May/June 2025 Paper 13 Worked Answers (IGCSE Maths 0580 Core)
33 questions · 33 marks · 90 minutes
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Worked answers for 33 questions
- Five hundred and three thousand = 503000, forty-one = 41. Combined: 503041. 50341 drops a zero. 503410 places 41 incorrectly. 5030041 adds an extra zero.Examiner tips
- Always check the number of digits in your answer matches what the question requires.
- Read the number aloud to verify it matches the words given.
- 4/5 = 4 ÷ 5 = 0.8. 0.45 concatenates 4 and 5. 4.5 is 4.5 not 4÷5. 0.08 divides by 50 instead.Examiner tips
- Remember that a fraction means division: numerator divided by denominator.
- For fifths, multiply by 2 to get tenths: 4/5 = 8/10 = 0.8.
- 0.65 = 65/100 = 13/20 (dividing by 5). 65/100 is not simplified. 6/5 misreads decimal. 13/25 divides incorrectly.Examiner tips
- Always check if your fraction can be simplified further.
- The HCF of 65 and 100 is 5, so divide both by 5.
- 8² = 8 × 8 = 64. 16 is 8 × 2. 80 is 8 × 10. 88 concatenates 8 and 8.Examiner tips
- Know your square numbers up to at least 15² = 225.
- Remember: squared means the number times itself, not times 2.
- ³√125 = 5 because 5 × 5 × 5 = 125. 25 is 125÷5. 41.67 is 125÷3. 11.18 is √125.Examiner tips
- Memorise common cube numbers: 1, 8, 27, 64, 125, 216.
- Check your answer by cubing it: 5³ = 5 × 5 × 5 = 125.
- 0.0000382 = 3.82 × 10⁻⁵ (decimal moves 5 places right). 3.82 × 10⁻⁴ counts 4 places. 38.2 × 10⁻⁶ is not standard form. 3.82 × 10⁵ has positive power.Examiner tips
- Standard form always has a number between 1 and 10 multiplied by a power of 10.
- For numbers less than 1, count zeros after the decimal point to find the negative power.
- 72 = 8 × 9 = 2³ × 3² (using prime factors). 8 × 9 uses non-prime factors. 2² × 3³ has wrong powers. 2⁴ × 3 is 48, not 72.Examiner tips
- Always check your answer by multiplying out: 2³ × 3² = 8 × 9 = 72.
- Use a factor tree or repeated division to find all prime factors.
- 1 cm = 10⁻² m. Number = 10⁻²/(1.2 × 10⁻¹⁰) = (1/1.2) × 10⁸ ≈ 8.3 × 10⁷. 8.3 × 10⁹ forgets cm conversion. 8.3 × 10⁻⁸ has wrong sign. 1.2 × 10⁸ doesn't divide properly.Examiner tips
- Always convert units so they match before calculating.
- When dividing powers of 10, subtract the indices: 10⁻² ÷ 10⁻¹⁰ = 10⁻²⁻⁽⁻¹⁰⁾ = 10⁸.
- 7 − (−4) = 7 + 4 = 11. 3 subtracts 4 instead. -11 makes both negative. -3 subtracts and makes negative.Examiner tips
- Remember: minus a minus equals a plus (two negatives make a positive).
- Think of it as: 7 − (−4) = 7 + 4.
- 5.4² = 29.16, 2.7³ = 19.683. Sum = 48.843. √48.843 ≈ 6.99 ≈ 6.80 (3 sf). 8.10 adds powers wrong. 46.3 forgets square root. 2.61 takes 4th root.Examiner tips
- Use brackets on your calculator to ensure correct order of operations.
- Check your answer is sensible - the square root should be smaller than the sum inside.
- 4x + 2x = 6x, −3y − 5y = −8y. Answer: 6x − 8y. 6x − 2y adds y terms wrong. 2x − 8y subtracts x terms. 6x + 8y ignores negative signs.Examiner tips
- Always group like terms together before simplifying.
- Be careful with negative signs - they stay with their terms.
- (2a³b²)³ = 2³ × a⁹ × b⁶ = 8a⁹b⁶. 6a⁹b⁶ multiplies 2 × 3 instead of 2³. 8a⁶b⁵ adds indices wrong. 2a⁹b⁶ forgets to cube the 2.Examiner tips
- Remember the power rule: (xᵐ)ⁿ = xᵐⁿ (multiply the powers).
- Apply the outside power to every part inside the brackets, including the coefficient.
- HCF is 4a. 8a² ÷ 4a = 2a, 12ab ÷ 4a = 3b. So 4a(2a + 3b). 4(2a² + 3ab), 2a(4a + 6b), and a(8a + 12b) don't fully factorise.Examiner tips
- Always check if the terms inside the brackets have any common factors left.
- Find the HCF of the coefficients AND the variables.
- From eq 2: y = 2x − 4. Sub: 3x + 2(2x − 4) = 13, 7x − 8 = 13, 7x = 21, x = 3. y = 6 − 4 = 2. Check: 3(3)+2(2)=13✓, 2(3)−2=4✓Examiner tips
- Always check your answer by substituting back into BOTH original equations.
- Use substitution or elimination method systematically.
- 1.24 = 124/100 = 31/25 (dividing by 4). 124/100 not simplified. 62/50 not fully simplified. 6/5 is 1.2 not 1.24.Examiner tips
- The HCF of 124 and 100 is 4, so divide both by 4.
- Check your simplified fraction cannot be reduced further.
- Let x = 0.6363... 100x = 63.6363... 99x = 63, x = 63/99 = 7/11. 63/99 not simplified. 63/100 wrong method. 21/33 not fully simplified.Examiner tips
- For 2-digit recurring decimals, multiply by 100 to shift the pattern.
- Always simplify your final fraction to its lowest terms.
- n=1: 1+3=4, n=2: 4+3=7, n=3: 9+3=12. 4, 5, 6 adds 1 each time. 3, 6, 11 starts at n=0. 4, 7, 10 uses 3n+1.Examiner tips
- Always start with n = 1 for the first term unless told otherwise.
- Calculate each term separately by substituting n values.
- y = kx, 8 = 5k, k = 1.6. When x = 15: y = 1.6 × 15 = 24. 18 adds 10. 40 is 5 × 8. 12 is 15 − 3.Examiner tips
- Direct proportion means y = kx. Find k first, then use it.
- Alternatively, if x triples (5 to 15), y also triples (8 to 24).
- 3⅔ + 1⅚ = 11/3 + 11/6 = 22/6 + 11/6 = 33/6 = 11/2 = 5½. 4 7/9 wrong denominator. 5 3/6 not simplified. 4½ adds wrong.Examiner tips
- Convert to improper fractions before adding for easier calculation.
- Always simplify your final answer and check if it's in simplest form.
- A parallelogram looks the same after rotation of 180°, so order = 2. 1 is for shapes with no symmetry. 4 is for squares. 0 is not valid.Examiner tips
- Order of rotational symmetry is how many times a shape looks the same in a full turn.
- A parallelogram maps onto itself at 180° and 360°, giving order 2.
- Isosceles triangle, so angles ABC = ACB. Sum = 180° − 50° = 130°. Each base angle = 65°. 50° uses apex angle. 130° is sum of base angles. 40° subtracts wrong.Examiner tips
- In an isosceles triangle, the angles opposite the equal sides are equal.
- Always check your angles add up to 180°.
- A cone has a circular base and tapers to a single point (vertex) at the top. Cylinder has two circular faces. Pyramid has polygonal base. Sphere is round everywhere.Examiner tips
- Learn the properties of common 3D shapes: faces, edges, vertices.
- A cone is like a pyramid but with a circular base instead of a polygon.
- Area of triangle = ½ × 8 × 5 = 20 cm². Volume = 20 × 12 = 240 cm³. 480 cm³ forgets to halve. 120 cm³ is just the area × 6. 200 cm³ miscalculates.Examiner tips
- Remember: volume of any prism = area of cross-section × length.
- For triangles: area = ½ × base × height.
- 4.5 × 2 = 9. 10⁶ × 10⁻³ = 10³. Answer: 9 × 10³. 9 × 10⁹ adds indices. 9 × 10⁻⁹ makes index negative. 6.5 × 10³ adds instead of multiplies.Examiner tips
- When multiplying in standard form: multiply the numbers, add the indices.
- Remember: 10⁶ × 10⁻³ = 10⁶⁺⁽⁻³⁾ = 10³.
- Inside B but outside A means B ∩ A' (B intersection not-A). A ∩ B' is A but not B. A ∪ B' is union. B − A' is wrong notation.Examiner tips
- A' (A complement) means 'not in A' or 'outside A'.
- ∩ means 'and' - both conditions must be true.
- Using n(F∪T) = n(F) + n(T) − n(F∩T): 40 = 25 + 20 − x, x = 5. 15 subtracts wrong way. 45 adds. 0 ignores overlap.Examiner tips
- If the sum of individual sets exceeds the total, there must be an overlap.
- Draw a Venn diagram to visualise the problem.
- When both variables increase together, it's positive correlation. Negative correlation is when one increases and other decreases. No correlation means no relationship. Perfect correlation means exactly on a line.Examiner tips
- Positive: both increase together (line goes up from left to right).
- Negative: one increases as the other decreases (line goes down from left to right).
- 6 km = 600000 cm. Map distance = 600000 ÷ 50000 = 12 cm. 120 cm uses wrong conversion. 1.2 cm divides by 500000. 300 cm multiplies wrong.Examiner tips
- Convert to the same units before applying the scale.
- 1 km = 100000 cm, so 6 km = 600000 cm.
- Area scale = 20000² = 4×10⁸. Actual = 5 × 4×10⁸ cm² = 2×10⁹ cm² = 0.2 km² (since 1 km² = 10¹⁰ cm²). 2 km² is ×10. 0.02 km² is ÷10. 20 km² way too big.Examiner tips
- For area, use (scale factor)² not just scale factor.
- 1 km = 100000 cm, so 1 km² = 10¹⁰ cm².
- 180° rotation about origin: (x, y) → (-x, -y). So (2, 3) → (-2, -3). (2, -3) reflects in x-axis. (-2, 3) reflects in y-axis. (3, 2) swaps coordinates.Examiner tips
- 180° rotation about origin: (x, y) → (-x, -y).
- This is the same as reflecting in both axes.
- 72 km/h = 72 × 1000 ÷ 3600 = 72000 ÷ 3600 = 20 m/s. 259.2 m/s multiplies by 3.6. 0.02 m/s divides too much. 1.2 m/s divides by 60 only.Examiner tips
- To convert km/h to m/s: divide by 3.6.
- To convert m/s to km/h: multiply by 3.6.
- 1.5 hours = 5400 s. Distance = 8 × 5400 = 43200 m = 43.2 km. 12 km is 8 × 1.5. 4.32 km divides by 10000. 432 km uses metres.Examiner tips
- Always check your units match before calculating.
- Distance = Speed × Time (when units are consistent).
- IQR = Q3 − Q1 = 73 − 45 = 28. 59 is average. 118 is sum. 14 is IQR ÷ 2.Examiner tips
- IQR = Upper Quartile − Lower Quartile = Q3 − Q1.
- The IQR measures the spread of the middle 50% of the data.
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