Class 8 maths · Original EZT practice
RS Aggarwal Class 8: original worked practice
Stuck halfway through a calculation? Start with the topic, not the answer. These examples show what to do next, why it works and how to check it.
This page gives Class 8 students 15 original maths examples with stepwise solutions, a check and a second question to try. Use them alongside your RS Aggarwal book to practise a method, not as an answer key to its exercises.
Original EZT practice with worked solutions. Match the topic to your own book; editions vary. This is not an official chapter index or a complete RS Aggarwal exercise-answer key.
Bharati Bhawan lists Mathematics for Class 8 Book 1 and Book 2. Those links identify the books; they do not verify a chapter order on this page. EZ Tuitions is not affiliated with the author or publisher.
Try first. Read one step. Check the result.
Give the example a genuine attempt before opening the solution. If you get stuck, read only the next step and carry on yourself. The check is part of the work: a correct-looking line of algebra can still hide a sign error. Finish with the second question, whose answer stays folded away until you need it.
Rational numbers
Add fractions with different denominators, including a negative term.
EZT practice question
Find −5/12 + 7/18.
Show the worked solution
- The smallest common denominator of 12 and 18 is 36.
- Rewrite −5/12 as −15/36 and 7/18 as 14/36.
- Add the numerators, keeping the denominator: (−15 + 14)/36 = −1/36.
Answer: −1/36
Check: The positive term is slightly smaller than the magnitude of the negative term, so a small negative answer fits.
Watch for this: Do not add the denominators. −5/12 + 7/18 is not 2/30.
Now try it yourself
Try −7/15 + 2/5.
Check your answer
−1/15: use fifteenths, then calculate −7 + 6.
Squares and square roots
Find a square root by pairing prime factors.
EZT practice question
Find the positive square root of 1,764.
Show the worked solution
- Factor 1,764: 1,764 = 4 × 441 = 2² × 3² × 7².
- Take one factor from each pair: 2 × 3 × 7.
- Multiply to get 42. The positive square root is 42.
Answer: 42
Check: 42 × 42 = 1,764. If the question were x² = 1,764, both x = 42 and x = −42 would work.
Watch for this: The square-root symbol asks for the non-negative root; an equation involving a square can have two roots.
Now try it yourself
Find the positive square root of 2,116.
Check your answer
46, because 46² = 2,116.
Cubes and cube roots
Group prime factors in threes rather than pairs.
EZT practice question
Find the cube root of 13,824.
Show the worked solution
- Write 13,824 = 512 × 27 = 2⁹ × 3³.
- There are three groups of three 2s and one group of three 3s.
- Take one factor from each group: 2³ × 3 = 8 × 3 = 24.
Answer: 24
Check: 24 × 24 × 24 = 13,824.
Watch for this: Pairing factors finds square roots. Cube roots need groups of three.
Now try it yourself
Find the cube root of −3,375.
Check your answer
−15, because (−15)³ = −3,375.
Exponents
Use index laws only after checking that the bases match.
EZT practice question
Simplify (3⁵ × 3²) ÷ 3⁴.
Show the worked solution
- Multiplication with the same base adds the exponents: 3⁵ × 3² = 3⁷.
- Division with the same non-zero base subtracts the exponents: 3⁷ ÷ 3⁴ = 3³.
- Evaluate 3³ = 27.
Answer: 27
Check: 243 × 9 ÷ 81 = 27.
Watch for this: Do not multiply the exponents in 3⁵ × 3². That rule applies to a power raised to a power.
Now try it yourself
Simplify (2⁶ × 2³) ÷ 2⁵.
Check your answer
16: 2⁶⁺³⁻⁵ = 2⁴.
Divisibility and number patterns
Use place value to solve a missing-digit problem.
EZT practice question
For which digits d is the number 4d2 divisible by 9?
Show the worked solution
- A whole number is divisible by 9 when its digit sum is divisible by 9.
- The sum is 4 + d + 2 = 6 + d. As d runs from 0 to 9, the sum runs from 6 to 15.
- The only multiple of 9 in that interval is 9, so 6 + d = 9 and d = 3.
Answer: d = 3
Check: 432 ÷ 9 = 48.
Watch for this: A missing digit must be from 0 to 9. Solving a congruence without checking that range can produce invalid digits.
Now try it yourself
Which digit makes 7d4 divisible by 9?
Check your answer
7: the digit sum is 11 + d = 18, giving 774 ÷ 9 = 86.
Angles in quadrilaterals
Use the angle sum before choosing any special-shape rule.
EZT practice question
A quadrilateral has angles 72°, 104° and 89°. Find its fourth angle.
Show the worked solution
- The interior angles of a quadrilateral total 360°.
- Add the three given angles: 72 + 104 + 89 = 265°.
- Subtract: 360 − 265 = 95°.
Answer: 95°
Check: 72 + 104 + 89 + 95 = 360.
Watch for this: Do not assume opposite angles are equal unless a property of the particular shape justifies it.
Now try it yourself
Three angles are 85°, 95° and 110°. Find the fourth.
Check your answer
70°, since the known angles total 290°.
Algebraic expressions
Expand brackets, then collect like terms.
EZT practice question
Simplify 3(2x − 5) − 2(x + 4).
Show the worked solution
- Distribute 3: 3(2x − 5) = 6x − 15.
- Distribute −2, including its sign: −2(x + 4) = −2x − 8.
- Collect like terms: 6x − 2x − 15 − 8 = 4x − 23.
Answer: 4x − 23
Check: At x = 5, the original expression is 3(5) − 2(9) = −3. The simplified expression gives 20 − 23 = −3 too.
Watch for this: The minus sign before the second bracket changes both terms, not just the first.
Now try it yourself
Simplify 4(y − 2) + 3(2y + 1).
Check your answer
10y − 5: expand to 4y − 8 + 6y + 3.
Factorisation
Reverse a familiar algebraic identity.
EZT practice question
Factorise 9x² − 25.
Show the worked solution
- Recognise two squares: 9x² = (3x)² and 25 = 5².
- Use a² − b² = (a − b)(a + b).
- Substitute a = 3x and b = 5 to get (3x − 5)(3x + 5).
Answer: (3x − 5)(3x + 5)
Check: Expanding gives 9x² + 15x − 15x − 25 = 9x² − 25.
Watch for this: A difference of squares factors this way. A sum of squares does not use the same identity over the real numbers.
Now try it yourself
Factorise 16y² − 81.
Check your answer
(4y − 9)(4y + 9).
Linear equations
Keep an equation balanced while undoing operations.
EZT practice question
Solve 5(x − 2) = 3x + 14.
Show the worked solution
- Expand the left side: 5x − 10 = 3x + 14.
- Subtract 3x from both sides, then add 10 to both sides: 2x = 24.
- Divide both sides by 2: x = 12.
Answer: x = 12
Check: 5(12 − 2) = 50 and 3 × 12 + 14 = 50.
Watch for this: Changing one side alone changes the equation. Write the same operation on both sides until the habit is secure.
Now try it yourself
Solve 4(y + 1) = 2y + 18.
Check your answer
y = 7. Both sides then equal 32.
Direct and inverse proportion
Decide whether the product or the ratio stays fixed.
EZT practice question
Six identical taps fill a tank in 10 hours. How long would four such taps take?
Show the worked solution
- Assume all taps run at the same constant rate and the tank has no leaks.
- Fewer taps mean more time, so this is inverse proportion. Taps × hours stays fixed: 6 × 10 = 60.
- For four taps, time = 60 ÷ 4 = 15 hours.
Answer: 15 hours
Check: 4 × 15 and 6 × 10 both give 60 tap-hours.
Watch for this: Do not use direct proportion here: fewer taps cannot fill the same tank faster under these assumptions.
Now try it yourself
Eight identical workers finish a job in 9 days. How long for twelve at the same constant rate?
Check your answer
6 days, since 8 × 9 ÷ 12 = 6.
Fractions, percentages and discounts
Name the base amount before calculating a percentage.
EZT practice question
A bag costs ₹960 after a 20% discount. What was its marked price?
Show the worked solution
- A 20% discount leaves 80% of the marked price.
- Let the marked price be M. Then 0.8M = 960.
- Divide: M = 960 ÷ 0.8 = ₹1,200.
Answer: ₹1,200
Check: 20% of ₹1,200 is ₹240. Subtracting ₹240 leaves ₹960.
Watch for this: Adding 20% of ₹960 does not undo a 20% discount; the original percentage was based on a different amount.
Now try it yourself
An item costs ₹630 after a 10% discount. Find its marked price.
Check your answer
₹700: 630 ÷ 0.9 = 700.
Right-angled triangles
Identify the hypotenuse before using the Pythagoras theorem.
EZT practice question
A right-angled triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse.
Show the worked solution
- The unknown side is opposite the right angle, so it is the hypotenuse c.
- Use c² = 9² + 12² = 81 + 144 = 225.
- Take the positive root because a length is positive: c = 15 cm.
Answer: 15 cm
Check: 15² = 225 = 9² + 12²; 15 cm is longer than either perpendicular side.
Watch for this: The theorem needs a right angle. Do not apply it to an arbitrary triangle.
Now try it yourself
The hypotenuse is 13 cm and one perpendicular side is 5 cm. Find the other side.
Check your answer
12 cm: the missing square is 13² − 5² = 144.
Area and perpendicular height
Use the height at right angles to the chosen base.
EZT practice question
A trapezium has parallel sides 8 cm and 14 cm, with perpendicular height 5 cm. Find its area.
Show the worked solution
- Add the parallel sides: 8 + 14 = 22 cm.
- Use area = ½ × (sum of parallel sides) × perpendicular height.
- Calculate ½ × 22 × 5 = 55 cm².
Answer: 55 cm²
Check: The average width is 11 cm. Multiplying it by the 5 cm height gives 55 cm².
Watch for this: A sloping side is not the perpendicular height. Area needs square units.
Now try it yourself
Parallel sides are 10 cm and 16 cm; the perpendicular height is 4 cm. Find the area.
Check your answer
52 cm²: ½ × 26 × 4.
Coordinates and graphs
Keep horizontal and vertical coordinates in the right order.
EZT practice question
Points A(2, 3) and B(7, 3) lie on a grid with one-unit spacing. Find the length AB.
Show the worked solution
- Both points have y = 3, so the segment is horizontal.
- Find the change in the x-coordinate: 7 − 2 = 5.
- AB is 5 grid units. There is no vertical change.
Answer: 5 units
Check: Count five one-unit intervals from x = 2 to x = 7 along the line y = 3.
Watch for this: Coordinates are ordered pairs (x, y). Swapping them changes the point.
Now try it yourself
Find the length between (4, 1) and (4, 8) on the same grid.
Check your answer
7 units, vertically.
Data and averages
Count every observation, including repeated values.
EZT practice question
Five quiz scores are 6, 8, 8, 9 and 14. Find their mean and median.
Show the worked solution
- Add all five scores: 6 + 8 + 8 + 9 + 14 = 45.
- Mean = total ÷ number of scores = 45 ÷ 5 = 9.
- The scores are already ordered. The third, middle score is 8, so the median is 8.
Answer: Mean 9; median 8
Check: Five scores with mean 9 must have total 45. The median has two observations on each side.
Watch for this: The mean and median need not match. A relatively large score can pull the mean upward.
Now try it yourself
Find the mean and median of 3, 5, 5, 7 and 10.
Check your answer
Mean 6; median 5.
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Questions about using these solutions
- Does this page contain every RS Aggarwal Class 8 solution?
- No. It contains original EZT practice questions, worked solutions and self-checks by topic. It does not reproduce textbook exercises or claim question-number coverage. Keep your own book open and match the topic, not an exercise number.
- Why does my book have a different chapter order?
- Bharati Bhawan lists separate Mathematics for Class 8 Book 1 and Book 2 titles. Editions vary. Check the title and contents page in your own copy before using any chapter-number guide. This page deliberately uses topic names rather than a claimed official order.
- Is RS Aggarwal enough for Class 8 maths?
- Start with the textbook and syllabus your school has assigned. Use a reference book for extra practice on the topics you need. More questions will not fix a misunderstood method: explain one worked solution, solve a similar question unaided, then revisit the mistake that caused trouble.
- Should I use NCERT or RS Aggarwal first?
- If your school assigns NCERT, finish the relevant explanation and school exercises first. Then use additional practice to test whether you can transfer the method. Follow your school’s assigned sequence if it differs; no reference book automatically replaces it.
- How should I use a worked solution without copying it?
- Attempt the question first. If stuck, read just the next step, close the solution and finish it yourself. Check the answer by substitution, estimation or reversing the calculation. Return to the try-it question later without looking at its answer.