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Mathematics 0580/23 October/November 2019: question paper and mark scheme

Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.

0580_w19_qp_230580_w19_ms_230580/23/O/N/19

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Paper
Paper 2 (Extended)
Total marks
70
Time
1 hour 30 minutes
Code on the paper
0580/23/O/N/19
0580_w19_ms_23.pdf

0580/23 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 11 mark

Question

Write down the temperature that is 7 °C below -3 °C. …… °C [1]

Mark scheme

1 –10 1

Question 21 mark

Question

Calculate 256 0.25 + 4 # 8 . …… [1]

Mark scheme

2 6 1

Question 32 marks

Question

Here is a list of numbers. 87 77 57 47 27 From this list, write down (a) a cube number, …… [1] (b) a prime number. …… [1]

Mark scheme

3(a) 27 1 3(b) 47 1

Question 42 marks

Question

Find the highest common factor (HCF) of 84 and 105. …… [2]

Mark scheme

4 21 2 M1 for [84 =] 2 × 2 × 3 × 7 or [105 =] 3 × 5 × 7 or 3 × 7 as final answer or B1 for 3 or 7 as final answer

Question 52 marks

Question

Write in standard form. (a) 72 000 …… [1] (b) 0.0018 …… [1]

Mark scheme

5(a) 7.2 × 104 1 5(b) 1.8 × 10–3 1

Question 62 marks

Question

Expand and simplify (x + 3) (x + 5) . …… [2]

Mark scheme

6 x2 + 8x + 15 final answer 2 M1 for three terms correct from x2 + 3x + 5x + 15

Question 72 marks

Question

Find the gradient of the line that is perpendicular to the line 2y = 3 + 5x. …… [2]

Mark scheme

7 2 2 5 − or – 0.4 M1 for gradient = oe soi 5 2

Question 82 marks

Question

When sin x° = 0.36, find (a) the acute angle x°, …… [1] (b) the obtuse angle x°. …… [1]

Mark scheme

8(a) 21.1 or 21.10… 1 8(b) 158.9 or 158.8 to 158.9 1 FT 180 – their (a) providing answer is an obtuse angle

Question 93 marks

Question

A cuboid measures 5 cm by 7 cm by 9.5 cm. NOT TO SCALE 7 cm 5 cm 9.5 cm Work out the surface area of this cuboid. …… cm2 [3]

Mark scheme

9 298 3 M2 for [2 ×] (5 × 7 + 5 × 9.5 + 7 × 9.5) oe or M1 for one correct area, 5 × 7 or 5 × 9.5 or 7 × 9.5

Question 103 marks

Question

5n is the mean of the three numbers 391, n and n - 1. Find the value of n. n = …… [3]

Mark scheme

10 30 3 391 + n + n −1 M1 for = 5n oe 3 M1 for correct first step for solving their equation 390 + 2 n e.g. 391+ n + n −1 = 3 × 5n , = 5n 3

Question 113 marks

Question

Factorise. (a) 12x + 15 …… [1] (b) xy - 2x + 3y - 6 …… [2]

Mark scheme

11(a) 3(4x + 5) final answer 1 11(b) (x + 3)(y – 2) final answer 2 B1 for y(x + 3) – 2(x + 3) or x(y – 2) + 3(y – 2) or correct answer seen then spoilt

Question 123 marks

Question

A is the point (2, 1) and B is the point (9, 4). Find the length of AB. …… [3]

Mark scheme

12 7.62 or 7.615 to 7.616 3 M2 for ( 9 − 2 )2 + ( 4 − 1)2 oe or M1 for ( 9 − 2 ) + ( 4 − 1) oe or 58 2 2

Question 133 marks

Question

A straight line joins the points (3k, 6) and (k, -5). The line has a gradient of 2. Find the value of k. k = …… [3]

Mark scheme

13 2.75 oe 3 M2 for 6 − −5 = 2 ( 3k − k ) oe or better 6 − −5 or M1 for oe 3k − k If 0 scored, SC1 for − 2.75 oe as answer

Question 143 marks

Question

Find the nth term of each sequence. 1 1 1 1 1 (a) , , , , , ... 2 4 6 8 10 …… [1] (b) 1, 5, 25, 125, 625, ... …… [2] 2 1 2

Mark scheme

14(a) 1 1 oe final answer 2n 14(b) 5n – 1 oe final answer 2 M1 for recognition of terms being powers of 5

Question 154 marks

Question

Without using a calculator, work out + # . 3 4 3 Write down all the steps of your working and give your answer as a fraction in its simplest form. …… [4]

Mark scheme

15 2 1 1 2 1 M1 M1 for correct first step to deal with oe or × 1 +  multiplication 12 2 3 3 4 8 2 2 5 M1 M1 for correct working for common [ + ] oe × 2 12 12 3 4 denominator with their oe or correct 12 evaluation of bracket 5 A2 10 cao A1 for oe 6 12

Question 164 marks

Question

Ten athletes compete in both the 100 metre race and the triple jump. Their results are shown in the scatter diagram. 13.4 13.3 13.2 13.1 13.0 Time for 100 m 12.9 (seconds) 12.8 12.7 12.6 12.5 12.4 14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5 Distance in the triple jump (m) (a) One of these athletes jumps 15.12 m in the triple jump. Write down his time for the 100 metre race. …… s [1] (b) The values for two other athletes are shown in the table. Distance in the 14.74 15.2 triple jump (m) Time for 100 m 13.2 12.76 (seconds) On the scatter diagram, plot these points. [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) What type of correlation is shown in the scatter diagram? …… [1]

Mark scheme

16(a) 12.88 1 16(b) two correct points plotted 1 16(c) ruled line of best fit 1 16(d) negative 1

Question 174 marks

Question

y 7 6 5 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 x –1 –2 –3 –4 –5 By shading the unwanted regions on the grid, draw and label the region R that satisfies the following inequalities. -2 1 x G 3 y G x+3 [4]

Mark scheme

17 4 B1 for x = –2 dashed ruled line and x = 3 solid ruled line B1 for y = x + 3 solid ruled line B2 for indication of correct region or B1 for shading that satisfies two of the inequalities, e.g. two of x > –2, x ⩽ 3 and y⩽x+3

Question 184 marks

Question

(a) M = {x | x is an integer and 2 G x 1 6} (i) Find n(M). …… [1] (ii) Write down a set N where N 1 M and N ! Q . { …… } [1] (b) In each Venn diagram, shade the required region. C D A B (A , B)l E (C + D l ) , E [2]

Mark scheme

18(a)(i) 4 1 18(a)(ii) At least one and fewer than four 1 numbers from {2, 3, 4, 5} 18(b) E 2 B1 for each A B E C D E

Question 194 marks

Question

18 16 14 12 10 Speed (m/s) 8 6 4 2 0 0 10 20 30 40 50 60 70 Time (s) The diagram shows the speed–time graph for 70 seconds of a car journey. (a) Calculate the deceleration of the car during the first 20 seconds. …… m/s2 [1] (b) Calculate the total distance travelled by the car during the 70 seconds. …… m [3]

Mark scheme

19(a) 3 1 0.3 or 10 19(b) 760 3 M2 for correct complete area statement 1 e.g. 70 × 10 + × 20 × 6 oe 2 or M1 for one of these area calculations 1 70 × 10, × 20 × 6, 50 × 10 or 2 1 × (16 + 10) × 20 2

Question 204 marks

Question

t is inversely proportional to the square of (x + 1). When x = 2, t = 5. (a) Write t in terms of x. t = …… [2] (b) When t = 1.8, find the positive value of x. x = …… [2] - 3 10

Mark scheme

20(a) 45 2 k final answer M1 for t = ( x + 1) 2 ( x + 1)2 20(b) 4 2 M1 for 1.8 × (x + 1)2 = their 45 or better

Question 215 marks

Question

(a) Work out the inverse of the matrix e o. 1 -5 f p [2] (b) Work out the value of x and the value of y in this matrix calculation. 1 5 -4 1 x 46 e oe o=e o 2 y 2 9 6 65 x = …… y = …… [3]

Mark scheme

21(a) 1  −5 −10  2  −5 −10    oe isw M1 for k   or det = 5 soi 5  −1 −3   −1 −3  21(b) [x = ] 6 3 B1 for x = 6 [y = ] 7 B2 for y = 7 or M1 for 2 × 1 + 9y = 65 or 2 × − 4 + 2y = 6

Question 225 marks

Question

A container is made from a cylinder and a cone, each of radius 5 cm. The height of the cylinder is 12 cm and the height of the cone is 4.8 cm. 4.8 cm NOT TO 12 cm SCALE 5 cm The cylinder is filled completely with water. The container is turned upside down as shown below. NOT TO SCALE d Calculate the depth, d, of the water. 1 [The volume, V, of a cone with radius r and height h is V = rr 2 h.] 3 d = …… cm [5] Question 23 is printed on the next page.

Mark scheme

22 15.2 5 M4 for   2 1 2  π × 5 × 12 − × π × 5 × 4.8  ÷ π × 5  3  (2 ) 1 or M3 for π × 52 × 12 − × π × 52 × 4.8 3 or M1 for π × 52 ×12 1 M1 for × π × 52 × 4.8 3

Question 234 marks

Question

The time, t minutes, it takes each of 50 students to travel to school is recorded. The table shows the results. Time (t minutes) 0 1 t G 10 10 1 t G 15 15 1 t G 20 20 1 t G 40 Frequency 7 19 16 8 (a) Write down the modal class. …… 1 t G …… min [1] (b) On the grid, complete the histogram to show the information in the table. 4 3 Frequency density 2 1 0 0 10 20 30 40 t Time (minutes) [3]

Mark scheme

23(a) 10 [< t ⩽] 15 1 23(b) Correct histogram 3 B1 for each correct block 4 If 0 scored, SC1 for correct frequency densities 3.8, 3.2, 0.4 soi by correct heights 3 2 1 0 t Time (minutes)

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Where can I find the 0580/23 October/November 2019 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/23, October/November 2019 (0580_w19_ms_23), and the question paper (0580_w19_qp_23), to read or download, with each question's marking points written out underneath.

How many marks is 0580/23 out of?

Mathematics 0580/23 for October/November 2019 is out of 70 marks, with 1 hour 30 minutes to answer it.

Can I get my 0580/23 answers marked?

Yes. Upload your answers to 0580/23/O/N/19 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.