Subject Code 1 0 9
BAF Shaheen College Dhaka
Practice Preparatory Test Examination-1 : 2020 Class VIII
(English Version) Subject : Mathematics
Time : 2 Hours 30 Minutes Full Marks⎯ 70 Part-A : Arithmetic
(Answer any two of the following questions) 1.
The above geometric figures are formed with sticks of equal length.
a. Form the 4th pattern and find out the number of lines. 2 b. Which algebraic expression is followed by the pattern?
Present it with logic. 4
c. Find, how many lines will be required to from the first 50
patterns of the pattern. 4
2. To meet an urgent family need, Selina Begum takes a loan of taka ‘x’ at the rate of 6% interest and taka ‘y’ at 4% interest.
She takes in total taka 56,000 as a loan and pays tk. 2840 as interest.
a. What will be annual interest if 5% interest is imposed on
total loan? 2
b. Find out the value of x and y. 4
c. How much interest will be paid by Selina Begum if 5%
compound interest is imposed for 2 years? 4 3. Sohel borrowed tk. 10,000 for 3 years and tk. 15,000 for 4
years from a bank and paid tk. 9,900 in total as a profit.
a. Write the formula of compound principal with introduce of
variables. 2
b. In both cases if the rate of profit is same, find the rate of
profit. 4
c. Find the difference between simple profit and compound
profit of 15,000 tk. after 5 years. 4
Part-B : Algebra
(Answer any two of the following) 4. a − 1
a = m, a = 4, b = 6, c = 3.
a. Find the square of (4x + 5y − 7z). 2
b. If a = 4, b = 6 and c = 3, find the value of 4a2b2 − 16 ab2c +
16b2c2. 4
c. If a − 1
a = m, show that a4 + 1
a4 = m4 + 4m2 + 2. 4 5. x2y(x3−y3), x2y2(x4 + x2y2 + y4) and x3y2 + x2y3 + xy4 are three
algebraic expressions.
a. Resolve into factor : x4 + x2y2 + y4. 2 b. Find the H.C.F of x2y (x3−y3), x2y2(x4 + x2y2 + y4) and x3y2
+ x2y3 + xy4. 4
c. If x2 + 1
x2 = 3 then find the value of x6+1
x3 . 4
6. P = 1
1−a + a2 , Q= 1
1+a+a2 , R = 2a 1+a2+a4
a. Resolve into factors : x2 − x −(m−1) (m−2). 2
b. Show that : P − Q − R = 0. 4
c. Simplify : a4 − b4
a2 + b2 − 2ab (a+b)2 − 4ab
a3 − b3 a + b
a2 + ab + b2 . 4 Part-C : Geometry
(Answer any two of the following)
7. ABCD is a parallelogram the diagonals AC and BD bisect at O.
a. Find out the value of BAD if ABC = 60. 2 b. If AC = BD, prove that ABCD is a rectangle. 4 c. If AB = AD, prove that AC and BD bisect at the point ‘O’
at right angle. 4
8. In the figure, ABC is an equilateral triangle. D, E and F are the mid-points of AB, BC and AC respectively.
a. What is the measurement of each angle of an equilateral
triangle. 2
b. Prove that BDF + DFE + FEB + EBD = 4 right
angles. 4
c. Prove that, DF || BC and DF = 1
2 BC. 4
9. Two adjacent sides of a parallelogram are 5 cm and 4 cm and their included angle is 70.
a. Draw the above information in a figure. 2 b. Draw the parallelogram with the description of drawing. 4 c. Draw a square with a diagonal equal to the larger diagonal of the parallelogram. Give the description of the drawing. 4
Part-D : Statistics
(Answer any one of the following)
10. The marks obtained by 25 students in the annual examination are given below :
72, 85, 78, 84, 78, 75, 69, 67, 88, 80, 74, 77, 79, 69, 74, 73, 83, 65, 75, 69, 63, 75, 86, 66, 71.
a. Find the arithmetic mean of the marks obtained directly. 2 b. Make the frequency distribution table with 5 as class
interval. 4
c. Find the arithmetic mean from the table. 4 11. A table is given below :
Marks obtained
6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45
Frequency 5 17 30 38 35 10 7 3
a. What is the mid-value of mode class. 2 b. Find the arithmetic mean of the table. 4
c. Draw the histogram of the data. 4
