ICSE Class 5 Mathematics · Exam Practice

Final Examination — Set 3

ICSE Class 5 Mathematics, covering all chapters, with a full answer key and worked solutions.

🎯 Full Marks: 80 ⏱️ Time: 2½ Hours 📝 Questions: 53
SectionTopicQsMarks
ANumber System1515
BFractions & Decimals1520
CRatio, Percentage & Profit & Loss1024
DGeometry & Measurement714
EData Handling & Logical Reasoning67
Total5380
Before you start
  • Attempt the paper first, without looking at the answer key at the bottom of the page.
  • Show your working for Sections C, D and E — method marks are given even if the final answer is wrong.
15 MARKS

Section A — Number System

1. Multiple Choice Questions (MCQs) (1 mark each)

1. The place value of 5 in 83,657 is

A. 5B. 50C. 500D. 5,000

2. Which of the following is a prime number?

A. 12B. 15C. 29D. 21

3. The expanded form of 70,605 is

A. 70,000+600+5B. 70,000+50+6C. 70,000+60+5D. 7,000+600+5

4. Which of the following is a multiple of both 4 and 6?

A. 20B. 18C. 24D. 14

5. The predecessor of 1,00,000 is

A. 99,999B. 1,00,001C. 1,01,000D. 98,999

6. Which of the following is a cube?

A. 64B. 28C. 16D. 120

7. HCF of 24 and 36 is

A. 6B. 8C. 12D. 18

8. Which of the following is a perfect square?

A. 18B. 36C. 40D. 50

9. Which of the following numbers is divisible by 2, 3 and 5?

A. 230B. 320C. 345D. 420

10. 9,28,070 rounded off to the nearest thousand is

A. 9,28,000B. 9,28,100C. 9,29,000D. 9,27,000

2. Fill in the Blanks (1 mark each)

1. The smallest 6-digit number is ______.

2. The place value of 2 in 52,08,749 is ______.

3. One million = ______ lakh.

4. 7,00,000 + 80,000 + 900 + 6 is written as ______.

5. The greatest 5-digit number is ______.

20 MARKS

Section B — Fractions & Decimals

3. True or False (1 mark each)

1. 2/3 is greater than 1/2. (   )

2. 0.375 is equal to 3/8. (   )

3. 7/10 is an improper fraction. (   )

4. A decimal has a finite number of digits. (   )

5. 1.25 lies between 1.2 and 1.3. (   )

4. Match the Following (1 mark each)

Column A
1.3/5 of 25
2.2.4 + 3.6
3.0.6 × 0.5
4.5/6 of 36
5.7.2 − 2.8
Column B
a)4.4
b)30
c)6
d)15
e)0.30

5. Very Short Answer Type Questions (2 marks each)

1. Write the decimal form of 7/8.

2. Arrange in ascending order: 0.3, 0.03, 0.303, 0.33.

3. Write the fraction for: five seventh.

4. Express 3.75 as a fraction in simplest form.

5. Find the sum: 12.75 + 8.5.

24 MARKS

Section C — Ratio, Percentage & Profit & Loss

6. Solve the Following (2 marks each)

1. Simplify the ratio 18 : 24.

2. A class has 20 boys and 15 girls. What is the ratio of boys to girls?

3. 25% of 240.

4. A shopkeeper bought a table for ₹2,400 and sold it for ₹3,000. Find his profit.

5. If the price of a shirt is ₹800 and there is a discount of 15%, find the discount amount.

7. Do As Directed (2 marks each)

1. Express 3 : 5 in the form of a fraction.

2. A number is increased by 20%. If the number is 150, find the increased number.

3. Find the selling price if the cost price is ₹1,250 and the profit is 25%.

8. Think & Solve (Word Problems) (4 marks each)

1. In a class of 45 students, 2/5 of the students like cricket and 1/3 like football. How many students like cricket? How many like football?

2. A shopkeeper buys an article for ₹560 and sells it at a loss of 12%. Find the selling price.

14 MARKS

Section D — Geometry & Measurement

9. Answer the Following (2 marks each)

1. Find the perimeter of a rectangle whose length is 16 cm and breadth is 9 cm.

2. Find the area of a square whose side is 12 cm.

3. Convert 4 m 25 cm into centimetres.

4. Convert 3 hours 15 minutes into minutes.

5. The length of a room is 7 m 50 cm and the breadth is 5 m 20 cm. Find its perimeter.

10. Draw & Label (2 marks each)

1. Draw a line segment AB of length 6.5 cm.

2. Draw a circle and show its centre O and a radius of 3.5 cm.

7 MARKS

Section E — Data Handling & Logical Reasoning

Number of Books Sold in a WeekBar graph. Mon: 30; Tue: 52; Wed: 20; Thu: 42; Fri: 35.Number of Books Sold in a Week010203040506030Mon52Tue20Wed42Thu35FriDayBooks sold
Bar graph — Number of Books Sold in a Week

11. Study the Bar Graph and Answer the Questions (1 mark each)

1. On which day were the maximum books sold?

2. How many books were sold on Thursday?

3. How many books were sold on Wednesday?

4. If 25 more books were sold on Friday, how many books would be sold?

5. Find the total number of books sold in the week.

12. Master Challenge (2 marks)

1. A number when divided by 7 leaves remainder 3. When the same number is divided by 5, it leaves remainder 2. What is the smallest such number?

ICSE Class 5 Mathematics · Final Examination — Set 3 · Answer Key

Answers & Worked Solutions

Mark your own paper, then read the solution for every question you got wrong. For the multiple-choice questions, the note in pink shows the answer most students pick by mistake, and why.

Section A — Number System (15 marks)
1. Multiple Choice Questions
Q1. B. 50

In 83,657 the digits are 8 (ten-thousands), 3 (thousands), 6 (hundreds), 5 (tens), 7 (ones). 5 is in the tens place: 50.

Q2. C. 29

29 has no factors other than 1 and itself. 12, 15, 21 are all composite.

Q3. A. 70,000+600+5

In 70,605 the digits are 7 (ten-thousands), 0 (thousands), 6 (hundreds), 0 (tens), 5 (ones) — the zeros contribute nothing.

Q4. C. 24

24 = 4 × 6, so it is a multiple of both 4 and 6.

Q5. A. 99,999

Predecessor = 1 less: 1,00,000 − 1 = 99,999.

Q6. A. 64

64 = 4 × 4 × 4.

Q7. C. 12

24 = 2³×3, 36 = 2²×3². HCF = 2²×3 = 12.

Q8. B. 36

36 = 6 × 6, a perfect square.

Q9. D. 420

Divisible by 2, 3 and 5 means divisible by 30. 420 ÷ 30 = 14 exactly.

Q10. A. 9,28,000

The hundreds digit in 9,28,070 is 0, which is less than 5, so round down to 9,28,000.

2. Fill in the Blanks
Q1. 1,00,000

The smallest 6-digit number is 1 followed by five zeros.

Q2. 2,00,000

In 52,08,749 the digit 2 is in the lakh place.

Q3. 10

1 million = 10,00,000 = 10 × 1,00,000 (10 lakh).

Q4. 7,80,906

7,00,000 + 80,000 + 900 + 6 = 7,80,906.

Q5. 99,999

Five 9s is the greatest 5-digit number.

Section B — Fractions & Decimals (20 marks)
3. True or False
Q1. True

2/3 ≈ 0.667 and 1/2 = 0.5, so 2/3 is greater.

Q2. True

3/8 = 0.375.

Q3. False

7/10 has a smaller numerator than denominator, making it a proper fraction, not improper.

Q4. True

At Class 5 level, a decimal such as 0.5 or 3.14 has a finite number of digits after the point.

Q5. True

1.2 < 1.25 < 1.3.

4. Match the Following
1 → d) 15

3/5 of 25 = (3 × 25) ÷ 5 = 15.

2 → c) 6

2.4 + 3.6 = 6.0 = 6.

3 → e) 0.30

0.6 × 0.5 = 0.30.

4 → b) 30

5/6 of 36 = (5 × 36) ÷ 6 = 30.

5 → a) 4.4

7.2 − 2.8 = 4.4.

5. Very Short Answer Type Questions
Q1. 0.875

7/8 = 7 ÷ 8 = 0.875.

Q2. 0.03, 0.3, 0.303, 0.33

Write with 3 decimal places: 0.300, 0.030, 0.303, 0.330. Ascending: 0.030 < 0.300 < 0.303 < 0.330.

Q3. 5/7

Five sevenths = 5/7.

Q4. 15/4

3.75 = 375/100. Dividing both by 25: 15/4 (or 3 3/4 as a mixed number).

Q5. 21.25

12.75 + 8.5 = 21.25.

Section C — Ratio, Percentage & Profit & Loss (24 marks)
6. Solve the Following
Q1. 3 : 4

18 and 24 share the common factor 6: 18÷6=3, 24÷6=4.

Q2. 4 : 3

Boys : girls = 20 : 15 = 4 : 3 (dividing both by 5).

Q3. 60

25% of 240 = (25 ÷ 100) × 240 = 60.

Q4. ₹600

Profit = Selling price − Cost price = 3,000 − 2,400 = ₹600.

Q5. ₹120

Discount = 15% of ₹800 = (15 ÷ 100) × 800 = ₹120.

7. Do As Directed
Q1. 3/5

3 : 5 written as a fraction is 3/5.

Q2. 180

Increase = 20% of 150 = 30. Increased number = 150 + 30 = 180.

Q3. ₹1,562.50

Profit = 25% of ₹1,250 = ₹312.50. Selling price = 1,250 + 312.50 = ₹1,562.50.

8. Think & Solve (Word Problems)
Q1. Cricket: 18 students; Football: 15 students
  1. Cricket: 2/5 of 45 = (2 × 45) ÷ 5 = 18.
  2. Football: 1/3 of 45 = 45 ÷ 3 = 15.
Q2. ₹492.80
  1. Loss = 12% of ₹560 = ₹67.20.
  2. Selling price = 560 − 67.20 = ₹492.80.
Section D — Geometry & Measurement (14 marks)
9. Answer the Following
Q1. 50 cm

Perimeter = 2 × (16 + 9) = 2 × 25 = 50 cm.

Q2. 144 sq cm

Area of a square = side × side = 12 × 12 = 144 sq cm.

Q3. 425 cm

4 m = 400 cm. 400 + 25 = 425 cm.

Q4. 195 minutes

3 hours = 180 minutes. 180 + 15 = 195 minutes.

Q5. 25 m 40 cm
  1. Length + breadth = 7 m 50 cm + 5 m 20 cm = 12 m 70 cm.
  2. Perimeter = 2 × 12 m 70 cm = 25 m 40 cm.
10. Draw & Label
Q1. Line segment AB = 6.5 cm

Use a ruler: mark point A at 0, mark point B at 6.5 cm, join with a straight line.

Q2. Circle with radius OP = 3.5 cm

Open the compass to 3.5 cm, place the point on centre O, and draw the circle. Mark a point P on the circle and label OP = 3.5 cm.

Section E — Data Handling & Logical Reasoning (7 marks)
11. Study the Bar Graph
Q1. Tuesday

Tuesday has the tallest bar (52).

Q2. 42 books

Read the top of the Thursday bar: 42.

Q3. 20 books

Read the top of the Wednesday bar: 20.

Q4. 60 books

Friday (35) + 25 = 60.

Q5. 179 books

30 + 52 + 20 + 42 + 35 = 179.

12. Master Challenge
Q1. 17
  1. Numbers leaving remainder 3 when divided by 7: 3, 10, 17, 24, …
  2. Check each ÷ 5: 3 → remainder 3 (no); 10 → remainder 0 (no); 17 → remainder 2 (yes).
  3. Check: 17 = 2×7+3 ✓, 17 = 3×5+2 ✓. So the smallest such number is 17.
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