The Four Operations (Copy)
IGCSE Mathematics Core Practice Exam
Topic: Four Operations with Integers, Fractions, Decimals & Practical Situations
Total Marks: 40
Time: 40 minutes
(With Detailed Solutions)
Section A: Short Questions (No Calculator)
Total Marks: 20
1. Calculate the following, using BIDMAS where necessary: (6 marks)
a) 6 − 4 × 3
b) (5 + 3) × 2
c) 10 − [6 ÷ 2 + 1]
2. Simplify and give your answer as a mixed number where necessary: (6 marks)
a) 2/3 + 1/6
b) 3 ½ − 1 ¼
c) 1 ⅓ × 2 ¼
3. Calculate the following decimal operations: (4 marks)
a) 2.5 + 1.75
b) 3.6 ÷ 0.6
4. Fill in the blanks with >, < or = : (4 marks)
a) −5 ___ −8
b) 2.4 ___ 2.40
c) 1 ½ ___ 3/2
d) 0.75 ___ ¾
Section B: Structured Questions (Calculator Allowed)
Total Marks: 20
5. The temperature at 6 AM was 4°C. By midnight, it had dropped by 11°C.
a) What was the temperature at midnight? (2 marks)
b) If the temperature then rose by 6°C, what would it be? (2 marks)
6. A diver is at −25 meters below sea level. He dives a further 18 meters, then ascends 12 meters.
a) What is his final position relative to sea level? (3 marks)
7. Work out the following and simplify your answer: (6 marks)
a) 5/6 ÷ 2/3
b) 4.2 × 1.5
c) (3 − 7) × (−2)
8. A shopkeeper buys 3.5 kg of apples and 2.75 kg of oranges. How much fruit did he buy in total? (2 marks)
9. Subtract 2 ¾ from 5 ⅓ and give your answer as a mixed number in simplest form. (2 marks)
Marking Scheme with Detailed Explanations
Section A
1.
a) 6 − 4 × 3 = 6 − 12 = −6 (2 marks)
b) (5 + 3) × 2 = 8 × 2 = 16 (2 marks)
c) 10 − [6 ÷ 2 + 1] = 10 − [3 + 1] = 10 − 4 = 6 (2 marks)
2.
a) 2/3 + 1/6 = 4/6 + 1/6 = 5/6 (2 marks)
b) 3 ½ − 1 ¼ = (7/2) − (5/4) = 14/4 − 5/4 = 9/4 = 2 ¼ (2 marks)
c) 1 ⅓ × 2 ¼ = (4/3) × (9/4) = 36/12 = 3 (2 marks)
3.
a) 2.5 + 1.75 = 4.25 (2 marks)
b) 3.6 ÷ 0.6 = 36 ÷ 6 = 6 (2 marks)
4.
a) −5 > −8 (1 mark)
b) 2.4 = 2.40 (1 mark)
c) 1 ½ = 3/2 (1 mark)
d) 0.75 = ¾ (1 mark)
Section B
5.
a) 4 − 11 = −7°C (2 marks)
b) −7 + 6 = −1°C (2 marks)
6.
−25 − 18 = −43
−43 + 12 = −31 meters (3 marks)
7.
a) 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1 ¼ (2 marks)
b) 4.2 × 1.5 = 6.30 (2 marks)
c) (3 − 7) × (−2) = (−4) × (−2) = 8 (2 marks)
8.
3.5 + 2.75 = 6.25 kg (2 marks)
9.
5 ⅓ − 2 ¾ = (16/3) − (11/4) = (64/12) − (33/12) = 31/12 = 2 7/12 (2 marks)