IGCSE Maths 0580 Paper 4 Practice Paper (Extended, 100 marks)

Level: Year 10–11 (IGCSE) | Subject: Maths 0580 | Time: 120 minutes | Total: 100 marks | Parts: 38

Paper at a glance

Item	Details
Paper	Paper 4 (Extended, calculator allowed)
Question style	Structured, multi-part questions
Mock layout	100 marks / 120 minutes

Questions

Question 1 (14 marks) — Number and percentages

(a) Work out 2/3 + 3/5 – 1/2, giving your answer as a fraction in its simplest form. (3 marks)

(b) A jacket costs $240 before a 15% discount. Find the sale price. (4 marks)

(c) Write 0.000048 in standard form (a x 10^n where a is between 1 and 10). (3 marks)

(d) $840 is shared in the ratio 3 : 4 : 5. Find each share. (4 marks)

Question 2 (16 marks) — Algebra

(a) Solve the simultaneous equations 3x + 2y = 16 and x + 2y = 8. (4 marks)

(b) Factorise x^2 – 7x + 12. (2 marks)

(c) Solve 2x^2 – 5x – 3 = 0. (4 marks)

(d) Solve the inequality 4 – 3x > -8. (2 marks)

(e) Given P = 2(L + W), P = 46 and L = 15, find W. (2 marks)

(f) Find the 20th term of the sequence 5, 8, 11, 14, … (2 marks)

Question 3 (16 marks) — Geometry

(a) Find the size of each interior angle of a regular octagon. (2 marks)

(b) Find the sum of the interior angles of a decagon. (1 marks)

(c) A triangle has angles 2x, 3x and 85 degrees. Find x and the smallest angle. (3 marks)

(d) The angle at the centre is twice the angle at the circumference. If the angle at the circumference is 32 degrees, find the angle at the centre. (3 marks)

(e) A trapezium has parallel sides 12 cm and 18 cm and height 7 cm. Find its area. (3 marks)

(f) A cylinder has radius 3.5 cm and height 12 cm. Use pi = 3.14 and find its volume correct to 1 decimal place. (4 marks)

Question 4 (14 marks) — Coordinates and functions

(a) Find the gradient of the line through (2, 5) and (8, 17). (2 marks)

(b) Hence write the equation of the line in the form y = mx + c. (2 marks)

(c) Find the y-intercept of the line 3x – 2y = 12. (2 marks)

(d) Find the midpoint of (4, -3) and (10, 7). (2 marks)

(e) Find the distance between (4, -3) and (10, 7), correct to 2 decimal places. (3 marks)

(f) Find the coordinates of the minimum point of y = x^2 – 4x + 1. (3 marks)

Question 5 (14 marks) — Trigonometry

(a) A right-angled triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg. (2 marks)

(b) If tan of theta = 7/24, find theta correct to 1 decimal place. (3 marks)

(c) A triangle has sides 8 cm and 11 cm with an included angle of 35 degrees. Find its area to 2 decimal places. (3 marks)

(d) In a triangle, A = 48 degrees, B = 72 degrees and a = 10 cm. Use the sine rule to find b to 2 decimal places. (3 marks)

(e) A boat sails on a bearing of 055 degrees. What bearing should it take to return? (3 marks)

Question 6 (14 marks) — Statistics and probability

(a) Find the mean of 4, 7, 7, 9, 12 and 15. (2 marks)

(b) Find the median of the same set of data. (2 marks)

(c) Find the mode of the same set of data. (1 marks)

(d) Find the range of the same set of data. (1 marks)

(e) A bag has 5 red, 3 blue and 2 green balls. Two balls are taken at random without replacement. Find the probability that both are green. (4 marks)

(f) The scores of 30 students are: 4 students scored 1, 7 scored 2, 9 scored 3, 6 scored 4 and 4 scored 5. Find the mean score to 2 decimal places. (4 marks)

Question 7 (12 marks) — Interest, proportion and speed

(a) $4,000 is invested at 3% per year compound interest. Find the amount after 2 years to 2 decimal places. (3 marks)

(b) A car worth $25,000 depreciates by 12% each year. Find its value after 3 years to 2 decimal places. (3 marks)

(c) A car travels 180 km in 2 hours 15 minutes. Find its average speed in km/h. (2 marks)

(d) One pound buys HK$9.8. How many pounds can HK$350 buy, to 2 decimal places? (2 marks)

(e) y is directly proportional to x^2. When x = 3, y = 45. Find y when x = 7. (2 marks)

Answers and marking notes

Question 1 — Number and percentages

(a) Common denominator 30: 20/30 + 18/30 – 15/30 = 23/30. [3 marks]

(b) 240 x (1 – 0.15) = 240 x 0.85 = $204. [4 marks]

(c) Move the decimal point 5 places right: 4.8 x 10^-5. [3 marks]

(d) 3 + 4 + 5 = 12 parts; 840 / 12 = $70 each; shares $210, $280, $350 (total $840). [4 marks]

Question 2 — Algebra

(a) Subtract: 2x = 8 so x = 4; substituting gives y = 2. [4 marks]

(b) (x – 3)(x – 4), since -3 + (-4) = -7 and (-3)(-4) = 12. [2 marks]

(c) (2x + 1)(x – 3) = 0, so x = -1/2 or x = 3. [4 marks]

(d) -3x > -12; dividing by a negative reverses the sign, so x is less than 4. [2 marks]

(e) W = (P – 2L) / 2 = (46 – 30) / 2 = 8. [2 marks]

(f) Common difference 3, nth term 3n + 2; with n = 20 this gives 62. [2 marks]

Question 3 — Geometry

(a) (8 – 2) x 180 / 8 = 1080 / 8 = 135 degrees. [2 marks]

(b) (10 – 2) x 180 = 1440 degrees. [1 marks]

(c) 5x + 85 = 180 so x = 19; smallest angle 2 x 19 = 38 degrees. [3 marks]

(d) 2 x 32 = 64 degrees. [3 marks]

(e) 1/2 x (12 + 18) x 7 = 1/2 x 30 x 7 = 105 cm^2. [3 marks]

(f) 3.14 x 3.5^2 x 12 = 3.14 x 147 = 461.6 cm^3 (1 d.p.). [4 marks]

Question 4 — Coordinates and functions

(a) (17 – 5) / (8 – 2) = 12 / 6 = 2. [2 marks]

(b) y = 2x + c; using (2, 5): 5 = 4 + c so c = 1, giving y = 2x + 1. [2 marks]

(c) Set x = 0: -2y = 12 so y = -6; the y-intercept is -6. [2 marks]

(d) ((4 + 10)/2, (-3 + 7)/2) = (7, 2). [2 marks]

(e) Square root of (36 + 100) = square root of 136, about 11.66. [3 marks]

(f) Completing the square: y = (x – 2)^2 – 3, so the minimum point is (2, -3). [3 marks]

Question 5 — Trigonometry

(a) Square root of (169 – 25) = square root of 144 = 12 cm. [2 marks]

(b) theta = inverse tan of 0.2917, about 16.3 degrees. [3 marks]

(c) 1/2 x 8 x 11 x sin 35 degrees, about 25.24 cm^2. [3 marks]

(d) b = 10 x sin 72 / sin 48, about 12.80 cm. [3 marks]

(e) Opposite bearing = 55 + 180 = 235 degrees. [3 marks]

Question 6 — Statistics and probability

(a) Total 54; 54 / 6 = 9. [2 marks]

(b) With 6 values the middle two are 7 and 9; (7 + 9)/2 = 8. [2 marks]

(c) 7 appears twice, so the mode is 7. [1 marks]

(d) 15 – 4 = 11. [1 marks]

(e) 2/10 x 1/9 = 2/90 = 1/45 (about 0.022). [4 marks]

(f) Total = 4 + 14 + 27 + 24 + 20 = 89; 89 / 30, about 2.97. [4 marks]

Question 7 — Interest, proportion and speed

(a) 4000 x 1.03^2 = 4000 x 1.0609 = $4,243.60. [3 marks]

(b) 25000 x 0.88^3 = 25000 x 0.681472 = $17,036.80. [3 marks]

(c) 2 hours 15 minutes = 2.25 hours; 180 / 2.25 = 80 km/h. [2 marks]

(d) 350 / 9.8, about 35.71 pounds. [2 marks]

(e) y = k x^2; 45 = 9k so k = 5; when x = 7, y = 5 x 49 = 245. [2 marks]

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