CBSE Class 7 Mathematics · Exam Practice

Practice Paper — Set 1

CBSE Class 7 Mathematics (Ganita Prakash), covering integers, fractions, algebra, and geometry (lines and angles), with a full answer key and worked solutions.

🎯 Full Marks: 63 ⏱️ Time: 2½ Hours 📝 Questions: 42
SectionTopicQsMarks
AIntegers & Number System1515
BFractions & Algebra1520
CGeometry — Lines & Angles1228
Total4263
Before you start
  • Attempt the paper first, without looking at the answer key at the bottom of the page.
  • Show your working for Sections B and C — method marks are given even if the final answer is wrong.
15 MARKS

Section A — Integers & Number System

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

1. (−8) + 5 =

A. −3B. 3C. −13D. 13

2. (−3) × (−4) =

A. −12B. 12C. −7D. 7

3. (−15) ÷ 3 =

A. 5B. −5C. −45D. 45

4. The successor of −1 is

A. −2B. 0C. 1D. −1

5. |−7| =

A. −7B. 7C. 0D. 1

6. Which of the following is the additive identity for integers?

A. 1B. −1C. 0D. There is none

7. 25 lakh, written in standard numeral form, is

A. 2,50,000B. 25,00,000C. 2,50,00,000D. 250,000

8. The largest among −5, −2, 0, 3 is

A. −5B. −2C. 0D. 3

9. (−6) − (−2) =

A. −8B. −4C. 4D. 8

10. Which of these is NOT an integer?

A. −5B. 0C. 1/2D. 100

2. Fill in the Blanks (1 mark each)

1. (−9) + (−4) = ______.

2. (−20) ÷ (−4) = ______.

3. The absolute value of −12 is ______.

4. 7 × (−3) = ______.

5. The successor of −100 is ______.

20 MARKS

Section B — Fractions & Algebra

3. True or False (1 mark each)

1. 2/3 + 1/3 = 1. (   )

2. The product of two negative integers is always negative. (   )

3. If x + 5 = 12, then x = 7. (   )

4. 3/4 is greater than 1/2. (   )

5. −5 is greater than −3. (   )

4. Match the Following (1 mark each)

Column A
1.2x + 3 = 11, find x
2.1/2 + 1/3
3.3/5 of 20
4.Value of 3x when x = 5
5.5/6 − 1/6
Column B
a)4
b)5/6
c)12
d)15
e)2/3

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

1. Solve for x: 3x − 4 = 11.

2. Simplify: 2/5 + 3/10.

3. Evaluate: (−8) + (−3) − (−5).

4. Find the value of 5y − 2 when y = 3.

5. Add: 1/4 + 1/6.

28 MARKS

Section C — Geometry: Lines & Angles

6. Solve the Following (2 marks each)

1. Two lines intersect, forming four angles. If one of the angles is 70°, find the other three.

2. Two parallel lines are cut by a transversal. If one angle is 65°, find the measure of its corresponding angle.

3. Find the angle vertically opposite to a 110° angle.

4. Two angles form a linear pair. If one angle is 75°, find the other.

5. Lines AB and CD intersect at point O. If ∠AOC = 40°, find ∠BOD.

7. Do As Directed (2 marks each)

1. Find the supplement of 65°.

2. Find the complement of 42°.

3. Two parallel lines are cut by a transversal. If one angle is 110°, find its alternate angle.

4. What is the sum of all angles around a point?

5. If two lines are perpendicular to each other, what angle do they form?

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

1. Two lines AB and CD intersect at point O. ∠AOC and ∠BOD are vertically opposite angles, measuring 3x° and (2x + 30)° respectively. Find x and the measure of each angle.

2. Two parallel lines are cut by a transversal. One pair of co-interior angles measure (2x + 10)° and (3x − 30)°. Find x and the measure of both angles.

CBSE Class 7 Mathematics · Practice Paper — Set 1 · 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 — Integers & Number System (15 marks)
1. Multiple Choice Questions
Q1. A. −3

(−8) + 5 = −3. Think of it as starting at −8 and moving 5 steps to the right.

Tempting wrong answer: −13 — this comes from adding the two numbers as if both were negative, instead of one being positive.

Q2. B. 12

A negative times a negative gives a positive: (−3) × (−4) = 12.

Tempting wrong answer: −12 — forgetting that two negatives multiplied together give a positive result.

Q3. B. −5

A negative divided by a positive gives a negative: (−15) ÷ 3 = −5.

Q4. B. 0

The successor is 1 more: −1 + 1 = 0.

Tempting wrong answer: −2 — this is the predecessor (1 less), not the successor.

Q5. B. 7

Absolute value is always the positive "distance from zero," regardless of sign: |−7| = 7.

Q6. C. 0

Adding 0 to any integer leaves it unchanged, so 0 is the additive identity.

Q7. B. 25,00,000

1 lakh = 1,00,000, so 25 lakh = 25 × 1,00,000 = 25,00,000.

Tempting wrong answer: 2,50,000 — this is 25 thousand-adjacent, not 25 lakh; check the place value carefully.

Q8. D. 3

On the number line, numbers further right are larger. 3 is the only positive number here, so it's the largest.

Q9. B. −4

Subtracting a negative is the same as adding the positive: (−6) − (−2) = (−6) + 2 = −4.

Tempting wrong answer: −8 — this comes from treating both signs as negative and adding them (−6 + −2), instead of converting the double-negative subtraction into addition first.

Q10. C. 1/2

Integers are whole numbers (positive, negative, or zero) — fractions like 1/2 are not integers.

2. Fill in the Blanks
Q1. −13

(−9) + (−4) = −13, adding two negatives makes a more negative number.

Q2. 5

A negative divided by a negative gives a positive: (−20) ÷ (−4) = 5.

Q3. 12

|−12| = 12.

Q4. −21

7 × (−3) = −21.

Q5. −99

−100 + 1 = −99.

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

2/3 + 1/3 = 3/3 = 1.

Q2. False

A negative times a negative gives a positive, not a negative.

Q3. True

x + 5 = 12 → x = 12 − 5 = 7.

Q4. True

3/4 = 0.75 and 1/2 = 0.5, so 3/4 is greater.

Q5. False

On the number line, −3 is to the right of −5, so −3 is greater than −5 (and hence −5 is NOT greater than −3).

4. Match the Following
1 → a) 4

2x + 3 = 11 → 2x = 8 → x = 4.

2 → b) 5/6

1/2 + 1/3 = 3/6 + 2/6 = 5/6.

3 → c) 12

3/5 of 20 = (3 × 20) ÷ 5 = 12.

4 → d) 15

3 × 5 = 15.

5 → e) 2/3

5/6 − 1/6 = 4/6 = 2/3.

5. Very Short Answer Type Questions
Q1. x = 5

3x − 4 = 11 → 3x = 15 → x = 5.

Q2. 7/10

2/5 + 3/10 = 4/10 + 3/10 = 7/10.

Q3. −6

(−8) + (−3) − (−5) = −8 − 3 + 5 = −6.

Q4. 13

5(3) − 2 = 15 − 2 = 13.

Q5. 5/12

1/4 + 1/6 = 3/12 + 2/12 = 5/12.

Section C — Geometry: Lines & Angles (28 marks)
6. Solve the Following
Q1. 70°, 110°, 110°
  1. The angle vertically opposite the 70° angle is also 70° (vertically opposite angles are equal).
  2. The other two angles are each supplementary to 70° (they form a linear pair): 180° − 70° = 110°.
Q2. 65°

When two parallel lines are cut by a transversal, corresponding angles are equal.

Q3. 110°

Vertically opposite angles are always equal.

Q4. 105°

A linear pair sums to 180°: 180° − 75° = 105°.

Q5. 40°

∠AOC and ∠BOD are vertically opposite angles, so they are equal: ∠BOD = 40°.

7. Do As Directed
Q1. 115°

Supplementary angles sum to 180°: 180° − 65° = 115°.

Q2. 48°

Complementary angles sum to 90°: 90° − 42° = 48°.

Q3. 110°

Alternate angles are equal when lines are parallel.

Q4. 360°

The angles all the way around a single point always add up to 360°.

Q5. 90°

Perpendicular lines meet at a right angle, 90°.

8. Think & Solve (Word Problems)
Q1. x = 30, each angle = 90°
  1. Vertically opposite angles are equal: 3x = 2x + 30.
  2. x = 30.
  3. Each angle = 3 × 30 = 90°.
Q2. x = 40, both angles = 90°
  1. Co-interior angles sum to 180°: (2x + 10) + (3x − 30) = 180.
  2. 5x − 20 = 180 → 5x = 200 → x = 40.
  3. First angle = 2(40) + 10 = 90°. Second angle = 3(40) − 30 = 90°.
  4. Check: 90 + 90 = 180° ✓.
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