Mathematics Model Question for Class viii

Mathematics Model Question for Class viii

Arithmetic 

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

a. Add: 7.23 + 4. 2+ 7. 23.

b. Simplify: (0.8of 0.)(0.50.) + (0.30.).

c. What percentage is 20 pencils of 150 pencils?

d. In a certain school number of male students is 55% of the number of pupils. If the number of male students is 1100, then what is the number of pupils in that school?

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. 15% commission is allowed for buying a book on Mathematics. The actual price of the book is Tk.120. How much will be needed to buy the book?    

g. Mr. Bakar’s salary increases from Tk.4000 to Tk. 4500. Find the rate of increase in his salary.

h. The population of a village increased by 8% and become 21600. What was the population of that village before?

i. 68% of S. S. C. examinees in a school came out successful. The percentage of pass would have been 75% if 14 more students passed. What is the number of the examinees?

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 = -2, y = – 2 and z = 3; find the value of 25(x + y)² – 20(x + y)(y + z) + 4(y + z)².

b. If a +  = 2; find the value of a⁴ + .

c. If a –  = x; show that a⁴ + = x⁴ + 4x² + 2

d. Express as the difference of two squares: (3a + 4b)(5b – 2a).

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

f. If a = – 1 and b = -2; find the value of  8a³ + 36a²b + 54ab² + 27b³.

g. If a +  = 3; find the value of a³ + .

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.