BAF Shaheen College Dhaka Practice Pre-Test Exam-2020
Class-X
Subject-Mathematics (Creative)
Time: 2 hours 30 minutes Full marks
Answer any two question from group-A, any two from-B, any two from-C and One from group-D
1. a=√27
3 , b= √17, c=5.639, d= 0.24
(a) Express с and d into simple fraction. 2
(b) Find the two rational numbers and two irrational numbers between a and b. 4
(c) Prove that b is an irrational number. 4
2. A=log2√5 8000
B = 𝑙𝑜𝑔10𝑙𝑜𝑔10 4.5√125 + 𝑙𝑜𝑔10 27−𝑙𝑜𝑔10 √1000
C= 9
𝑚+1
3𝑚−1÷(3𝑚)3𝑚+1𝑚−1
(a) Find the value of A. 2
(b) find the value of B. 4
(c) Prove that C= AB. 4
3. Suppose, the three quantities a, b, с are to be of same kind.
(a) If b2 =ac then prove that 𝑎
2+𝑏2
𝑏2+𝑐2 = (𝑎+𝑏)
2
(𝑏+𝑐)2 2
(b) If a = √1+𝑏+√1+𝑏
√1+𝑏−√1−𝑏, then prove that a2-2𝑎𝑏 +1=0 4
(c) If a:b= 7:8 and L.C.M of a and b is 224, then find the H.C.F of a and b. 4
Group -B: Geometry
4. ABCD is a quadrilateral inscribed in a circle with centre O. The diagonals AC and BD intersect at the point E.
(a) Draw the figure with the above information. 2
(b) Prove that, the sum of the two opposite angles of the quadrilateral ABCD is two right angles.
4 (c) Prove that, <AOB + <COD = 2<AEB 4
5. The perimeter of an equilateral triangle is 12 cm.
(a) Draw the triangle according to the stem. 2
(b) Draw an ex-circle of the triangle and give a short description. 4 (c) If the length of the square region is equal to the 1
2 of that of the perimeter of the triangle, then draw the inscribed and the circumscribed circles of the square.
4
6. The bisector PE of <P of the triangle PQR intersects QR at E. The line segment RF parallel to PE intersects the line segment QP extended.
(a) Draw the specified figure. 2
(b) Prove that, QE : ER = PQ : PR. 4
(c) If a line segment parallel to QR intersects PQ and PR at M and N respectively. Prove that,
QE : ER = QM:RN 4
7. ten𝜃+sin𝜃 =m and tan𝜃-sin𝜃= n
(a) In the light of the stem prove that, m+n = 2 sec𝜃. sin𝜃 2
(b) Prove that m2 - n2 = 4√𝑚𝑛 4
(c) If𝑚
𝑛 =2+√32−√3, then find the value of 0, when 0o < 𝜃 < 90𝑜 4 8. From a helicopter above a point О between two kilometer posts, the angles of depression of the two points A and В are 60° and 30° respectively.
(a) Draw a figure with short description. 2
(b) Find the height of the helicopter from the ground. 4
(c) Find the direct distance from the points A of the helicopter. 4 9. The radius of a circle is 14 c.m. and an arc subtends an angle 75° at the centre.
(a) Determine the area of the circular segment. 2
(b) Determine the length of the side of the inscribed square in the circle. 4 (c) There is a road of 3 c.m. width around the circle outside. Determine the area of the road.
4
Group-D: Statistics
10. The frequency distribution table of the marks obtained in Mathematics by 70 students of Milestone College in Pre-Test exam of class X are provided below :
Marks 50- 56- 62- 68- 74- 80- obtained 55 61 67 73 79 85 Frequency 3 18 10 25 6 8
(a) What are discrete and Indiscrete variables with examples. 2
(b) Determine the median from the table. 4
(c) Draw the frequency polygon of the given data. 4
11. The weights (in kg) of 25 students in your class are provided below:-
60, 55, 58, 48, 61, 65, 80, 70, 46, 60, 65, 70, 59, 60, 68, 70, 45, 86, 60, 50, 46, 65, 55, 61, 72.
(a) Find the number of classes considering 5 as a class interval. 2 (b) Considering 5 as a class interval, find the Arithmetic Mean from the table in the short-cut
method. 4
(c) Draw the histogram and polygon of the histogram with the help of the frequency
distribution table. 4
