**Mental Maths
for Class 8**

**Mental Maths for
Class 8** covers all types of problems of mental maths for class 8 students. It
is very helpful to sharp the brain of class 8 students.

The** Mental Maths
for Class 8** covers the following topics:

- Rational Numbers
- Powers and Exponents
- Squares and Square Roots
- Cubes and Cube Roots
- Playing with Numbers
- Algebraic Expressions and Identities
- Factorisation
- Linear Equations
- Applications of Percentages
- Compound Interest
- Direct and Inverse Proportions
- Understanding Quadrilaterals
- Representing Solids on a Paper
- Area of Polygons
- Surface Area and Volume
- Data Handling and Graphs
- Probability

- Mental Maths for Class 1
- Mental Maths for Class 2
- Mental Maths for Class 3
- Mental Maths for Class 4
- Mental Maths for Class 5
- Mental Maths for Class 6
- Mental Maths for Class 7
- Mental Maths for Class 8

**Mental Maths Questions for Class 8**

**1.** Which positive number
is its own reciprocal?

**2.** Which negative number is its own reciprocal?

**3.** Find
the absolute value of -3/7.

**4.** Which number should be
multiplied with –6/11 to get the product 1?

**5.** Write a rational number between -4 and -5.

**6.** Divide
the following rational numbers: 2/5 ÷ 5/2

**7.** What number should be added to –1 so as to get
7/9?

**8.** Find the reciprocal of –5/9.

**9.** Solve for *x*.
5^{2x}* *÷ 5^{7} = 5^{3}

**10.** Find
the value of *m *for which *x*^{m}
÷ *x *= 1.

**11.** Evaluate
the following.

a.** **3^{0} – 3^{–2}

b.** **5^{–9} ×
5^{6}

**12.** If *x *= 3*, y *= 2, *z
*= 1, compute *x ^{y} *+

*y*+

^{z}*z*

^{x}.**13.** Write in the standard
form.

a. 7892.3

b. 248.05

**14.** Express
the following numbers as integers.

a. 9.8 × 10^{3}

b.** **1.06 × 10^{8}

**15. **Express the following numbers as decimals.

a.** **4 × 10^{–3}

b.** **3.6 × 10^{–5}

**16.** Find out if 200 is a perfect
square or not.

**17.** Express 36 as the sum of 6 odd numbers.

**18.** Find a Pythagorean
triplet whose greatest member is 17.

**19.** Find a Pythagorean triplet whose smallest member
is 22.

**20.** Estimate
the square root of 360.

**21.** Find the least number of three digits which is a
perfect square.

**22.** Find the smallest
square number, which is divisible by each of the numbers 4, 8 and 12.

**23.** Express
the following as a sum of odd numbers.

a.** **7^{3}

b.**
**9^{3}^{}

**24.** Find
the cube root of 0.125 × 0.000216 × 8.

**25.** What is the cube root of 343 × 27?

**26.** A number is divisible by 4 and 6. Can you say
that the number is divisible by 24?

**27.** Write the greatest number of 3 digits which
is divisible by 2 and 5.

**28.** If
48*x*07 is divisible by 9, find the value of *x*.

**29.** Add
11*a*2 +
2*ab *+ 8 and 4*ab *+ 6.

**30. **Subtract 2*a *+ *ab *+ 6*b *from 5*a *+
4*ab *+ 10*b*.

**31.** What must be subtracted from 5*a *– 2*b *+ *c *to
get 3*a *– *b *+ 4*c*?

**32.** What should be added to 6*a*^{2}
– 4*ab *+ *b*^{2} to get 9*a*^{2} + 2*ab *–
*b*^{2}?

**33.** Find the value using
suitable identity.

a. (98)^{2}

b. 103 × 97

c. 110 × 101

d.
33^{2} – 17^{2}

**34.** Find
the value of *x *if 8*x *= 37^{2} – 29^{2}.

**35.** Factorise the following algebraic
expressions.

a.** ***ax *+ *bx *– *ay *– *by *

b.** **1 + 2*t *– *k
*– 2*kt*

**36.** Factorise the
following.

a. *ax *–
*b *+ *ab *– *x *

b.
*x *+ 6*y *– 6 – *xy*

**37.** Factorise
each of the following.

a.** ***a*^{2}
– 9

b.** **49*b*^{2} – 1

**38.** Solve the following.

a.** **5*y *+ 2 = 12

b.** **2 + 2*p *= 20

**39.** My father is four times my age. If I am 11 years old, what is
my father’s age?

**40.** In a class of 41 students, the number of girls is
7 more than boys. How many girls are there in the class?

**41.** Find:

a. 20% of 1250 m

b. 18% of 990 kg

**42.** Raj scored 75% in an
exam. If his score was 180, find the maximum marks of the exam.

**43.** A
number is increased by 20% and then decreased by 20%. Find the net increase or
decrease per cent.

**44.** The marked price of a
pair of shoes is ₹ 1500. If the rate of discount is 5%, what is the sale
price?

**45.** An
article is purchased for ₹ 20,240 including GST of 18%. Find the price of the
article before GST was added.

**46.** The cost price of 10 oranges is equal to the
selling price of 9 oranges. Find the profit per cent.

**47.** What sum will amount to ₹ 9,261 at
5% per annum compound interest after 3 years?

**48.** Find the single discount which is equivalent to
two successive discounts of 40% and 20%.

**49.** The population of a town is
increasing at the rate of 4% per annum. If two years ago, the population of the
town was 70,000, find its present population.

**50.** A car travels 47 km
with 4 litres of petrol. How much petrol will be needed to travel a distance of
235 km?

**51.** A
car is running at 80 km/h. How long will it take to cover 540 km at the same
speed?

**52.** If 16 men can finish a
work in 12 days, how long will 12 men take to finish the same work?

**53.** The angles of a quadrilateral are 120°, 82°, 48° and
*x*°. Find the value of *x*.

**54.** If
each interior angle of a regular polygon is 140°, find the number of sides of
the polygon.

**55.** Find the sum of the interior angles of a 20-sided polygon.

**56.** If the length of a
diagonal of a square is 8 cm, find the length of the side of the square.

**57.** The sides of a rectangle are in the ratio 3 : 5. Find
its sides if the perimeter is 160 cm.

**58.** In
a six-faced polyhedron, there are 6 vertices. How many edges does the
polyhedron have?

**59.** Find the area of a
rhombus, the lengths of whose diagonals are 44 cm and 26 cm.

**60.** The
area of a rectangle of length 16 cm is the same as the area of a square of side
12 cm. Find the perimeter of the rectangle.

**61.** Find the area of a trapezium the lengths of whose
parallel sides are 16 cm and 20 cm and the distance between them is 12 cm.

**62.** Find the volume of wood used to make a closed
box with outer dimensions 13 m × 16 m × 10 m and thickness 50 cm.

**63.** Find the volume of a
cylinder of height 8 cm and radius 14 cm.

**64.** Find the surface area of a cylinder whose base radius
is 14 cm and height is 28 cm.

**65.** The circumference of the base of a cylinder is 15
m and its height is 84 m. Find the volume of the cylinder.

**66.** Find the height
of a cylinder whose radius is 7 cm and total surface area is 1056 cm^{2}.

**67.** The ratio of the curved surface area to the total surface area
of a right circular cylinder is 3 : 5. Find the ratio of the height to the
radius of the cylinder.

**68.** In which quadrant do the points A(3, -2) and B(-4, 6) lie?

**69.** Find the
probability of getting a spade from a pack of 52 cards in a random experiment.

**70.** A
bag contains 5 red, 10 black and 15 green balls. A ball is taken out at random.
Find the probability that the ball taken out is a
red ball.

**Worksheets for Maths**