ICSE Class 5 Mathematics · Exam Practice

Final Examination — Set 6

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 9 in 7,95,824 is

A. 9B. 900C. 90,000D. 9,00,000

2. Which of the following is the greatest number?

A. 8,67,999B. 8,76,999C. 8,67,909D. 8,76,909

3. The expanded form of 3,25,409 is

A. 3,00,000+20,000+5,000+400+9B. 3,00,000+20,000+5,000+40+9C. 3,00,000+2,000+500+40+9D. 30,000+2,000+500+400+9

4. Which of the following is a multiple of both 4 and 9?

A. 28B. 32C. 36D. 42

5. The predecessor of 1,00,000 is ____.

A. 99,998B. 99,999C. 1,00,001D. 1,01,000

6. Which of the following is a cube?

A. 64B. 50C. 81D. 72

7. LCM of 15 and 20 is

A. 30B. 40C. 50D. 60

8. Which of the following is a perfect square?

A. 33B. 49C. 60D. 66

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

A. 125B. 135C. 150D. 175

10. Which of the following is NOT a composite number?

A. 37B. 57C. 91D. 99

2. Fill in the Blanks (1 mark each)

1. The smallest 6-digit number is ______.

2. The place value of 8 in 6,48,257 is ______.

3. One lakh = ______ thousands.

4. 9,00,000 + 60,000 + 400 + 8 is written as ______.

5. The greatest 5-digit number is ______.

20 MARKS

Section B — Fractions & Decimals

3. True or False (1 mark each)

1. 3/8 is greater than 2/8. (   )

2. 0.625 is equal to 5/8. (   )

3. 7/9 is an improper fraction. (   )

4. A fraction with denominator 8 is a decimal. (   )

5. 1.45 lies between 1.4 and 1.5. (   )

4. Match the Following (1 mark each)

Column A
1.2/3 of 24
2.3.6 + 4.7
3.0.9 × 0.6
4.5/6 of 30
5.7.8 − 2.9
Column B
a)4.9
b)8.3
c)25
d)0.54
e)16

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

1. Write the decimal form of 6/25.

2. Arrange in ascending order: 0.41, 0.14, 0.104, 0.401.

3. Write the fraction for: seven tenths.

4. Express 3.75 as a fraction in simplest form.

5. Find the sum: 2.87 + 4.36.

24 MARKS

Section C — Ratio, Percentage & Profit & Loss

6. Solve the Following (2 marks each)

1. Simplify the ratio 21 : 35.

2. A class has 30 boys and 42 girls. What is the ratio of boys to girls?

3. 25% of 320.

4. A shopkeeper bought a table for ₹3,200 and sold it for ₹3,840. Find his profit.

5. If the price of a book is ₹600 and there is a discount of 15%, find the discount amount.

7. Do As Directed (2 marks each)

1. Express 2/5 in the form of a decimal.

2. A number is decreased by 30%. If the number is 240, find the decreased number.

3. Find the selling price if the cost price is ₹960 and the profit is 25%.

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

1. In a class of 36 students, 2/9 of the students like art and 3/4 like music. How many students like art? How many like music?

2. A shopkeeper buys an article for ₹1,250 and sells it at a loss of 10%. 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 8 cm.

2. Find the area of a square whose side is 14 cm.

3. Convert 3 m 50 cm into centimetres.

4. Convert 2 hours 25 minutes into minutes.

5. The length of a room is 7 m 20 cm and the breadth is 4 m 80 cm. Find its perimeter.

10. Draw & Label (2 marks each)

1. Draw a line segment AB of length 8 cm.

2. Draw a circle and show its centre O and a radius of 5 cm.

7 MARKS

Section E — Data Handling & Logical Reasoning

Favourite FruitBar graph. Mango: 30; Banana: 55; Orange: 20; Apple: 40; Grapes: 30.Favourite Fruit010203040506030Mango55Banana20Orange40Apple30GrapesFruitNumber of students
Bar graph — Favourite Fruit

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

1. Which fruit is liked by the most students?

2. How many students like orange?

3. How many students like apple?

4. How many more students like banana than grapes?

5. Find the total number of students.

12. Master Challenge (2 marks)

1. A number when divided by 7 leaves remainder 4. When the same number is divided by 9, it leaves remainder 5. What is the smallest such number?

ICSE Class 5 Mathematics · Final Examination — Set 6 · 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. C. 90,000

In 7,95,824 the digits are 7 (lakhs), 9 (ten-thousands), 5 (thousands), 8 (hundreds), 2 (tens), 4 (ones). 9 is in the ten-thousands place: 90,000.

Q2. B. 8,76,999

Comparing digit by digit: 8,76,999 is the largest of the four.

Q3. A. 3,00,000+20,000+5,000+400+9

In 3,25,409 the digits are 3 (lakhs), 2 (ten-thousands), 5 (thousands), 4 (hundreds), 0 (tens), 9 (ones).

Q4. C. 36

36 = 4 × 9, so it is a multiple of both 4 and 9.

Q5. B. 99,999

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

Q6. A. 64

64 = 4 × 4 × 4.

Tempting wrong answer: C. 81 — that is 3⁴ (a power of 3, but not a perfect cube).

Q7. D. 60

15 = 3×5, 20 = 2²×5. LCM = 2²×3×5 = 60.

Q8. B. 49

49 = 7 × 7, a perfect square.

Q9. C. 150

Divisible by 2, 3 and 5 means divisible by 30. 150 ÷ 30 = 5 exactly.

Q10. A. 37

57 = 3×19, 91 = 7×13, 99 = 9×11 are all composite. 37 has no factor other than 1 and itself, so it is the one that is NOT composite.

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

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

Q2. 8,000

In 6,48,257 the digit 8 is in the thousands place.

Q3. 100

1,00,000 ÷ 1,000 = 100.

Q4. 9,60,408

9,00,000 + 60,000 + 400 + 8 = 9,60,408.

Q5. 99,999

Five 9s is the greatest 5-digit number.

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

Same denominator 8, and 3 > 2, so 3/8 > 2/8.

Q2. True

5/8 = 0.625.

Q3. False

7/9 has a smaller numerator than denominator, making it a proper fraction, not improper.

Q4. False

Only fractions with denominator 10, 100, 1000 (and so on) are called "decimal fractions" and can be written directly as a decimal just by moving the point. A denominator of 8 is not one of these — although 5/8 happens to equal the terminating decimal 0.625, that's not true for every fraction with denominator 8 in general, so a fraction with denominator 8 is not automatically "a decimal" the way a denominator-10 fraction is.

Q5. True

1.4 < 1.45 < 1.5.

4. Match the Following
1 → e) 16

2/3 of 24 = (2 × 24) ÷ 3 = 16.

2 → b) 8.3

3.6 + 4.7 = 8.3.

3 → d) 0.54

0.9 × 0.6 = 0.54.

4 → c) 25

5/6 of 30 = (5 × 30) ÷ 6 = 25.

5 → a) 4.9

7.8 − 2.9 = 4.9.

5. Very Short Answer Type Questions
Q1. 0.24

6/25 = 24/100 = 0.24.

Q2. 0.104, 0.14, 0.401, 0.41

Write with 3 decimal places: 0.410, 0.140, 0.104, 0.401. Ascending: 0.104 < 0.140 < 0.401 < 0.410.

Q3. 7/10

Seven tenths = 7/10.

Q4. 15/4

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

Q5. 7.23

2.87 + 4.36 = 7.23.

Section C — Ratio, Percentage & Profit & Loss (24 marks)
6. Solve the Following
Q1. 3 : 5

21 and 35 share the common factor 7: 21÷7=3, 35÷7=5.

Q2. 5 : 7

Boys : girls = 30 : 42 = 5 : 7 (dividing both by 6).

Q3. 80

25% of 320 = (25 ÷ 100) × 320 = 80.

Q4. ₹640

Profit = Selling price − Cost price = 3,840 − 3,200 = ₹640.

Q5. ₹90

Discount = 15% of ₹600 = (15 ÷ 100) × 600 = ₹90.

7. Do As Directed
Q1. 0.4

2/5 = 2 ÷ 5 = 0.4.

Q2. 168

Decrease = 30% of 240 = 72. Decreased number = 240 − 72 = 168.

Q3. ₹1,200

Profit = 25% of ₹960 = ₹240. Selling price = 960 + 240 = ₹1,200.

8. Think & Solve (Word Problems)
Q1. Art: 8 students; Music: 27 students
  1. Art: 2/9 of 36 = (2 × 36) ÷ 9 = 8.
  2. Music: 3/4 of 36 = (3 × 36) ÷ 4 = 27.
Q2. ₹1,125
  1. Loss = 10% of ₹1,250 = ₹125.
  2. Selling price = 1,250 − 125 = ₹1,125.
Section D — Geometry & Measurement (14 marks)
9. Answer the Following
Q1. 48 cm

Perimeter = 2 × (16 + 8) = 2 × 24 = 48 cm.

Q2. 196 sq cm

Area of a square = side × side = 14 × 14 = 196 sq cm.

Q3. 350 cm

3 m = 300 cm. 300 + 50 = 350 cm.

Q4. 145 minutes

2 hours = 120 minutes. 120 + 25 = 145 minutes.

Q5. 24 m
  1. Length + breadth = 7 m 20 cm + 4 m 80 cm = 12 m (20 cm + 80 cm = 100 cm = 1 m).
  2. Perimeter = 2 × 12 m = 24 m.
10. Draw & Label
Q1. Line segment AB = 8 cm

Use a ruler: mark point A at 0, mark point B at 8 cm, join with a straight line.

Q2. Circle with radius OP = 5 cm

Open the compass to 5 cm, place the point on centre O, and draw the circle. Mark a point P on the circle and label OP = 5 cm.

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

Banana has the tallest bar (55).

Q2. 20 students

Read the top of the Orange bar: 20.

Q3. 40 students

Read the top of the Apple bar: 40.

Q4. 25 students

Banana (55) − Grapes (30) = 25.

Q5. 175 students

30 + 55 + 20 + 40 + 30 = 175.

12. Master Challenge
Q1. 32
  1. Numbers leaving remainder 4 when divided by 7: 4, 11, 18, 25, 32, …
  2. Check each ÷ 9: 4 → remainder 4 (no); 11 → remainder 2 (no); 18 → remainder 0 (no); 25 → remainder 7 (no); 32 → remainder 5 (yes).
  3. Check: 32 = 4×7+4 ✓, 32 = 3×9+5 ✓. So the smallest such number is 32.
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