List of top Mathematics Questions asked in CBSE Class VIII

A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time -
(i) the length of the shadow cast by another pole 10 m 50 cm high
(ii) the height of a pole which casts a shadow 5 m long.
Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q
Factorise the following expressions. 
  1.  \(a^ 2 + 8a + 16 \)
  2. \(p^ 2 - 10p + 25 \)
  3. \(25m^2 + 30m + 9 \)
  4. \(49y^ 2 + 84yz + 36z ^2 \)
  5. \(4x^ 2 - 8x + 4 \)
  6. \(121b ^2 - 88bc + 16c ^2 \)
  7. \((l + m) ^2 - 4lm \) (Hint: Expand \((l + m) ^2 \) first)
  8.  \(a^ 4 + 2a ^2b ^2 + b^ 4\)
Add the following. l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
Complete the following table of products:
 

First monomial → Second monomial ↓

2x    

–5y

 3x2

– 4xy

7x 2 y

–9x 2 y 2

2x 

4x2

. . .

. . .

. . .

. . .

. . .

–5y

. . .

. . .

-15x2y

. . .

. . .

. . .

3x2

. . .

. . .

. . .

. . .

. . .

. . .

– 4xy

. . .

. . .

. . .

. . .

. . .

. . .

7x 2 y

. . .

. . .

. . .

. . .

. . .

. . .

–9x2 y2

. . .

. . .

. . .

. . .

. . .

. . .

Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
Explain how a square is. 
  1. a quadrilateral 
  2. a parallelogram 
  3. a rhombus 
  4. a rectangle
Solve the linear equation: \(\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t\)
Simplify.
(i) (x2– 5) (x + 5) + 25
(ii) (a2+ 5) (b3+ 3) + 5
(iii) (t + s2) (t2 – s)
(iv) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
(v) (x + y) (2x + y) + (x + 2y) (x – y)
(vi) (x + y) (x2– xy + y2)
(vii) (1.5x – 4y) (1.5x + 4y + 3) – 4.5x + 12y
(viii) (a + b + c) (a + b – c)
Factorise the following expressions 
  1.  \(7x - 42\) 
  2.  \(6p - 12q\) 
  3.  \(7a ^2 + 14a\) 
  4.  \(-16z + 20z ^3\) 
  5.  \(20l^ 2m + 30\, alm\) 
  6.  \(5x^ 2 y - 15xy^2\) 
  7.  \(10a^ 2 - 15b^ 2 + 20c^ 2 \)
  8.  \(-4a^ 2 + 4ab - 4 ca\) 
  9.  \(x ^2 yz + xy^2 z + xyz^2\)
  10.  \(ax^2 y + bxy^2 + cxyz\)
Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
Find \(x\) in the following figures.
Polygon a   Polygon b
Carry out the multiplication of the expressions in each of the following pairs.
(i) 4p, q + r
(ii) ab, a – b
(iii) a + b, 7a²b²
(iv) a2 – 9, 4a
(v) pq + qr + rp, 0
Factorise 
  1. \(x^ 2 + xy + 8x + 8y\)
  2.  \(15xy - 6x + 5y - 2 \)
  3.  \(ax + bx - ay - by\) 
  4.  \(15pq + 15 + 9q + 25p\) 
  5.  \(z - 7 + 7xy - xyz\)
Add the following. a – b + ab, b – c + bc, c – a + ac.
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 
  1. 81 
  2. 128 
  3.  135 
  4.  192 
  5.  704
Express the following numbers in standard form.
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000
Consider the following parallelograms. Find the values of the unknowns \(x, y, z\).
parallelograms
For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained. 
  1. 252 
  2. 2925 
  3. 396 
  4. 2645 
  5. 2800 
  6.  1620
Add the following.2p2q2 – 3pq + 4, 5 + 7pq – 3p2q.
Factorise 
  1.  \(4p^ 2 - 9q ^2\) 
  2.  \(63a^ 2 - 112b ^2\) 
  3.  \(49x^ 2 - 36\) 
  4.  \(16x^ 5 - 144x^ 3\)
  5.  \((l + m)^ 2 - (l - m) ^2\) 
  6.  \(9x^ 2 y^ 2 - 16 \)
  7.  \((x^ 2 - 2xy + y^ 2 ) - z^ 2\) 
  8.  \(25a ^2 - 4b^ 2 + 28bc - 49c ^2\)
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
The following numbers are obviously not perfect squares. Give reason. 
  1. 1057 
  2. 23453 
  3. 7928 
  4. 222222 
  5. 64000 
  6. 89722 
  7. 222000 
  8. 505050
Explain how this figure is a trapezium. Which of its two sides are parallel?
figure KLMN
Solve and check result: \(x = \frac{4}{5}(x+10)\)