Paper 4 style: Extended (calculator) — question paper (print)

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IGCSE · Cambridge IGCSE Mathematics (Extended)

Paper 4 style practice paper

Extended (calculator)

Duration: 120 minutes

Total: 100 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Answer all questions.
Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
Section B contains structured questions. Write your answers in the spaces provided.
A calculator may be used. Show all your working — marks are given for method.
Give non-exact numerical answers correct to 3 significant figures, or as required.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total mark for this paper is 100.

Original practice material written against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Extended content across the 0580 syllabus, calculator allowed.

For Examiner’s Use
Section A	/ 10
Section B	/ 90
Total	/ 100

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

1
Written as a decimal, ⅜ is
1. A0.38
2. B0.375
3. C0.83
4. D2.67
( )
2
Work out 15% of 68.
1. A10.2
2. B10.7
3. C8.8
4. D57.8
( )
3
Work out 4.7 × 10³ + 2.1 × 10², giving your answer in standard form.
1. A6.8 × 10³
2. B49.1 × 10²
3. C4.91 × 10³
4. D6.8 × 10²
( )
4
A sequence has nth term n² + 4n. Its 8th term is
1. A96
2. B92
3. C100
4. D88
( )
5
The solutions of 3x² = 27 are
1. Ax = 3 only
2. Bx = 9
3. Cx = ±3
4. Dx = −3 only
( )
6
The gradient of the line 4x + 2y = 8 is
1. A−2
2. B4
3. C2
4. D−4
( )
7
A cylinder has radius 5 cm and height 12 cm. Its volume is closest to
1. A188.5 cm³
2. B942.5 cm³
3. C3770 cm³
4. D471.2 cm³
( )
8
sin x = 0.5 has the solution x = 30°. The other solution in 0° ⩽ x ⩽ 360° is
1. A60°
2. B150°
3. C210°
4. D330°
( )
9
A triangle has sides 7 cm and 10 cm with 68° between them. Its area is closest to
1. A9.83 cm²
2. B70 cm²
3. C65 cm²
4. D32.5 cm²
( )
10
A team wins each game with probability 0.35. In 80 games, the expected number of wins is
1. A2.3
2. B46
3. C280
4. D28
( )

Section B: Structured questions[90 marks]

Answer all questions in the spaces provided. Show all your working.

11
Number work.
1. (a)
  Write 0.00497 in standard form.
  [1]
2. (b)
  A car travels 168 km on 14 litres of petrol. Find the distance it can travel on 20 litres.
  [2]
3. (c)
  The exchange rate is £1 = $1.27. Convert $190.50 to pounds.
  [2]
12
Percentages.
1. (a)
  A town of 24 000 people grows by 6% each year. Find the population after 2 years, to the nearest whole number.
  [3]
2. (b)
  A jacket costs $95 after a 24% discount. Find its original price.
  [2]
13
Indices and standard form.
1. (a)
  Evaluate 8^(4⁄3).
  [2]
2. (b)
  Work out (6 × 10⁸) ÷ (3 × 10⁻²), giving your answer in standard form.
  [2]
3. (c)
  Work out 7.2 × 10⁵ + 4.6 × 10⁴, giving your answer in standard form.
  [2]
14
a = 6.3 correct to 1 decimal place and b = 4.8 correct to 1 decimal place.
1. (a)
  Write down the upper and lower bounds of a.
  [2]
2. (b)
  Calculate the upper bound of a + b.
  [1]
3. (c)
  Calculate the lower bound of a ÷ b, giving your answer to 3 significant figures.
  [2]
15
Algebra.
1. (a)
  Expand and simplify (x + 3)(x − 5).
  [2]
2. (b)
  Factorise 2x² + 7x + 3.
  [2]
3. (c)
  Simplify (x² − 25) ÷ (x + 5).
  [1]
16
Equations.
1. (a)
  Solve 5(2x − 1) = 3x + 24, giving your answer to 2 decimal places.
  [3]
2. (b)
  Solve the simultaneous equations 3x + 2y = 16 and x = y + 2.
  [3]
17
Solve x² − 7x + 2 = 0 using the quadratic formula. Give both solutions correct to 3 significant figures.
1. (a)
  Show that the discriminant is 41, and hence find both solutions.
  [5]
18
Inequalities.
1. (a)
  Solve x² − 3x − 10 > 0.
  [3]
2. (b)
  List the integer values satisfying 2 ⩽ 3x − 1 < 11.
  [2]
19
f(x) = 3x + 1 and g(x) = x² − 2.
1. (a)
  Find fg(3).
  [2]
2. (b)
  Find gf(−1).
  [2]
3. (c)
  Find f⁻¹(x).
  [2]
20
A cyclist rides 200 m in 25 seconds at constant speed, then decelerates uniformly to rest in the next 15 seconds.
1. (a)
  Find the constant speed, in m/s.
  [1]
2. (b)
  Find the deceleration, in m/s².
  [2]
3. (c)
  Find the total distance travelled in the 40 seconds.
  [2]
21
A(−2, 3) and B(4, 11).
1. (a)
  Find the gradient of AB.
  [2]
2. (b)
  Find the exact length AB.
  [2]
3. (c)
  Show that the equation of the line AB is 3y = 4x + 17.
  [1]
22
A right cone has radius 6 cm and perpendicular height 8 cm.
1. (a)
  Show that the slant height is 10 cm.
  [1]
2. (b)
  Find the volume of the cone, to 3 significant figures.
  [2]
3. (c)
  Find the total surface area of the cone (curved surface plus base), to 3 significant figures.
  [3]
23
Trigonometry.
1. (a)
  A ladder of length 7.5 m leans against a wall at 62° to the horizontal ground. Find the height it reaches up the wall, to 3 significant figures.
  [2]
2. (b)
  A triangle has sides 12 cm and 9 cm with an angle of 42° between them. Find the third side, to 3 significant figures.
  [3]
3. (c)
  Find the area of the same triangle, to 3 significant figures.
  [1]
24
A bag holds 7 red and 5 blue counters. Two counters are drawn without replacement.
1. (a)
  Write the probabilities on the branches of a tree diagram for the two draws.
  [1]
2. (b)
  Find P(both counters are red).
  [2]
3. (c)
  Find P(the two counters have different colours), giving your answer as a fraction in its lowest terms.
  [3]
25
The heights of 80 plants are grouped. Cumulative frequencies: ⩽10 cm (8), ⩽20 cm (32), ⩽30 cm (60), ⩽40 cm (76), ⩽50 cm (80). A smooth cumulative frequency curve is drawn through these points.
1. (a)
  Use the curve to estimate the median height, giving your answer to the nearest centimetre.
  [2]
2. (b)
  Estimate the interquartile range of the heights, to the nearest centimetre.
  [3]
26
Goals scored by a team in 20 matches: 0 goals ×4, 1 goal ×8, 2 goals ×5, 3 goals ×2, 4 goals ×1.
1. (a)
  Calculate the mean number of goals.
  [3]
2. (b)
  Find the median number of goals.
  [2]
27
A, B and C are points on a circle, centre O.
1. (a)
  Angle AOB at the centre is subtended by the same arc as angle ACB at the circumference. Given angle ACB = 48°, find angle AOB.
  [2]
2. (b)
  ABCD is a cyclic quadrilateral with angle ABC = 78°. Find angle ADC.
  [2]

— End of paper —

Paper 4 style practice paper: Extended (calculator) — question paper