Question 11 mark
Question
The temperature at midnight is -8.5 °C. The temperature at 11 am is -1 °C. Work out the difference between the temperature at midnight and the temperature at 11 am. …… °C [1]
Mark scheme
1 7.5 1
Mathematics 0580/22 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_220580_w21_ms_220580/22/O/N/21
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/22/O/N/21
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 23 marks
Question
The stem-and-leaf diagram shows the age, in years, of each of 15 women. 3 1 5 8 9 4 1 1 2 3 5 6 9 5 0 2 3 8 Key: 3 | 1 represents 31 years Complete these statements. The modal age is …… The median age is …… The percentage of women that are older than 51 years is …… %. [3]
Mark scheme
2 41 3 B1 for each 43 20
Question 31 mark
Question
Change 2.15 hours into minutes. …… min [1]
Mark scheme
3 129 1
Question 43 marks
Question
A B 86° x° NOT TO SCALE C 58° D Triangle ABC and triangle ACD are isosceles. Angle DAB = 86° and angle ADC = 58°. Find the value of x. x = …… [3]
Mark scheme
4 79 nfww 3 M2 for x + x + 58 + 58 + 86 = 360 oe or 86 – (180 – 2 × 58) implied by CAB = 22 or B1 for DCA = 58 or BCA = x or DAC = 64
Question 53 marks
Question
Angelique rents a room for a party. The cost of renting the room is $15.50 for the first hour and then $7.25 for each additional hour. She pays $95.25 in total. Work out the total number of hours she rents the room for. …… hours [3] 1 7 1
Mark scheme
5 12 3 M2 for (95.25 – 15.5) ÷ 7.25 oe or (95.25 – (15.5 – 7.25)) ÷ 7.25 oe or M1 for 95.25 – 15.5 or B1 for 79.75
Question 64 marks
Question
Without using a calculator, work out ' + . 3 6 5 You must show all your working and give your answer as a fraction in its simplest form. …… [4]
Mark scheme
6 1 6 2 7 M1 × oe or ÷ oe 3 7 6 6 2 A1 oe 7 2 1 M1 10 7 their + with a correct method to find e.g. + oe 7 5 35 35 fractions with a common denominator 17 A1 If order of operations not correct SC2 for cao 35 10 answer with correct working for 41 1 7 1 ÷ + 3 6 5 35 6 or SC1 for + oe 30 30
Question 74 marks
Question
Katy has 5 white flowers, x red flowers and (2x + 1) yellow flowers. She picks a flower at random. 1 The probability that it is white is . 12 Find the probability that it is yellow. …… [4] 4 1
Mark scheme
7 37 4 B3 for x = 18 or 37 [yellow] oe 60 5 or SC2 for answer 12 1 5 or M2 for = oe 12 5 + x + 2 x + 1 or M1 for 5 + x + 2x + 1 oe or [total number of flowers =] 60
Question 81 mark
Question
Calculate 39 16 . …… [1] 24
Mark scheme
8 2.5 oe 1
Question 92 marks
Question
2.1 # 10 -1 0.2o 22% 0.2 1000 Write these values in order of size, starting with the smallest. …… 1 …… 1 …… 1 …… 1 …… [2] smallest
Mark scheme
9 24 2 M1 for four values in the correct order < 2.1 × 10–1 < 22% < 0.2 < 0.2 1000 or for conversion to consistent comparable form e.g. 0.21, 0.22…, 0.22, 0.4.., 0.024
Question 102 marks
Question
The interior angle of a regular polygon is 156°. Work out the number of sides of this polygon. …… [2]
Mark scheme
10 15 2 M1 for 360 ÷ (180 – 156) or 180 ( n – 2 ) =156 oe n
Question 113 marks
Question
A car starts its journey by accelerating from rest at a constant rate of 0.7 m/s 2 for 20 seconds, before reaching a constant speed of 14 m/s. It then travels at 14 m/s for a distance of 210 m. The car then decelerates at a constant rate of 1.4 m/s 2 , before coming to a stop. On the grid, complete the speed–time graph for the car’s journey. 16 14 12 10 Speed 8 (m/s) 6 4 2 0 0 5 10 15 20 25 30 35 40 45 50 Time (s) [3]
Mark scheme
11 Straight line from (20, 14) to (35, 14) 3 M1 for 210 ÷ 14 soi and straight line from (35, 14) to (45, 0) M1 for 14 ÷ 1.4 or any line with gradient –1.4 ending at x axis
Question 125 marks
Question
The table shows the first five terms of sequences A, B and C. 1st term 2nd term 3rd term 4th term 5th term nth term Sequence A 8 3 -2 -7 -12 Sequence B 2 3 4 5 6 2 3 4 5 Sequence C 1 1 2 4 8 2 Complete the table to show the nth term of each sequence. [5]
Mark scheme
12 13 – 5n oe final answer 5 B2 for 13 – 5n oe final answer n +1 or B1 for – 5n + c or 13 – kn k ≠ 0 oe final answer or 13 – 5n seen then spoilt n 2n – 2 oe final answer n +1 B1 for oe final answer n B2 for 2n –2 oe final answer or B1 for 2n – k oe k can be 0
Question 134 marks
Question
(a) Write 243 # 27 2n as a single power of 3 in terms of n. …… [2] (b) k = 2 # 3 2 # p 3 , where p is a prime number greater than 3. Write 6k 2 as a product of prime factors in terms of p. …… [2]
Mark scheme
13(a) 36n + 5 final answer 2 B1 for 35 or (33)2n or better or answer 6n + 5 13(b) 23 × 35 × p6 final answer 2 B1 for two parts correct or 2 × 3 × 2 × 32 × p3 × 2 × 32 × p3 or 1944p6 or k2 = 22 × 34 × p6
Question 143 marks
Question
Q 65° S x° NOT TO 55° 60° SCALE P R T P, Q and R are points on a circle. ST is a tangent to the circle at R. (a) Write down the value of x. Give a geometrical reason for your answer. x = …… because…… …… [2] (b) Another tangent from the point S touches the circle at V. Give a geometrical reason why triangle SVR is isosceles. …… [1]
Mark scheme
14(a) 55 2 B1 for 55 Alternate segment theorem 14(b) Tangents from an external point are equal 1 in length
Question 154 marks
Question
(a) A is the point (3, 16) and B is the point (8, 31). Find the equation of the line that passes through A and B. Give your answer in the form y = mx + c . y = …… [3] (b) The line CD has equation y = 0.5x - 11. Find the gradient of a line that is perpendicular to the line CD. …… [1]
Mark scheme
15(a) [y =] 3x + 7 final answer 3 31−16 M1 for . oe 8−3 M1 for correct substitution of (3, 16) or (8, 31) into y = (their m)x + c 15(b) –2 1
Question 164 marks
Question
Sachin picks a number at random from the first three multiples of 3. He then picks a number at random from the first three prime numbers. He adds the two numbers to find a score. (a) Complete the table. Multiples of 3 3 9 2 5 11 Prime numbers 3 6 [2] (b) Given that the score is even, find the probability that one of the numbers he picks is 9. …… [2]
Mark scheme
16(a) Multiples of 3 2 B1 for at least 4 correct entries + 3 6 9 2 5 8 11 Prime numbers 3 6 9 12 5 8 11 14 16(b) 2 2 their 2 oe B2FT for 5 their 5 their 2 or B1FT for k is any integer in the k range 1 ⩽ k ⩽ 7 c or c is 0, 1 or 2 their 5
Question 171 mark
Question
Solve. (5x - 3) (2x + 7) = 0 x = …… or x = …… [1]
Mark scheme
17 3 7 1 oe and – oe 5 2
Question 185 marks
Question
Solve the simultaneous equations. You must show all your working. y = x 2 - 9x + 21 y = 2x - 3 x = …… y = …… x = …… y = …… [5]
Mark scheme
18 x² – 11x + 24 [= 0] M2 M1 for x² – 9x + 21 = 2x – 3 oe or y +3 2 y +3 y² – 16y + 39 [= 0] or y = − 9 + 21 oe 2 2 (x – 8)(x – 3) [= 0] M1 or for correct factors for their quadratic or equation (y – 13)(y – 3) [= 0] or for correct use of quadratic formula for their equation [x =] 3 [y =] 3 B2 B1 for one correct pair or two correct [x =] 8 [y =] 13 x values or two correct y values. If B0 scored and at least 2 method marks scored SC1 for correct substitution of both of their x values or their y values into y = x2 – 9x + 21 or y = 2x – 3
Question 192 marks
Question
In these Venn diagrams, shade the given regions. A B C D Al , Bl E (C , D) + E l [2] 5
Mark scheme
19 C D 2 B1 for each E
Question 205 marks
Question
f (x) = 2 x - 3 g (x) = 2x - 1 h (x) = x-4 (a) Find ff(6). …… [2] (b) Find g -1 g (x + 21) . …… [1] (c) Find x when f (x) = h (84) . x = …… [2]
Mark scheme
20(a) 32 2 M1 for f(6) = 8 ( 2 ) – 3 oe or ff ( x ) = 2 x –3 20(b) x + 21 1 20(c) –1 2 1 M1 for oe or 2–4 oe 16
Question 213 marks
Question
Expand and simplify. (x - 3) 2(2x + 5) …… [3]
Mark scheme
21 2 x 3 − 7 x 2 − 12 x + 45 3 B2 for unsimplified expansion of the three final answer brackets with at most one error or for simplified four-term expression of correct form with three terms correct or B1 for correct expansion of two of the given brackets with at least three terms out of four correct
Question 223 marks
Question
Solve the equation 7 sin x + 2 = 0 for 0° G x G 360° . …… [3] Question 23 is printed on the next page.
Mark scheme
22 196.6 or 196.60… 3 B2 for one correct angle and 343.4 or 343.39… 2 or M1 for sin x = − or better 7 If 0 scored SC1 for two angles that sum to 540°
Question 234 marks
Question
Simplify. 3xy + 36y - 5x - 60 2x 2 - 288 …… [4]
Mark scheme
23 3y – 5 3y – 5 4 3y – 5 or final answer SC3 for answer 2 ( x –12 ) 2 x – 24 x –12 or B3 for (3y – 5)(x + 12) and 2(x – 12)(x + 12) or (2x – 24)(x + 12) or B2 for (3y – 5)(x + 12) or 2(x – 12)(x + 12) or (2x – 24)(x + 12) or (2x + 24)(x – 12) or B1 for 3y(x + 12) – 5(x + 12) or x(3y – 5) + 12(3y – 5) or 2(x2 – 144) or (x – 12)(x + 12)
Checked your answers against these? Let AI mark the whole paper, on your own working.
Mark my 0580/22How this paper is marked
Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
Check your answers against it
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Other variants, October/November 2021
Find another Mathematics paper
Every IGCSE Mathematics mark schemeQuestion papers and mark schemes © Cambridge University Press & Assessment. CIE Buddy is independent and not connected to Cambridge.
0580/22 questions
Where can I find the 0580/22 October/November 2021 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, October/November 2021 (0580_w21_ms_22), and the question paper (0580_w21_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 October/November 2021 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/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.