A Peek Beyond the Point — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "A Peek Beyond the Point" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "A Peek Beyond the Point" — 8 important questions with detailed answers for CBSE boa…
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NCERT Solutions for Class 7 Mathematics — A Peek Beyond the Point. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
A Peek Beyond the Point — All 8 Questions Solved
Q1. Express 3.45 in expanded form using place value.
Step 1: Identify each digit and its place value:
3 is in the ones place = 3 × 1 = 3
4 is in the tenths place = 4 × 1/10 = 4 × 0.1 = 0.4
5 is in the hundredths place = 5 × 1/100 = 5 × 0.01 = 0.05
Step 2: Write the expanded form:
3.45 = 3 + 0.4 + 0.05
Or: 3.45 = 3 + 4/10 + 5/100
Answer: 3 + 4 × 0.1 + 5 × 0.01
Q2. Compare 0.5 and 0.50. Are they equal?
Step 1: Write 0.5 in expanded form:
0.5 = 5 × 1/10 = 0.5
Step 2: Write 0.50 in expanded form:
0.50 = 5 × 1/10 + 0 × 1/100 = 0.5
Step 3: Both represent the same value:
0.5 = 0.50
Trailing zeros after the decimal do not change the value.
Answer: Yes, 0.5 and 0.50 are equal.
Q3. Arrange in ascending order: 2.05, 2.5, 2.005, 2.50
Step 1: Write all numbers with the same number of decimal places:
2.05 = 2.050
2.5 = 2.500
2.005 = 2.005
2.50 = 2.500
Step 2: Compare the decimal parts:
2.005 < 2.050 < 2.500 = 2.500
Step 3: Arrange in ascending order:
2.005, 2.05, 2.5, 2.50
Or: 2.005, 2.05, 2.5 (since 2.5 = 2.50)
Answer: 2.005 < 2.05 < 2.5 = 2.50
Q4. Convert the fraction 7/20 to a decimal.
Step 1: To convert fraction to decimal, divide numerator by denominator:
7 ÷ 20
Step 2: Perform long division:
7.00 ÷ 20 = 0.35
Working: 20 goes into 70 three times (3 × 20 = 60)
Remainder: 70 - 60 = 10
Bring down 0: 100
20 goes into 100 five times (5 × 20 = 100)
Remainder: 0
Answer: 7/20 = 0.35
Q5. Which is greater: 3/8 or 0.35?
Step 1: Convert 3/8 to decimal:
3 ÷ 8 = 0.375
Working: 3.000 ÷ 8
8 goes into 30 three times (3 × 8 = 24)
Remainder: 6, bring down 0 = 60
8 goes into 60 seven times (7 × 8 = 56)
Remainder: 4, bring down 0 = 40
8 goes into 40 five times (5 × 8 = 40)
Step 2: Compare:
0.375 vs 0.35
0.375 > 0.35
Answer: 3/8 is greater than 0.35
Q6. Add: 2.15 + 3.7
Step 1: Align decimal points and write with same decimal places:
2.15
+ 3.70
------
Step 2: Add column by column from right to left:
Hundredths: 5 + 0 = 5
Tenths: 1 + 7 = 8
Ones: 2 + 3 = 5
Step 3: Write the answer:
2.15
+ 3.70
------
5.85
Answer: 5.85
Q7. What is 0.6 expressed as a fraction in lowest terms?
Step 1: Write 0.6 as a fraction:
0.6 = 6/10
Step 2: Simplify by finding GCD of 6 and 10:
GCD(6, 10) = 2
Step 3: Divide both numerator and denominator by 2:
6 ÷ 2 / 10 ÷ 2 = 3/5
Answer: 0.6 = 3/5
Q8. Compare 0.25, 1/4, and 25%.
Step 1: Convert all to decimals:
0.25 = 0.25
1/4 = 0.25 (since 1 ÷ 4 = 0.25)
25% = 25/100 = 0.25
Step 2: All three represent the same value.
Answer: 0.25 = 1/4 = 25% (all are equal)
A Peek Beyond the Point — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. An angle measuring exactly 90 degrees is called a/an:
- A. Acute angle
- B. Obtuse angle
- C. Right angle
- D. Straight angle
Answer: C. Right angle — An angle of 90 degrees is defined as a right angle. Acute angles are less than 90, obtuse angles are between 90 and 180, and a straight angle is 180 degrees.
MCQ 2. How many points can two distinct lines intersect at most?
- A. Zero
- B. One
- C. Two
- D. Infinitely many
Answer: B. One — Two distinct lines can intersect at exactly one point. If they intersected at more than one point, they would be the same line.
MCQ 3. What is the complement of an angle measuring 30 degrees?
- A. 60 degrees
- B. 150 degrees
- C. 30 degrees
- D. 90 degrees
Answer: A. 60 degrees — Two angles are complementary if their sum is 90 degrees. So, the complement of 30 degrees is 90 - 30 = 60 degrees.
MCQ 4. When two lines intersect, the angles opposite to each other at the intersection point are called:
- A. Adjacent angles
- B. Linear pair
- C. Complementary angles
- D. Vertically opposite angles
Answer: D. Vertically opposite angles — Vertically opposite angles are formed when two lines intersect, and they are always equal.
MCQ 5. How many endpoints does a line segment have?
- A. Zero
- B. One
- C. Two
- D. Three
Answer: C. Two — A line segment is a part of a line that has two distinct endpoints.
MCQ 6. Which of the following is an exact location or position and has no dimension (length, width, or height)?
- A. Line
- B. Ray
- C. Point
- D. Plane
Answer: C. Point — A point is a fundamental concept in geometry, representing a specific position without any size.
MCQ 7. An angle that measures less than 90 degrees but greater than 0 degrees is called a/an:
- A. Right angle
- B. Obtuse angle
- C. Acute angle
- D. Reflex angle
Answer: C. Acute angle — An acute angle is an angle whose measure is greater than 0 degrees and less than 90 degrees.
MCQ 8. Two lines are perpendicular if they intersect to form an angle of:
- A. 45 degrees
- B. 90 degrees
- C. 180 degrees
- D. 360 degrees
Answer: B. 90 degrees — Perpendicular lines are defined as lines that intersect at a right angle (90 degrees).
MCQ 9. An angle that measures greater than 180 degrees but less than 360 degrees is called a/an:
- A. Acute angle
- B. Obtuse angle
- C. Straight angle
- D. Reflex angle
Answer: D. Reflex angle — A reflex angle is larger than a straight angle (180 degrees) but less than a full circle (360 degrees).
MCQ 10. An angle is formed by how many rays originating from a common endpoint?
- A. One
- B. Two
- C. Three
- D. Four
Answer: B. Two — An angle is defined as the union of two rays (called sides) that share a common endpoint (called the vertex).
MCQ 11. If an angle measures 110 degrees, what is its supplementary angle?
- A. 70 degrees
- B. 110 degrees
- C. 180 degrees
- D. 90 degrees
Answer: A. 70 degrees — Two angles are supplementary if their sum is 180 degrees. So, the supplement of 110 degrees is 180 - 110 = 70 degrees.
MCQ 12. Two adjacent angles form a linear pair if their sum is:
- A. 90 degrees
- B. 180 degrees
- C. 360 degrees
- D. 0 degrees
Answer: B. 180 degrees — A linear pair consists of two adjacent angles whose non-common sides are opposite rays, forming a straight line, hence their sum is 180 degrees.
MCQ 13. A line that intersects two or more distinct lines at different points is called a:
- A. Parallel line
- B. Perpendicular line
- C. Transversal
- D. Ray
Answer: C. Transversal — A transversal is a line that cuts across two or more other lines, creating various angles.
MCQ 14. If two parallel lines are intersected by a transversal, which of the following angle pairs are equal?
- A. Consecutive interior angles
- B. Corresponding angles
- C. Consecutive exterior angles
- D. Interior angles on the same side of the transversal
Answer: B. Corresponding angles — When two parallel lines are intersected by a transversal, corresponding angles are equal. Consecutive interior angles and interior angles on the same side of the transversal are supplementary.
MCQ 15. How many vertices does a triangle have?
- A. Two
- B. Three
- C. Four
- D. Five
Answer: B. Three — A triangle is a polygon with three sides and three vertices (corners).
MCQ 16. If two lines intersect and one of the angles formed is 75 degrees, what is the measure of its vertically opposite angle?
- A. 105 degrees
- B. 75 degrees
- C. 90 degrees
- D. 15 degrees
Answer: B. 75 degrees — Vertically opposite angles are always equal. Therefore, if one angle is 75 degrees, its vertically opposite angle is also 75 degrees.
MCQ 17. Two angles are complementary. If one angle is 'x' degrees, what is the other angle?
- A. (x - 90) degrees
- B. (90 - x) degrees
- C. (180 - x) degrees
- D. 90x degrees
Answer: B. (90 - x) degrees — Complementary angles sum up to 90 degrees. If one angle is x, the other angle is 90 - x.
MCQ 18. Which of the following statements is true about parallel lines?
- A. They intersect at one point
- B. They never intersect
- C. They are always perpendicular
- D. They form a linear pair
Answer: B. They never intersect — Parallel lines are lines in a plane that never meet or intersect, no matter how far they are extended.
MCQ 19. How many diagonals does a quadrilateral have?
- A. One
- B. Two
- C. Three
- D. Four
Answer: B. Two — A quadrilateral has four vertices. A diagonal connects two non-adjacent vertices. A quadrilateral has exactly two diagonals.
MCQ 20. When a transversal intersects two lines, angles on the same side of the transversal and in corresponding positions are called:
- A. Alternate interior angles
- B. Vertically opposite angles
- C. Corresponding angles
- D. Consecutive interior angles
Answer: C. Corresponding angles — Corresponding angles are found in the same relative position at each intersection, one interior and one exterior. If the lines are parallel, these angles are equal.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.