Cambridge IGCSE Mathematics 0580 — 2023 Oct/Nov Paper 1 · Variant 3
0580/13/O/N/23 · 23 questions · 56 marks · ≈63 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper16 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · E B C A D Write down the letter of the shape that is congruent to the shaded shape
1 E B C A D Write down the letter of the shape that is congruent to the shaded shape. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 D 1
Q2 · Write down (a) all the factors of 32…
2 Write down (a) all the factors of 32 ................................................................................................. [2] 1 (b) the reciprocal of 8 ................................................. [1] (c) the value of the 7 in the number 473 285. ................................................. [1]
Mark scheme: 2(a) 1, 2, 4, 8, 16, 32 2 B1 for 4 or 5 correct and no extras or 6 correct and one extra 2(b) 8 1 2(c) 70 000 1
Q3 · Draw the lines of symmetry on this rhombus
3 Draw the lines of symmetry on this rhombus. [2]
Mark scheme: 3 2 correct lines of symmetry 2 B1 for 1 correct line and no incorrect lines or 2 correct lines and 1 incorrect line
Q4 · 61 63 64 66 68 69 From this list, write down (a) a cube number…
4 61 63 64 66 68 69 From this list, write down (a) a cube number ................................................. [1] (b) a prime number. ................................................. [1]
Mark scheme: 4(a) 64 1 4(b) 61 1
Q5 · Tara goes on a journey by train
5 Tara goes on a journey by train. The train leaves at 06 48. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives. ................................................. [1]
Mark scheme: 5 19 23 or 7 23 pm 1
Q6 · Jamie records the masses of two samples of oranges, type A and type B
6 Jamie records the masses of two samples of oranges, type A and type B. The stem-and-leaf diagram shows the mass, in grams, of each of 30 oranges of type A. 17 6 8 8 9 18 0 1 2 2 4 7 19 1 2 2 3 6 7 8 20 0 2 5 5 5 6 7 7 8 21 1 5 6 8 Key: 17 6 represents 176 grams (a) Complete the table to show the range for type A oranges. Type A Type B Mean (g) 195.7 215.8 Range (g) 35 [1] (b) Use the information in the table to write down two comments comparing the masses of type A oranges with the masses of type B oranges. 1. .................................................................................................................................................. .................................................................................................................................................. 2. .................................................................................................................................................. .................................................................................................................................................. [2]
Mark scheme: 6(a) 42 1 6(b) Type A [masses] lighter on average 2 B1 for each oe Type A [masses] more varied/less strict FT their range in part (a) consistent oe
Q7 · In triangle LMN, LN = 7.5 cm and MN = 8 cm
7 In triangle LMN, LN = 7.5 cm and MN = 8 cm. (a) Using a ruler and compasses only, construct triangle LMN. Leave in your construction arcs. The line LM has been drawn for you. M L [2] (b) Write down the mathematical name for this type of triangle. ................................................. [1]
Mark scheme: 7(a) Correct construction 2 B1 for accurate triangle with incorrect or no arcs or for 2 correct arcs If 0 scored, SC1 for accurate triangle with arcs but lines interchanged 7(b) Scalene 1
Q8 · The surface area of a cube is 73.5 cm2
8 The surface area of a cube is 73.5 cm2. Find the length of one side of the cube. ............................................ cm [2]
Mark scheme: 8 3.5 2 73.5 M1 for or better 6
Q9 · NOT TO SCALE x° x° The diagram shows an equilateral triangle
9 NOT TO SCALE x° x° The diagram shows an equilateral triangle. Find the value of x. x = ................................................ [2]
Mark scheme: 9 150 2 M1 for 360 – 60
Q10 · - 6 13 10 a = b = c = e9o e 1o e- 2o Work out
4 - 6 13 10 a = b = c = e9o e 1o e- 2o Work out. (a) a + b [1] f p (b) 3c [1] f p
Mark scheme: 10(a) −2 1 10 10(b) 39 1 −6
Question 11
11 Factorise completely. 15v 2 - 3v ................................................. [2]
Mark scheme: 11 3v(5v – 1) final answer 2 B1 for 3(5v2 – v) or v(15v – 3) as final answer or 3v(5v – 1) seen and spoilt
Q12 · Rama asks a group of students how they travel to school
12 Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school. Bus Walk Car Other Probability 0.4 0.32 0.17 (a) Complete the table. [2] (b) There are 1800 students at the school. Find the expected number of students that walk to school. ................................................. [1]
Mark scheme: 12(a) 0.11 oe 2 M1 for 1 – (0.4 + 0.32 + 0.17) oe 12(b) 576 1
Q13 · 1113 Without using a calculator, work out 1 '
5 1113 Without using a calculator, work out 1 ' . 6 15 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 13 11 15 55k 22 k M2 11 or oe with B1 for oe 6 11 30 k 30 k 6 common denominator their 11 15 or M1 for 6 11 1 A1 2 cao 2
Q14 · B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC
14 B NOT TO 112° SCALE 44° C M A The diagram shows triangle ABC. M is the midpoint of AC. Triangle ABC is rotated 180° about centre M. The image and the original triangle together form a quadrilateral ABCD. (a) Write down the mathematical name of the quadrilateral ABCD. ................................................. [1] (b) Find angle BAD. Angle BAD = ................................................ [2]
Mark scheme: 14(a) Parallelogram 1 14(b) 68 2 M1 for 180 – 112 or for 180 – 112 – 44 oe
Q15 · Shubhu invests $750 in a savings account for 5 years
15 Shubhu invests $750 in a savings account for 5 years. The account pays simple interest at a rate of 1.8% per year. Calculate the total interest she earns during the 5 years. $ ................................................ [2]
Mark scheme: 15 67.5[0] 2 750 1.8 5 M1 for oe 100
Question 16
16 Solve the equation. 5x + 7 = 9x - 3 x = ................................................ [2]
Mark scheme: 16 2.5 2 M1 for 7 + 3 = 9x – 5x or better
Q17 · Y 4 3 2 L 1 -2 -1 0 1 2 3 4 x -1 (a) Find the equation of line L in the form y = mx + c
17 y 4 3 2 L 1 -2 -1 0 1 2 3 4 x -1 (a) Find the equation of line L in the form y = mx + c . y = ................................................ [2] (b) On the grid, draw a line that is perpendicular to line L. [1]
Mark scheme: 17(a) 1 2 1 [y =] x + 1 B1 for x + c oe 3 3 or for mx + 1 where m is their gradient m ≠ 0 17(b) Any ruled perpendicular line 1
Q18 · A bar of chocolate costs $3 and a bag of sweets costs $5
18 A bar of chocolate costs $3 and a bag of sweets costs $5. Write down an expression for the total cost, in dollars, of x bars of chocolate and y bags of sweets. $ ................................................ [2]
Mark scheme: 18 3x + 5y final answer 2 B1 for 3x or 5y in final answer or for 3x + 5y seen then spoilt
Q19 · A bag contains these cards
19 (a) A bag contains these cards. 1 7 3 9 4 5 2 One of these cards is picked at random. Find the probability that the number on the card is greater than 3. ................................................. [1] (b) A box contains 3 blue cards and 7 red cards. Kim picks one card at random, notes its colour and then replaces it in the box. She then picks another card at random. (i) Complete the tree diagram. First card Second card 3 Blue 10 Blue 3 10 Red .......... 3 Blue 10 .......... Red Red .......... [1] (ii) Work out the probability that both of the cards Kim picks are blue. ................................................. [2]
Mark scheme: 19(a) 4 1 oe 7 19(b)(i) 7 1 in each space on tree diagram 10 19(b)(ii) 9 2 3 3 oe M1 for oe 100 10 10
Q20 · 72° r cm NOT TO SCALE The diagram shows a sector of a circle with radius r cm and sector…
20 72° r cm NOT TO SCALE The diagram shows a sector of a circle with radius r cm and sector angle 72°. The arc length is 9.35 cm. Calculate the value of r. r = ................................................ [2]
Mark scheme: 20 7.44 or 7.439 to 7.440… 2 72 M1 for 2 × π × r × = 9.35 oe or better 360
Q21 · = {2, 4, 8, 9, 10, 12} Q = {square numbers} R = {multiples of 4} (a) Use this…
21 = {2, 4, 8, 9, 10, 12} Q = {square numbers} R = {multiples of 4} (a) Use this information to complete the Venn diagram. Q R [2] (b) Write down n ( Q + R ) . ................................................. [1]
Mark scheme: 21(a) 2 B1 for 4 or 5 numbers in the correct place Q R 8 4 12 9 2 10 21(b) 1 1 FT their Venn diagram dep on not empty set
Q22 · Find the highest common factor (HCF) of 48 and 80
22 Find the highest common factor (HCF) of 48 and 80. ................................................. [2]
Mark scheme: 22 16 2 B1 for answer 2, 4 or 8 or M1 for 2 2 2 2 oe as final answer or [48 =] 2 2 2 2 3 and [80 =] 2 2 2 2 5 or 2 correct factor trees or tables
Q23 · Solve the simultaneous equations
23 Solve the simultaneous equations. You must show all your working. 3x + 5y = 23 6x - 4y = 11 x = ................................................ y = ................................................ [3]
Mark scheme: 23 Correctly eliminates one variable M1 [x =] 3.5 A1 [y =] 2.5 A1 If M0 scored, SC1 for 2 values satisfying one of the original equations
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Angles2Equations2Algebraic manipulation1Circles, arcs and sectors1Equations of linear graphs1Fractions, decimals and percentages1Geometrical constructions1Interpreting statistical data1Introduction to algebra1Introduction to probability1Percentages1Probability of combined events1Sets1Similarity1Surface area and volume1Symmetry1Time1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2023 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.