BAF Shaheen College Dhaka
Practice Preparatory Test Examination-1 : 2020 Class X
(English Version)
Subject: Mathematics (Creative)
Time : 2 Hours 30 Minutes Full Marks:70
[ Answer any two from group-A, two from group-B, two from group-C and one from group-D ] Group-A
1. i. y2 − 2√30 = 11, when y > 0 ii. P = √3 + √2
a. Resolve into factors : x3 - 9y3 + (x + y)3. 2
b. Find the value of y3−1/y3 4
c. Prove the relation (ii) if P3 +1/p3 = 18√3. 4
2. If 1 is subtracted from numerator and 2 is added to denominator of a fraction, the fraction will be 1/2. Again if 2 is subtracted from numerator and 3 is subtracted from denominator it will be 1.
a. Form two equations, considering x and y as numerator and denominator respectively. 2
b. Determine the fraction. 4
c. Solve the getting equations with the help of graph. 4
3. If the 1st term of a geometric series is and 7th term is . Again the sum of 1st 5 term of an arithmetic series is 35 and sum of 1st 10 terms is 120.
a. Find the common difference of the series; log3 + log9 + log27 +.... 2
b. Find the sum of 1st 7 terms of the geometric series. 4
c. Find the 20th term of the arithmetic series. 4
Group-B
4. The two parallel sides of a trapezium are g = 5 cm, h = 11 cm and two angles adjacent to the larger sides are
<x = 60° and <y = 45°.
a. Draw and describe a rhombus whose side is equal to ‘g’ and an angle is equal to <x. 2
b. Draw and describe the trapezium. 4
c. Draw a triangle whose base adjacent two angles are <x and <y and perimeter is equal to ‘h’. 4 5. ΔABC and ΔDEF are two equiangular triangles. AG, GH are perpendicular to base.
a. Draw the figure in the light of the stem. 2
b. Prove that, AG : DH = AB : DE. 4
c. Prove that, ΔABC : ΔDEF = BC2 : EF2. 4
6. In a right angled triangle PQR, <Q is right angle and PR is hypotenuse.
a. State Pythagoras theorem. 2
b. Prove that, PR2 = PQ2 + QR2. 4
c. If PQ = QR and A is any point on PR. Then prove that, PA2 + RA2 = 2QA2. 4 Group-C
7. A pole is broken by a storm such that the broken part makes angles of 30° with the standing part and touches the ground at a distance of 6m from its foot.
a. Draw the figure with a short description. 2
b. Find the total length of the pole. 4
c. If the broken part makes an angle of 60° with standing part, find out at which distance from its foot, the
top of the pole touches the ground? 4
Subject Code 1 0 9
8. The circumference of a circle is 44 metre.
a. Determine the radius of the circle. 2
b. Determine the length of the side of the square which is inscribed in the circle. 4 c. If the circumference of the circle is equal to the perimeter of an equilateral triangle, then find the ratio of
their areas. 4
9. The inner and outer diameter of an iron pipe are 18 cm and 20 cm respectively and the height of the pipe is 5 m. The weight of 1c.c. iron is 7.2 gram.
a. Find the whole area of the surface of a cube having the edge of 5 cm. 2
b. Find the weight of the pipe. 4
c. A solid bar of radius 6 cm is formed by melting the pipe. Find the height of the bar. 4 Group-D
10.
Class 41-45 46-50 51-55 56-60 61-65 66-70
Frequency 4 6 12 20 15 3
a. Write the formula of mode using the symbol. 2
b. Find the median. 4
c. Draw the histogram. 4
11.
Class 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
Frequency 5 8 13 15 35 25 5 4
a. Find the mid value of mode class. 2
b. Find the arithmetic mean using short-cut method. 4
c. Draw the ogive curve. 4
