List of top Mathematics Questions asked in CBSE Class VIII

Factorise the expressions and divide them as directed. 
  1. \((y^ 2 + 7y + 10) ÷ (y + 5)\) 
  2.  \((m^2 – 14m – 32) ÷ (m + 2)\) 
  3.  \((5p^ 2 – 25p + 20) ÷ (p – 1)\) 
  4.  \(4yz(z ^2 + 6z – 16) ÷ 2y(z + 8)\)
  5.  \(5pq(p^ 2 – q^ 2 ) ÷ 2p(p + q)\) 
  6.  \(12xy(9x^ 2 – 16y ^2 ) ÷ 4xy(3x + 4y)\) 
  7.  \(39y^ 3 (50y ^2 – 98) ÷ 26y ^2 (5y + 7)\)
Two persons could fit new windows in house in 3 days.
(i) One of the persons fell ill before the work started. How long would the job take now?
(ii) How many persons would be needed to fit the windows in one day?
Without adding find the sum 
  1. \(1 + 3 + 5 + 7 + 9\) 
  2. \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \)
  3. \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\)
Factorise the expressions 
  1.  \(ax^2 + bx\) 
  2.  \(7p^ 2 + 21q^ 2\) 
  3.  \(2x^ 3 + 2xy^2 + 2xz^2\) 
  4.  \(am^2 + bm^2 + bn^2 + an^2\) 
  5.  \((lm + l) + m + 1\) 
  6.  \(y(y + z) + 9(y + z)\) 
  7.  \(5y^ 2 - 20y - 8z + 2yz\) 
  8.  \(10ab + 4a + 5b + 2\) 
  9.  \(6xy - 4y + 6 - 9x\)
Following are the car parking charges near a railway station up to
4 hours Rs 60
8 hours Rs 100
12 hours Rs 140
24 hours Rs 180
Check if the parking charges are in direct proportion to the parking time.
A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?
A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. how long will it take when the car travels at the speed of 80 km/h?
A factory required 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
A contractor estimates that 3 persons could rewire Jasminder's house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
 
Number of winners124581020
Prize for each winner (in Rs)10000050000……………
Which of the following are in inverse proportion? 
(i) The number of workers on a job and the time to complete the job. 
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested. 
(iv) The time taken for a fixed journey and the speed of the vehicle. 
(v) The population of a country and the area of land per person.
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. If 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
Parts of red pigment1471220
parts of base8…………
Divide as directed. 
  1.  \(5(2x + 1) (3x + 5) ÷ (2x + 1) \)
  2.  \(26xy(x + 5)(y – 4) ÷ 13x(y – 4) \)
  3.  \(52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p) \)
  4.  \(20(y + 4) (y^ 2 + 5y + 3) ÷ 5(y + 4) \)
  5.  \(x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)\)
Work out the following divisions. 
  1. \((10x – 25) ÷ 5\) 
  2.  \((10x – 25) ÷ (2x – 5) \)
  3.  \(10y(6y + 21) ÷ 5(2y + 7) \)
  4.  \(9x^ 2 y^ 2 (3z – 24) ÷ 27xy(z – 8) \)
  5. \( 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)\)
Divide the given polynomial by the given monomial. 
  1. \((5x^ 2 – 6x) ÷ 3x \)
  2. \( (3y^ 8 – 4y^ 6 + 5y ^4 ) ÷ y ^4 \)
  3.  \(8(x^ 3y^ 2 z^ 2 + x^ 2y ^3 z^ 2 + x^ 2y ^2 z ^3 ) ÷ 4x ^2y ^2 z ^2 \)
  4.  \((x^ 3 + 2x^ 2 +3x) ÷ 2x \)
  5.  \((p^ 3q^ 6 – p^ 6q ^3 ) ÷ p^ 3q ^3\)
Draw a graph for the following.
(i)
Side of square(in cm)233.556
Perimeter (in cm)812142024

Is it a linear graph?
(ii)
Side of square(in cm)23456
Area (in cm2)49162536


Is it a linear graph?

Carry out the following divisions. 
  1. \(28x^ 4 ÷ 56x\) 
  2.  \(–36y^ 3 ÷ 9y ^2\) 
  3.  \(66pq^2 r^ 3 ÷ 11qr^2 \)
  4.  \(34x^ 3y^ 3 z^ 3 ÷ 51xy^2 z^ 3 \)
  5.  \(12a ^8b^ 8 ÷ (– 6a^ 6b ^4 )\)
Factorise the following expressions 
  1. \(p^ 2 + 6p + 8\) 
  2.  \(q^ 2 - 10q + 21\) 
  3.  \(p^ 2 + 6p - 16\)