May/June 2025 Paper 32 Worked Answers (IGCSE Maths 0580 Core)

29 questions · 29 marks · 90 minutes

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1. Question 1a

   1 marksPolygons
   An 8-sided polygon is an octagon. Hexagon has 6 sides, heptagon has 7, decagon has 10.
   Examiner tips

   • Memorize the Greek prefixes for polygon names: penta (5), hexa (6), hepta (7), octa (8), nona (9), deca (10).
   • Use memory aids like 'octopus' for octagon (8) or 'decimal' for decagon (10).

2. Question 1b

   1 marksInterior Angles of Polygons
   Sum = (8-2) × 180° = 1080°. Each angle = 1080° ÷ 8 = 135°. 120° is hexagon. 144° is decagon. 108° is pentagon.
   Examiner tips

   • Always write the formula first: Sum = (n-2) × 180°, then substitute.
   • For regular polygons, divide the sum by the number of sides to get each interior angle.

3. Question 1c

   1 marksInterior Angles of Polygons
   (n-2) × 180 = 1440, n-2 = 8, n = 10. 8 gives 1080°. 9 gives 1260°. 12 gives 1800°.
   Examiner tips

   • To find n from sum: n = (sum ÷ 180°) + 2. This is the rearranged formula.
   • Check your answer by substituting back: (10-2) × 180° = 1440°.

4. Question 2a

   1 marksMultiplying Fractions
   2/5 × 3/8 = 6/40 = 3/20. 6/40 not simplified. 5/13 and D add instead of multiply.
   Examiner tips

   • Multiply straight across: numerator × numerator, denominator × denominator.
   • Always check if your answer can be simplified - the question asks for simplest form.

5. Question 2b

   1 marksDividing Mixed Numbers
   3½ = 7/2, 1¼ = 5/4. 7/2 ÷ 5/4 = 7/2 × 4/5 = 28/10 = 14/5 = 2⅘. 4⅜ multiplies. 2⅖ and 1¾ calculate wrong.
   Examiner tips

   • Always convert mixed numbers to improper fractions before dividing.
   • Keep, Change, Flip: Keep first fraction, Change ÷ to ×, Flip the second fraction.

6. Question 3a

   1 marksExpanding and Simplifying
   2(3x + 4) + 5(x − 1) = 6x + 8 + 5x − 5 = 11x + 3. 11x + 9 adds 8+5. 8x + 3 misses 5x. 11x − 1 subtracts wrong.
   Examiner tips

   • Expand each bracket separately, writing out all terms before simplifying.
   • Be very careful with negative signs, especially when multiplying a positive by a negative.

7. Question 3b

   1 marksFactorisation
   HCF = 5a. 15ab ÷ 5a = 3b, 20a² ÷ 5a = 4a. So 5a(3b − 4a). 5(3ab − 4a²), a(15b − 20a), and 5a(3b − 4) don't fully factorise.
   Examiner tips

   • The question says 'completely' - make sure you've taken out ALL common factors.
   • Check your answer by expanding: 5a × 3b = 15ab and 5a × 4a = 20a².

8. Question 3c

   1 marksSolving Linear Equations
   6x − 15 = 4x + 7, 2x = 22, x = 11. x = 4 doesn't expand correctly. x = −4 and x = 1 have sign errors.
   Examiner tips

   • Always expand brackets first before trying to solve.
   • Check your answer by substituting back: 3(2×11 − 5) = 3(17) = 51; 4×11 + 7 = 51. Correct!

9. Question 4a

   1 marksLaws of Indices
   Any non-zero number to power 0 equals 1. 0 confuses with x×0. 7 is 7¹. 70 concatenates.
   Examiner tips

   • The zero power rule: n⁰ = 1 for any n ≠ 0. This is a fundamental rule to memorize.
   • This rule works because n⁰ = nᵃ ÷ nᵃ = nᵃ⁻ᵃ = n⁰, and any number divided by itself is 1.

10. Question 4b

    1 marksNegative Indices
    4⁻³ = 1/4³ = 1/64. 64 ignores negative. -64 confuses negative index with negative value. 1/12 calculates 1/(4×3).
    Examiner tips

    • Negative index means 'one over': a⁻ⁿ = 1/aⁿ
    • Calculate the positive power first (4³ = 64), then write as 1/64.

11. Question 4c

    1 marksLaws of Indices
    (2x³)⁴ = 2⁴ × x¹² = 16x¹². 8x¹² is 2³. 16x⁷ adds indices. 2x¹² doesn't raise 2 to power.
    Examiner tips

    • Use the rule (aᵐ)ⁿ = aᵐⁿ - multiply the powers.
    • Don't forget the coefficient: (2x³)⁴ means 2⁴ and (x³)⁴.

12. Question 4d

    1 marksLaws of Indices
    y⁴ × y² = y⁶, then y⁶ ÷ y³ = y³. y⁹ adds all. y²⁴ multiplies. y subtracts wrong.
    Examiner tips

    • For same base: multiply → add indices; divide → subtract indices.
    • Work left to right or group multiplications together first: y⁴⁺²⁻³ = y³.

13. Question 5a

    1 marksSimple Interest
    Interest = 5000 × 0.02 × 4 = $\$400$. Total = $\$5400$. $\$400$ is just interest. $\$5408$ uses compound interest. $\$5800$ uses 4% per year.
    Examiner tips

    • Simple Interest formula: I = P × R × T (Principal × Rate × Time)
    • Remember to add the interest to the principal for the TOTAL amount.

14. Question 5b

    1 marksCompound Interest
    6000 × 1.03² = 6000 × 1.0609 = $\$6365.40$. $\$6360$ uses simple interest. $\$6180$ uses 1 year. $\$7128.54$ uses 9%.
    Examiner tips

    • Compound Interest: A = P × (1 + r)ⁿ where r is decimal rate, n is years.
    • For 3% growth, multiply by 1.03 each year, not 0.03.

15. Question 6a

    1 marksPie Charts
    Angle = (25/100) × 360° = 90°. 25° uses frequency as angle. 45° halves incorrectly. 72° uses 20% formula.
    Examiner tips

    • Pie chart angle = (part/whole) × 360°
    • 25 out of 100 is 25%, and 25% of 360° = 90°.

16. Question 6b

    1 marksMode
    Green and Yellow both have frequency 15 (highest). This is bimodal. Green only lists one. 15 gives frequency not category. Red is not highest.
    Examiner tips

    • Mode = most frequent category/value. Give the category name, not the frequency.
    • Data can be bimodal (two modes) or multimodal (more than two) if there are ties.

17. Question 7a

    1 marksBearings
    Back bearing = 85° + 180° = 265°. 085° is the original. 275° adds 190°. 095° adds 10°.
    Examiner tips

    • Back bearing = bearing ± 180°. Add 180° if under 180°, subtract 180° if over 180°.
    • Always check your answer is between 000° and 360°.

18. Question 7b

    1 marksScale Drawings
    15 km ÷ 2 = 7.5 cm. 30 cm multiplies by 2. 15 cm doesn't convert. 13 cm subtracts 2.
    Examiner tips

    • Scale 1:n means divide real distance by n to get map distance.
    • Think: bigger in real life, smaller on map - so divide.

19. Question 8a

    1 marksSubstitution
    y = 25 − 20 + 3 = 8. 3 just uses constant. -2 subtracts wrong. 13 adds all.
    Examiner tips

    • Replace every x with the given value, including in x² terms.
    • Follow BIDMAS: powers first, then multiplication, then addition/subtraction.

20. Question 8b

    1 marksQuadratic Graphs
    x² − 2x − 3 = 0, (x+1)(x−3) = 0, x = −1 or x = 3. x = 1 and x = −3 has signs wrong. x = 0 and x = 3 includes 0. x = −1 and x = −3 has both negative.
    Examiner tips

    • X-axis crossings are where y = 0, so solve the quadratic equation.
    • Check: (−1)² − 2(−1) − 3 = 1 + 2 − 3 = 0 ✓ and 3² − 2(3) − 3 = 9 − 6 − 3 = 0 ✓

21. Question 8c

    1 marksSolving Equations Graphically
    x² − 4 = 5, x² = 9, x = ±3. x = −1 and x = 1 solves x² = 1. x = −2 and x = 2 solves x² = 4. x = −9 and x = 9 uses x² = 81.
    Examiner tips

    • To solve graphically: draw the horizontal line y = k and read where it intersects the curve.
    • Algebraically: set curve = line value and solve.

22. Question 9a

    1 marksVolume of Cylinder
    V = πr²h = π × 64 × 10 = 640π cm³. 80π cm³ is πrh. 160π cm³ is 2πrh. 1280π cm³ doubles.
    Examiner tips

    • Cylinder volume = πr²h (base area × height).
    • Leave answer in terms of π - don't evaluate π unless asked.

23. Question 9b

    1 marksVolume of Cone
    V = ⅓πr²h = ⅓ × π × 36 × 10 = 120π cm³. 360π cm³ forgets ⅓. 60π cm³ uses ⅓πrh. 180π cm³ uses ½.
    Examiner tips

    • Cone volume = ⅓πr²h (one-third of cylinder volume).
    • Remember: Cone = ⅓, Sphere = 4/3 - don't confuse the fractions.

24. Question 10a

    1 marksCoordinates and Distance
    Distance = √[(4−1)² + (6−2)²] = √[9 + 16] = √25 = 5. 7 adds differences. 25 doesn't take root. 3 is just x-difference.
    Examiner tips

    • Distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²]
    • This is a 3-4-5 right triangle: √(3² + 4²) = √(9 + 16) = √25 = 5.

25. Question 10b

    1 marksReflections
    P is 2 units left of x=5. Image is 2 units right, at x = 7. y stays same. (7, 4). (3, 6) reflects in y. (−3, 4) reflects in y-axis. (5, 4) is on mirror line.
    Examiner tips

    • For vertical mirror line x = k: new x = 2k − old x; y stays the same.
    • Check: distance from (3, 4) to x = 5 is 2. Distance from (7, 4) to x = 5 is also 2. ✓

26. Question 10c

    1 marksReflections
    Point is 2 above y=1. Image is 2 below, at y = −1. x stays same. (2, −1). (2, 5) goes wrong direction. (−2, 3) reflects in y-axis. (0, 3) reflects in x=1.
    Examiner tips

    • For horizontal mirror line y = k: x stays the same; new y = 2k − old y.
    • Point (2, 3) is 2 above y = 1. Image is 2 below y = 1, at y = −1.

27. Question 11a

    1 marksProbability
    P(blue) = 6/10 = 3/5. 2/5 is P(red). 6/4 has ratio inverted. 2/3 simplifies wrong.
    Examiner tips

    • P(event) = favorable outcomes ÷ total outcomes.
    • Always simplify fractions: 6/10 = 3/5.

28. Question 11b

    1 marksProbability Trees
    P(R then B) = 3/5 × 2/4 = 6/20 = 3/10. 6/25 uses replacement. 6/20 not simplified. 1/5 is wrong calculation.
    Examiner tips

    • Without replacement: total decreases by 1 after each pick.
    • P(A and B) = P(A) × P(B given A has happened).

29. Question 11c

    1 marksProbability - Combined Events
    P(RR) + P(BB) = (4/7 × 3/6) + (3/7 × 2/6) = 12/42 + 6/42 = 18/42 = 9/21. 12/21 is different colours. 6/21 is just P(BB). 7/21 is wrong.
    Examiner tips

    • Same colour = P(RR) + P(BB). Different colour = P(RB) + P(BR).
    • Check: P(same) + P(different) should equal 1.