List of top Mathematics Questions asked in CBSE Class VIII

Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
raised platform of a regular octagon
 
Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
Suppose 2 kg of sugar contains 9 x 106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?
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.  \(ax^2 y + bxy^2 + cxyz\)
The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet.
Add the following. l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
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.
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.  \(25a ^2 - 4b^ 2 + 28bc - 49c ^2\)
When a die is thrown, list the outcomes of an event of getting 
  1. (a) a prime number (b) not a prime number. 
  2. (a) a number greater than 5 (b) a number not greater than 5.
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.  \(a^ 4 + 2a ^2b ^2 + b^ 4\)
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)
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.