/23 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.