Arithmatic Sample Questions for

Class - VIII

Subject: Mathematics

Total Time: 3 Hours                                                                                                               Total Marks: 100

Arithmetic

1. Answer any eight (08):                                                                                           68 = 48.

a. Add: 8 + 2. 3+ 7. 23.

b. Simplify: (.8of .)(.5.) + (.3.0).

c. Popy has to pay house-rent at 7% of his basic pay. After deduction of house-rent, she gets Tk.3600 per month. What is her monthly basic pay?  

d. Mr. Moin uddin transferred 12% of his property to his wife, 20% to his son and the rest of Tk.816000 to his daughter. What was the value of his whole property?

e. The number of male and female students in a school is 900. 4% male students left the school and 5% female students got themselves admitted afresh. Thus there was no change in the original total number of male and female students. How many female students were in that school before and at present how many male students are there?   

f. In an electoral college 75% voters were present. One of the two candidates got 55% votes of voters present and it was seen that his number of votes was more by 75000 than the number of votes of the other candidate. What was the total number of voters?   

g. When the price of banana is reduced by 16% then by Tk.75 five more bananas can buy. What is the present price of each dozen of banana?

h. When the price of fish is reduced by 25%, then at what percentage in the use of fish should be increased so that there will be no change of expenditure for use of fish in the family?

i. How much is the interest on Tk.800 in 4 years 3 months at 3% per annum?

j. How much will be the sum of money if that sum at 4% per annum for 5 years becomes Tk.900 as interest-principal?

Algebra

2. Answer any six (06):                                                                                              46 = 24.

a. If x = 4, y = – 8 and z = 5; find the value of 25(x + y)² – 20(x + y)(y + z) + 4(y + z)².

b. If a +  = 4; find the value of a⁴ + .

c. If a –  = m; show that a⁴ + = m⁴ + 4m² + 2

d. Express as the difference of two squares: (6a + 9b)(7b – 8a).

e. Simplify: (3a – 8b)³ – (2a – 7b)³ – 3(3a – 8b) (2a – 7b)(a – b).

f. If a = – 3 and b = 2; find the value of  8a³ + 36a²b + 54ab² + 27b³.

g. If a +  = 3; show that a³ + = 18.

Geometry

3. Answer any two (02):                                                                                             27 = 14.       

a. Prove that if three sides of one triangle are equal to the corresponding three sides of the other triangle, two triangles are congruent.

b. If the hypotenuse of two right-angled triangles are equal and one side of one triangle is equal to the corresponding side of another triangle; two triangles are congruent. Prove it.

c. In triangle DABC, AD is a median. Prove that AB + AC > 2AD.

4. Answer any two (02): (Sign of drawing and construction is a must):                   27 = 14.

a. The length of four arms and one diagonal of a quadrilateral are given. Draw it.

b. The length of three sides and two adjacent angles of a quadrilateral are given. Draw it.

c. The length of a diagonal of a square is given. Draw the square.