ICSE Class 5 Mathematics · Exam Practice

Final Examination — Set 2

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

🎯 Full Marks: 74 ⏱️ Time: 2½ Hours 📝 Questions: 50
SectionTopicQsMarks
ANumber System1515
BFractions & Decimals1520
CMeasurement & Geometry922
DData Handling & Graphs55
EApplications & Logical Reasoning612
Total5074
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 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 7 in 83,742 is

A. 7B. 70C. 700D. 7,000

2. Which of the following is a multiple of both 6 and 9?

A. 24B. 36C. 45D. 30

3. What is the expanded form of 60,509?

A. 60,000+500+9B. 60,000+5,000+9C. 60,000+500+90+9D. 60,000+50+9

4. Which of the following is the smallest 5-digit number?

A. 9,999B. 10,000C. 10,001D. 11,000

5. The successor of 7,99,999 is

A. 7,99,998B. 8,00,000C. 8,00,001D. 7,99,990

6. Which of the following is a composite number?

A. 11B. 13C. 15D. 17

7. HCF of 36 and 48 is

A. 6B. 12C. 18D. 24

8. Which of the following is a prime number between 40 and 50?

A. 41B. 45C. 49D. 51

9. Which of the following is written in words correctly? (4,50,309)

A. Four lakh fifty thousand three hundred nineB. Four hundred five thousand three hundred nineC. Four lakh five thousand three hundred nineD. Four lakh fifty thousand three hundred ninety

10. 3,50,000 rounded off to the nearest thousand is

A. 3,49,000B. 3,50,000C. 3,51,000D. 3,00,000

2. Fill in the Blanks (1 mark each)

1. 9,99,999 + 1 = ______.

2. The greatest 5-digit number is ______.

3. 1 lakh = ______ thousand.

4. 5,60,000 is written as ______ in the international system.

5. The smallest prime number is ______.

20 MARKS

Section B — Fractions & Decimals

3. True or False (1 mark each)

1. 3/7 is equal to 0.43. (   )

2. A fraction with denominator 10 is a decimal. (   )

3. 0.75 is greater than 3/4. (   )

4. 2 1/2 is an improper fraction. (   )

5. 0.05 is less than 0.5. (   )

4. Match the Following (1 mark each)

Column A
1.2/3
2.5/8
3.1/4
4.1.5
5.3 1/4
Column B
a)1 1/2
b)3.25
c)0.625
d)0.25
e)0.666...

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

1. Write the decimal form of 4 3/10.

2. Arrange in ascending order: 0.6, 0.06, 0.606, 0.660.

3. Write the fraction for: seven tenths.

4. Express 2.08 as a fraction in simplest form.

5. Find the sum: 3.52 + 2.48.

22 MARKS

Section C — Measurement & Geometry

6. Solve the Following (2 marks each)

1. A rectangular plot is 25 m long and 18 m wide. Find its perimeter.

2. A square park has a side of 22 m. Find its area.

3. Convert: 2 km 350 m into metres.

4. A water tank can hold 1,500 L of water. If 735 L is used, how much water is left?

5. Convert: 4 hours 25 minutes into minutes.

7. Do As Directed (2 marks each)

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

2. Construct a perpendicular to line l at point P.

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

1. Riya has 3,675 stickers. She gives 1,248 stickers to her friend and 956 stickers to her brother. How many stickers are left with her?

2. A school library has 24,560 story books and 18,735 science books. How many books are there in all?

5 MARKS

Section D — Data Handling & Graphs

Books SoldBar graph. Mon: 60; Tue: 80; Wed: 50; Thu: 90; Fri: 70.Books Sold010203040506070809010060Mon80Tue50Wed90Thu70FriDayBooks sold
Bar graph — Books Sold

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

1. How many books were sold on Monday?

2. On which day were the maximum books sold?

3. How many books were sold on Wednesday?

4. How many more books were sold on Thursday than on Wednesday?

5. Find the total number of books sold in five days.

12 MARKS

Section E — Applications & Logical Reasoning

10. Solve the Following (2 marks each)

1. If the cost of 12 pencils is ₹36, what is the cost of 1 pencil?

2. A shopkeeper sells a pen for ₹18 and makes a profit of ₹3. What is the cost price?

3. Find the unknown number: a) 4,567 + ______ = 9,876 b) 7 × ______ = 4,893

4. In a class of 45 students, 1/5 of them like cricket and 2/9 like football. How many students like cricket? How many like football?

5. Find the sum of the first 10 natural numbers.

11. Master Challenge (2 marks)

1. A number when divided by 6, 8 and 10 leaves remainder 2 in each case. If the number is less than 200, what is the greatest such number?

ICSE Class 5 Mathematics · Final Examination — Set 2 · 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. 700

In 83,742 the digits are 8 (ten-thousands), 3 (thousands), 7 (hundreds), 4 (tens), 2 (ones). 7 is in the hundreds place: place value = 700.

Q2. B. 36

36 = 6 × 6 = 9 × 4, so it's a multiple of both 6 and 9.

Q3. A. 60,000+500+9

In 60,509 the digits are 6 (ten-thousands), 0 (thousands), 5 (hundreds), 0 (tens), 9 (ones) — the zeros contribute nothing.

Tempting wrong answer: C. 60,000+500+90+9 — adds an extra 90 that isn't in the number.

Q4. B. 10,000

The smallest 5-digit number is 1 followed by four zeros. 9,999 has only 4 digits.

Q5. B. 8,00,000

Successor = 1 more: 7,99,999 + 1 = 8,00,000.

Q6. C. 15

15 = 3 × 5, so it has factors other than 1 and itself. 11, 13, 17 are all prime.

Q7. B. 12

36 = 2²×3², 48 = 2⁴×3. HCF = 2²×3 = 12.

Q8. A. 41

41 has no factors other than 1 and itself. 45=9×5, 49=7×7, 51=3×17.

Q9. A. Four lakh fifty thousand three hundred nine

4,50,309 = 4 lakh + 50 thousand + 3 hundred + 9.

Tempting wrong answer: D — says "three hundred ninety" instead of "nine", changing the value to 4,50,390.

Q10. B. 3,50,000

3,50,000 already ends in three zeros, so rounding to the nearest thousand leaves it unchanged.

2. Fill in the Blanks
Q1. 10,00,000

9,99,999 + 1 = 10,00,000.

Q2. 99,999

Five 9s is the greatest 5-digit number.

Q3. 100

1,00,000 ÷ 1,000 = 100.

Q4. 560,000

The Indian system groups as 5,60,000; the international system groups in threes: 560,000.

Q5. 2

2 is the smallest, and only even, prime number.

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

3/7 = 0.4285714… which is not exactly 0.43 (0.43 is just a rounded approximation).

Q2. True

A fraction with denominator 10 (or 100, 1000…) is called a "decimal fraction" because it can be written directly as a decimal, e.g. 3/10 = 0.3.

Q3. False

0.75 = 3/4 exactly — they are equal, not one greater than the other.

Q4. False

2 1/2 is a mixed number (a whole number plus a proper fraction), not an improper fraction. As an improper fraction it would be written 5/2.

Q5. True

0.05 is much smaller than 0.5 (5 hundredths vs 5 tenths).

4. Match the Following
1 → e) 0.666...

2/3 = 0.666… (repeating).

2 → c) 0.625

5/8 = 0.625.

3 → d) 0.25

1/4 = 0.25.

4 → a) 1 1/2

1.5 = 1 1/2.

5 → b) 3.25

3 1/4 = 3.25.

5. Very Short Answer Type Questions
Q1. 4.3

4 3/10 = 4 + 0.3 = 4.3.

Q2. 0.06, 0.6, 0.606, 0.66

Write with 3 decimal places: 0.600, 0.060, 0.606, 0.660. Ascending: 0.060 < 0.600 < 0.606 < 0.660.

Q3. 7/10

Seven tenths = 7/10.

Q4. 52/25

2.08 = 208/100. Dividing both by 4: 52/25 (or 2 2/25 as a mixed number).

Q5. 6

3.52 + 2.48 = 6.00 = 6.

Section C — Measurement & Geometry (22 marks)
6. Solve the Following
Q1. 86 m

Perimeter = 2 × (25 + 18) = 2 × 43 = 86 m.

Q2. 484 sq m

Area of a square = side × side = 22 × 22 = 484 sq m.

Q3. 2,350 m

2 km = 2,000 m. 2,000 + 350 = 2,350 m.

Q4. 765 L

1,500 − 735 = 765 L.

Q5. 265 minutes

4 hours = 240 minutes. 240 + 25 = 265 minutes.

7. Do As Directed
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. Perpendicular to line l at P

Use a compass or set square to construct a 90° angle to line l at the point P.

8. Think & Solve (Word Problems)
Q1. 1,471 stickers
  1. 3,675 − 1,248 = 2,427.
  2. 2,427 − 956 = 1,471.
Q2. 43,295 books
  1. 24,560 + 18,735 = 43,295.
Section D — Data Handling & Graphs (5 marks)
9. Study the Bar Graph
Q1. 60 books

Read the top of the Monday bar: 60.

Q2. Thursday

Thursday has the tallest bar (90).

Q3. 50 books

Read the top of the Wednesday bar: 50.

Q4. 40 books

Thursday (90) − Wednesday (50) = 40.

Q5. 350 books

60 + 80 + 50 + 90 + 70 = 350.

Section E — Applications & Logical Reasoning (12 marks)
10. Solve the Following
Q1. ₹3

36 ÷ 12 = 3.

Q2. ₹15

Cost price = Selling price − Profit = 18 − 3 = 15.

Q3. a) 5,309 b) 699
  1. a) 9,876 − 4,567 = 5,309.
  2. b) 4,893 ÷ 7 = 699.
Q4. Cricket: 9 students; Football: 10 students
  1. Cricket: 1/5 of 45 = 9.
  2. Football: 2/9 of 45 = (2 × 45) ÷ 9 = 10.
Q5. 55

1+2+3+...+10 = (10 × 11) ÷ 2 = 55.

11. Master Challenge
Q1. 122
  1. LCM(6, 8, 10) = 120.
  2. Numbers leaving remainder 2 when divided by 6, 8, and 10 are of the form 120k + 2: 2, 122, 242, …
  3. The greatest such number less than 200 is 122. Check: 122 ÷ 6 = 20 r 2, 122 ÷ 8 = 15 r 2, 122 ÷ 10 = 12 r 2 ✓.
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