Question 12 marks
Question
P is a prime number where 60 1 P 1 80 . P is 2 less than a square number. Find the value of P. P = …… [2]
Mark scheme
1 79 2 B1 for 64 or 81 seen or for answer 61, 62, 67, 71 or 73
Mathematics 0580/21 October/November 2021: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_w21_qp_210580_w21_ms_210580/21/O/N/21
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/21/O/N/21
0580/21 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 24 marks
Question
Hank flies from Los Angeles to Shanghai. (a) The flight departs on Friday 22 July at 21 40. The flight takes 13 hours 35 minutes. The local time in Shanghai is 15 hours ahead of the local time in Los Angeles. Find the day, date and time in Shanghai when Hank’s flight arrives. Day …… , Date …… , Time …… [3] (b) The cost of the flight is $920. The exchange rate is $1 = 6.87 Chinese yuan. Find the cost of the flight in yuan. …… yuan [1]
Mark scheme
2(a) Sunday 24 [July] 02 15 3 B1 for Sunday 24th [July] as final answer B2 for 02 15 oe as final answer or B1 for sight of any of these 12 40 oe, 11 15 oe, 28h 35min, 50 15, 35 15 or 0215 oe spoilt or M1 for departure time + 13h35min + 15h evaluated as a time with one interval correctly added 2(b) 6320.4[0] 1
Question 31 mark
Question
Calculate. 4.87 - 2.7 - 0.2 + 3 0.729 …… [1]
Mark scheme
3 3.1 1
Question 42 marks
Question
The number of items that each of 22 people buy in a supermarket is shown in the stem-and-leaf diagram. 1 1 3 6 6 2 0 2 2 2 4 8 9 3 1 1 5 8 9 9 4 2 4 6 7 8 Key: 1 | 1 represents 11 items (a) Find the mode. …… [1] (b) Find the median. …… [1]
Mark scheme
4(a) 22 1 4(b) 30 1
Question 53 marks
Question
The table shows the relative frequency of the games won by a football team. Result of game won lost drawn Relative frequency 0.1 The number of games lost is twice the number of games drawn. Complete the table. [3]
Mark scheme
5 3 B2 for 0.6 oe or 0.3 oe lost drawn 0.6 oe 0.3 oe or M1 for 1 – 0.1 or 0.9 seen
Question 65 marks
Question
The scale drawing shows the positions of two towns, P and Q. The scale is 1 cm represents 4 km. North Q North P Scale: 1 cm to 4 km (a) Find the actual distance between town P and town Q. …… km [2] (b) Measure the bearing of town Q from town P. …… [1] (c) Town X is 28 km from town P on a bearing of 140°. On the scale drawing, mark the position of town X. [2] 5 2
Mark scheme
6(a) 32.8 2 M1 for 8[cm] to 8.4[cm] seen or for their measurement [in cm] multiplied by 4 6(b) 065 1 6(c) X correctly placed 7 cm from P 2 M1 for X on bearing of 140 from P on a bearing of 140° or for X 7 cm from P If 0 scored SC1 for X on bearing of 140 from Q and 7 cm from Q
Question 73 marks
Question
Without using a calculator, work out 1 + . 6 5 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
7 25 or 55 12 M1 25k or 55k 12k and Accept and 30 30 30k 30k 7 A2 67k 37k 2 cao A1 for or1 30 30k 30k
Question 83 marks
Question
Solve the simultaneous equations. You must show all your working. 4x - 2y =- 13 - 3x + 4y = 11 x = …… y = …… [3]
Mark scheme
8 Correctly eliminates one M1 variable [x =] – 3 , [y =] 0.5 oe A2 A1 for either correct If M0 scored, SC1 for 2 values satisfying one of the original equations If 0 scored, SC1 for correct answers from no working
Question 92 marks
Question
NOT TO 12 cm SCALE x° 7 cm Calculate the value of x. x = …… [2]
Mark scheme
9 54.3 or 54.31… 2 7 M1 for cos [x] = oe 12
Question 102 marks
Question
A regular polygon has an interior angle of 174°. Find the number of sides of this polygon. …… [2]
Mark scheme
10 60 2 M1 for 360 ÷ (180 – 174) 180 ( n − 2 ) or for = 174 oe n
Question 113 marks
Question
Line L has equation y = 4 - 5x . Find the equation of a line that is perpendicular to line L and passes through the point (0, 6). …… [3]
Mark scheme
11 1 3 1 1 y= x + 6 oe final answer B2 for y = x + c oe or x + 6 oe or 5 5 5 y = mx + 6 oe 1 or B1 for [gradient =] oe or mx + 6 5
Question 123 marks
Question
Chai invests some money. By the end of the first year, the value of the investment has decreased by 35%. By the end of the second year, the value of the investment has increased by 40% of its value at the end of the first year. Find the overall percentage change in the value of the investment. …… % [3]
Mark scheme
12 [– ] 9 3 M2 for [k × ] 1 − 35 40 × 1 + oe or 100 100 better 35 35 40 or for [k × ] − 1 − × 100 100 100 or M1 for [k × ] 1 − 35 oe 100 or [k × ] 1 + 40 or better 100
Question 136 marks
Question
Solve. 6-x 4 - 3x H 5 …… [3] 14 y is inversely proportional to the square root of (x - 2) . When x = 4.25, y = 12 . Find x when y = 3. x = …… [3]
Mark scheme
13 x 1 final answer 3 6 x M1 for 20 – 15x ⩾ 6 – x or 4 − 3x − 5 5 M1 for correctly isolating terms in x FT their first step of dealing with the 5 x 6 20 – 6 ⩾ – x + 15x or −3x + − 4 5 5
Question 14
Question
In the question paper above.
Mark scheme
14 38 3 M2 for 12 × 4.25 − 2 = 3 × x − 2 OR k M1 for y = oe x−2 their k M1 for 3 = oe x−2
Question 154 marks
Question
NOT TO SCALE The diagram shows three shapes that are mathematically similar. The heights of the shapes are in the ratio small : medium : large = 1 : 5 : 8. Find the ratio shaded area : total unshaded area. Give your answer in its simplest form. …… : …… [4]
Mark scheme
15 3 : 5 nfww 4 M3 for 52 – 1 oe and 82 – 52 + 1 oe or M2 for 52 – 1 oe or 82 – 52 + 1 oe or M1 for 52 oe or 82 oe seen
Question 165 marks
Question
Find the nth term of each sequence. (a) 8, 15, 34, 71, 132, .... …… [2] 2 3 4 5 6 (b) , , , , , .... 1 4 16 64 256 …… [3] 3x - 2
Mark scheme
16(a) n3 + 7 oe final answer 2 B1 for any cubic or for 3rd differences of 6 16(b) n +1 3 B1 for n + 1 oe final answer 4n −1 B2 for 4n – 1 oe or B1 for 4n – k oe k can be 0 Maximum 2 marks if not correctly combined as a fraction
Question 174 marks
Question
y= 1-x Make x the subject of the formula. x = …… [4]
Mark scheme
17 y+2 4 M1 y (1 – x) = 3x – 2 or better [x = ] oe final answer y +3 M1 for correctly isolating x terms on one side FT their first step/bracket expansion M1dep for correctly removing factor of x FT their previous step M1dep for correct division to isolate x Max 3 marks for an incorrect answer
Question 183 marks
Question
B NOT TO 800 m SCALE 30° A C 2300 m The diagram shows some land in the shape of a triangle ABC. Houses are built on this land. Each house requires 400 m 2 of land. Find the greatest number of houses that can be built on this land. …… [3]
Mark scheme
18 1150 3 M2 for × 800 × 2300 × sin 30 ÷ 400 oe 1 2 1 or M1 for × 800 × 2300 × sin30 oe 2
Question 193 marks
Question
Write as a single fraction in its simplest form. 2 x+2 - x+3 7 …… [3]
Mark scheme
19 8 − 5x − x2 8 − 5x − x2 3 B1 for 7 × 2 – (x + 2)(x + 3) or better seen or 7( x + 3) 7 x + 21 B1 for common denominator 7(x + 3) oe isw final answer
Question 203 marks
Question
Solve 3 (2 + cos x) = 5 for 0° G x G 360° . …… [3]
Mark scheme
20 109.4 to 109.5 3 B2 for one correct angle and 250.5 to 250.6 5 or M1 for cos x = − 2 or better 3 If 0 scored SC1 for two angles that sum to 360
Question 214 marks
Question
E NOT TO SCALE 9 cm D C O 5 cm A 5 cm B The diagram shows a pyramid ABCDE. The pyramid has a square horizontal base ABCD with side 5 cm. The vertex E is vertically above the centre O of the base. The height OE of the pyramid is 9 cm. Calculate the angle that EC makes with the base ABCD. …… [4] Question 22 is printed on the next page.
Mark scheme
21 68.6 or 68.55 to 68.56 4 9 M3 for tan[..] = oe 1 2 2 5 +5 2 1 2 2 or M2 for 5 + 5 oe 2 or M1 for 52 + 52 oe or 2.52 + 2.52 oe or x2 + x2 = 52 oe or B1 for indicating required angle
Question 225 marks
Question
(a) Simplify. 2 x3 8 x3 …… [1] (b) 16 = 64 k Find the value of k. k = …… [1] (c) Solve. 4 - 3x 1 3 #e o 3x =3 9 x = …… [3]
Mark scheme
22(a) 1 1 x –2 or final answer x2 22(b) 2 1 3 22(c) 1 nfww 3 M1 for 3–2(4 – 3x) oe or better 3x 1 or 9 2 × 9 − ( 4 − 3 x ) = 9 2 oe or better M1 for 3x + (their– 2) × (4 – 3x)= 1 oe or better 3x 1 or their − ( 4 − 3x ) = their oe or better 2 2
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0580/21 questions
Where can I find the 0580/21 October/November 2021 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/21, October/November 2021 (0580_w21_ms_21), and the question paper (0580_w21_qp_21), to read or download, with each question's marking points written out underneath.
How many marks is 0580/21 out of?
Mathematics 0580/21 for October/November 2021 is out of 70 marks, with 1 hour 30 minutes to answer it.
Can I get my 0580/21 answers marked?
Yes. Upload your answers to 0580/21/O/N/21 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.