May/June 2025 Paper 11 Worked Answers (IGCSE Maths 0580 Core)

52 questions · 80 marks · 90 minutes

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1. Question 1a

   1 marksPlace value
   20045 = 20000 + 45 = Twenty thousand and forty-five
   Examiner tips

   • Read each digit carefully and identify its place value
   • Remember that 'and' is typically used before the tens and units

2. Question 1b

   1 marksRounding
   Look at the units digit (6). Since 6 ≥ 5, round up. 7836 → 7840
   Examiner tips

   • Identify the rounding digit (units) first
   • Check if it's 5 or above to decide whether to round up

3. Question 1c

   1 marksUnit conversion
   To convert cm to m, divide by 100. 4523 ÷ 100 = 45.23 m
   Examiner tips

   • Remember: 100 cm = 1 m, so divide by 100
   • Move the decimal point 2 places to the left

4. Question 2

   2 marksMoney calculations
   Cost = 8 × $\$0.35$ = $\$2.80$. Change = $\$5$ - $\$2.80$ = $\$2.20$
   Examiner tips

   • Show your working: cost = quantity × price
   • Change = amount given - total cost

5. Question 3

   2 marksNumber properties
   Check: 4 + (-3) = 1 ✓ and 4 × (-3) = -12 ✓
   Examiner tips

   • Test each pair by checking both conditions
   • Remember: negative × negative = positive, positive × negative = negative

6. Question 4a

   1 marksNumber properties
   An even number is divisible by 2. 82 ÷ 2 = 41, so 82 is even.
   Examiner tips

   • Just check the last digit
   • Even numbers are divisible by 2

7. Question 4b

   1 marksSquare numbers
   36 = 6², so 36 is a square number.
   Examiner tips

   • Know the first few square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
   • Check if the number has an integer square root

8. Question 4c

   1 marksFactors
   48 ÷ 12 = 4, so 12 is a factor of 48.
   Examiner tips

   • Divide the target number by each option
   • A factor gives a whole number result

9. Question 4d

   1 marksPrime numbers
   29 has only two factors: 1 and 29, so it is prime.
   Examiner tips

   • Check if the number can be divided by any prime less than its square root
   • Know common primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

10. Question 5

    1 marksReciprocals
    The reciprocal of a number n is 1/n. Reciprocal of 8 = 1/8
    Examiner tips

    • Reciprocal means 'flip' the fraction - put 1 over the number
    • Check: number × reciprocal should equal 1

11. Question 6a

    1 marksOrder of operations
    (3 + 2) × 5 - 5 = 5 × 5 - 5 = 25 - 5 = 20
    Examiner tips

    • Remember BODMAS/BIDMAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction
    • Try different bracket positions systematically

12. Question 6b

    1 marksOrder of operations
    2 - 4 × (3 + 2) = 2 - 4 × 5 = 2 - 20 = -18.
    Examiner tips

    • Evaluate each option step by step
    • Be careful with negative numbers in calculations

13. Question 7a

    1 marksAlgebraic expressions
    Cost = price per book × number of books = 12 × b = 12b
    Examiner tips

    • Total cost = unit price × number of items
    • In algebra, write 12 × b as 12b

14. Question 7b

    1 marksAlgebraic expressions
    Total = blue pens + black pens = m + 9
    Examiner tips

    • Total = quantity 1 + quantity 2
    • Keep variable terms separate from constant terms

15. Question 8a

    1 marksPercentages and fractions
    60% = 60/100 = 6/10 = 3/5
    Examiner tips

    • Write percentage over 100 first
    • Divide numerator and denominator by their HCF

16. Question 8b

    1 marksFractions and decimals
    7/100 = 7 ÷ 100 = 0.07
    Examiner tips

    • Dividing by 100 moves decimal point 2 places left
    • 7/100 means 7 hundredths = 0.07

17. Question 9ai

    1 marksSequences
    45 - 38 = 7, 38 - 31 = 7, 31 - 24 = 7. The rule is subtract 7.
    Examiner tips

    • Calculate the difference between consecutive terms
    • State whether you add or subtract

18. Question 9aii

    2 marksSequences
    The rule is subtract 6. 10 - 6 = 4, then 4 - 6 = -2
    Examiner tips

    • Continue the pattern using the rule you identified
    • Be careful with negative numbers

19. Question 9b

    2 marksSequences - nth term
    Common difference = 5, so coefficient of n is 5. When n=1: 5(1) + c = 7, so c = 2. nth term = 5n + 2
    Examiner tips

    • Find common difference first - this is the coefficient of n
    • Substitute n=1 to find the constant

20. Question 10d

    2 marksSpeed, distance, time
    Time = distance ÷ speed = 24 ÷ 48 = 0.5 hours = 30 minutes
    Examiner tips

    • Time = Distance ÷ Speed
    • Convert decimal hours to minutes: 0.5 hours = 30 minutes

21. Question 11

    1 marksVolume of cube
    Volume of cube = side³ = 5³ = 125 cm³
    Examiner tips

    • Remember: Volume of cube = s³ (all sides equal)
    • Include the correct units (cm³)

22. Question 12

    2 marksSolving linear equations
    $4x + 7 = 2x - 3$. Subtract $2x$: $2x + 7 = -3$. Subtract $7$: $2x = -10$. Divide by $2$: $x = -5$
    Method:

    4x + 7 = 2x - 3. Subtract 2x: 2x + 7 = -3. Subtract 7: 2x = -10. Divide by 2: x = -5
    Examiner tips

    • Whatever you do to one side, do to the other
    • Check your answer by substituting back

23. Question 13a

    1 marksNegative numbers
    Negative × negative = positive. -6 × -7 = 42
    Examiner tips

    • Remember: negative × negative = positive
    • Calculate the absolute values first, then apply the sign rule

24. Question 13b

    1 marksNegative numbers
    Adding a negative is the same as subtracting. -5 + (-9) = -5 - 9 = -14
    Examiner tips

    • Adding two negatives: add absolute values, keep negative sign
    • Think of moving left on the number line

25. Question 14

    1 marksLaws of indices
    When multiplying with same base, add powers: $n + 3 = 8$, so $n = 5$
    Method:

    When multiplying with same base, add powers: n + 3 = 8, so n = 5
    Examiner tips

    • Same base means add the powers when multiplying
    • Set up equation: n + 3 = 8, then solve

26. Question 15

    3 marksNets of 3D shapes
    A cuboid has 6 faces, so its net must have 6 rectangles.
    Examiner tips

    • A cuboid has 6 rectangular faces
    • Check dimensions of each face match the cuboid

27. Question 16a

    2 marksSimplifying expressions
    Collect like terms: 8x - 2x = 6x and 3y - 7y = -4y. Answer: 6x - 4y
    Examiner tips

    • Group like terms: x terms with x, y terms with y
    • Be careful with signs when subtracting

28. Question 16bi

    1 marksFactorisation
    HCF of 8 and 12 is 4. Factor out: 8a + 12b = 4(2a + 3b)
    Examiner tips

    • Find the HCF of all terms
    • Check by expanding your answer

29. Question 16bii

    2 marksFactorisation
    Common factor is $ab$. $a^2b - 3ab = ab(a - 3)$
    Method:

    Common factor is ab. a²b - 3ab = ab(a - 3)
    Examiner tips

    • Factor out all common letters and numbers
    • Check by expanding to verify

30. Question 17

    2 marksEstimation
    Round: $38.7 \approx 40$, $21.2 \approx 20$, $2.89 \approx 3$, $4.12 \approx 4$. Calculate: $\frac{40+20}{3 \times 4} = \frac{60}{12} = 5$
    Method:

    Round: 38.7≈40, 21.2≈20, 2.89≈3, 4.12≈4. Calculate: (40+20)/(3×4) = 60/12 = 5
    Examiner tips

    • Round each number before calculating
    • Show your rounded values clearly

31. Question 18b

    2 marksAngles in parallel lines
    Corresponding angles are equal. The corresponding angle is 72°.
    Examiner tips

    • Identify the 'F' pattern for corresponding angles
    • Always state the geometric reason

32. Question 18c

    2 marksAngles in triangles
    Angles in triangle sum to 180°. Third angle = 180 - 55 - 75 = 50°
    Examiner tips

    • Remember: angles in a triangle sum to 180°
    • Third angle = 180° - (first angle + second angle)

33. Question 19a

    3 marksProbability
    P(blue) = number of blue ÷ total = 3/10
    Examiner tips

    • Probability = favourable ÷ total
    • Always simplify your fraction

34. Question 19b

    2 marksProbability - combined events
    P(Head) = 1/2. P(Head and Head) = 1/2 × 1/2 = 1/4
    Examiner tips

    • Use multiplication for 'and' (both events)
    • Draw a tree diagram if it helps

35. Question 20a

    1 marksScatter diagrams
    The coordinates (2.5, 40) mean x = 2.5 and y = 40.
    Examiner tips

    • Read x-value first (horizontal), then y-value (vertical)
    • Plot points accurately using the grid

36. Question 20b

    1 marksCorrelation
    When one variable increases and the other decreases, it is negative correlation.
    Examiner tips

    • Look at the general direction of the points
    • Negative means downward slope from left to right

37. Question 20ci

    1 marksLine of best fit
    A line of best fit should pass through the middle of the scattered points.
    Examiner tips

    • Use a ruler for a straight line
    • Balance points above and below the line

38. Question 20cii

    1 marksUsing line of best fit
    Read the y-value from the line at x = 10, which is 25.
    Examiner tips

    • Find x-value on horizontal axis, draw vertical line to the line of best fit
    • Then read across to the y-axis

39. Question 21

    2 marksCircle theorems
    Angle at centre = 2 × angle at circumference. So angle ACB = 84° ÷ 2 = 42°
    Examiner tips

    • Angle at centre = 2 × angle at circumference
    • Identify which angle is at the centre vs circumference

40. Question 22a

    1 marksHCF
    HCF = 2¹ × 5¹ = 10 (take lowest power of common factors)
    Examiner tips

    • List common prime factors only
    • Take the lowest power of each common prime

41. Question 22b

    2 marksLCM
    LCM = 2² × 3² = 4 × 9 = 36 (take highest power of all factors)
    Examiner tips

    • List ALL prime factors from both numbers
    • Take the highest power of each prime

42. Question 23a

    2 marksRotations
    90° clockwise: (x, y) → (y, -x). So (3, 2) → (2, -3)
    Examiner tips

    • For 90° clockwise: (x, y) → (y, -x)
    • Check each vertex carefully

43. Question 23b

    2 marksTranslations
    Moving right is positive x, moving down is negative y. Vector is (5, -3)
    Examiner tips

    • Vector notation: (horizontal change, vertical change)
    • Right is positive x, up is positive y

44. Question 23c

    3 marksEnlargements
    Multiply coordinates by scale factor: (2×3, 1×3) = (6, 3)
    Examiner tips

    • Scale factor = new length ÷ original length
    • Find centre where lines through corresponding points meet

45. Question 24

    3 marksAdding mixed numbers
    2¼ + 1⅔ = 9/4 + 5/3 = 27/12 + 20/12 = 47/12 = 3 11/12
    Examiner tips

    • Convert mixed numbers to improper fractions first
    • LCM of denominators gives common denominator
    • Simplify final answer

46. Question 25a

    1 marksStandard form
    47000 = 4.7 × 10⁴ (move decimal 4 places left)
    Examiner tips

    • A must be between 1 and 10
    • Count decimal places moved to get power of 10

47. Question 25b

    1 marksStandard form
    10⁻⁴ means move decimal 4 places left: 3.2 × 10⁻⁴ = 0.00032
    Examiner tips

    • Negative power means small number (less than 1)
    • Move decimal point left for negative powers

48. Question 26

    4 marksSimultaneous equations
    Add equations: 4x = 12, so x = 3. Then 3 - 2y = -1, 2y = 4, y = 2
    Examiner tips

    • Make coefficients of one variable equal
    • Add or subtract equations to eliminate
    • Substitute back to find the other variable
    • Check by substituting both values into original equations