X Maths SQP1 QP

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Mock Test Paper – I

MathematicsClass X

General Instructions

1. All questions are compulsory.

2. The question paper consists of 30 questions divided into 4 sections A, B, C and D. Section Acomprises of 10 questions of 1 mark, Section B is of 5 questions of 2 marks each. Section C is of10 questions of 3 marks each and section D is of 5 question of 6 marks each.

3. There is no overall choice. Internal choice has been provided with.

Section A1. Find without actual division whether the rational number is a terminating or non-terminating repeating

decimal : 9017

.

2. Find the number of zeroes of the polynomial as depicted in the figure below:

3. State whether the pair of linear equation is consistent / inconsistent.

3x + y = 1

2y = 2 – 6x

4. Determine whether 3x is a solution of the equation or not, 06332 xx .

5. In a right angled ABC, right angled at C, if tan = 1, then verify that 2 sin cos = 1.

6. In a ABC, AD is the bisector of A meeting side BC at D, if AB = 5.6 cm, BC = 6 cm andBD = 3.2 cm, find AC.


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7. If TP and TQ are the two tangents to a circle with centre O, sothat POQ = 110°,then PTQ is equal to x°. Find x°.

8. The difference between circumference and diameter of circle is 105 cm. Find the radius of the circle.

9. If P(not E) = 61

then P(E) is given by a, find a.

10. The mean of five numbers is 10. If each number is decreased by 3, find the mean of new numbers.

Section B11. Find the sum of the product of the zeroes of the following quadratic polynomial.

x2 – (c – ab)x – abcOr

Find the quotient and the remainder, when 6x2 – 31x + 47 is divided by 2x – 5.

12. If sin 5A = cos 4A, where 5A and 4A are acute angles, find the value of A.

13.

ABCD is a parllelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove thatthe rectangle contained by BP and DQ is equal to the rectangle contained by AB and BC.

14. The circle is divided into three regions - I, II and III. A spinner is fixed atthe centre O of the circle of ROQ = 45°, find the probability that thespinner will land in the region II.

15. If A(6, –1), B(1, 3) and C(K, 8) are three points such that AB = BC, find the value of K.

CQ

BA

D

o

Q

P

Tx°

P


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Section C

16. The length of the hypotenuse of a right angled triangle exceeds the length of the base by 2 cm andexceeds twice the length of the altitude by 1cm. Find the length of each side of the triangle.

17. Solve 4x2 + 4bx – (a2 – b2) = 0 by method of completing the squares.

18. Find the sum of n terms of an A.P. whose nth term is given by tn = 5 – 6n.

19. Prove that the square of any positive integer of the form 5q + 1 is of the same form.

20. Prove that

cos A sin A sin A cos A1 tan A 1 cot A

Or

4 cos 70 .cosec203cos557sin 35 7 tan 5 .tan 25 . tan 45 . tan 65 .tan85

21. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents tothe circle and measure their lengths.

22. Find the coordinates of the circumcentre of a whose vertices are A (4, 6) , B(0, 4) and C (6, 2).

23. Find the point on the y-axis which is equidistant from (–5, –2) and (3, 2).

24. A circle touches the side BC of ABC, at P and touch AB and AC produced at a Q and R respectively.

Prove that 1AQ2

Perimeter of ABC.

Or

In a quad – ABCD , CA = CD, B = 90° and AD² = AB2 + BC² + CA². Prove that ACD = 90°.

C

B

D

A


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25. Find the area of the shaded region.

OR

A field is in the form of a circle. The cost of ploughing the field at Rs. 1.50 per m² is Rs. 5775. Find thecost of fencing the field at Rs. 8.50 per metre.

Section D26. State and prove Thales Theorem. In the figure

LM | | AB. If AL = x – 3, AC = 2x,

BM = x – 2 and BC = 2x + 3, find the value of x.

27. A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere.The external diameter of the frustum are 5 cm and 2 cm and the height of the entire shuttle cock is 8 cm.Find its external surface area.

Or

A juice seller serves his customer using glasses (as shown in thefigure). The inner diameter of these cylindrical glasses is 7 cm andheight is 12 cm. The bottom of the glass has a raised hemisphericalportion. Find the apparent and actual capacities of the glass.

12 cm

7 cm

C

L M

A B

40°DB

A C

o

7cm

14 cm


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28. There are two class rooms A and B containing students. If 5 students are shifted from room A to roomB, the resulting number of students in the two rooms become equal. If 5 students are shifted from roomB to room A, the resulting number of students in room A becomes double the number of students left inroom B. Represent this situation algebraically and solve graphically.

29. From a window, h metres high above the ground of a house in a street, the angles of elevation of the topand angle of depression of the foot of another house on the opposite side of the street are and respectively. Show that the height of the opposite house is h (1 + tan cot ) metres.

30. The mean of the following frequency table is 50, but the frequencies f1 and f2 in class 20-40 & 60-80 aremissing. Find the missing frequencies if the total frequencies are 120.

Class 0-20 20-40 40-60 60-80 80-100

Frequency 17 f 1 32 f 2 19

Or

The following distribution shows the height of students of certain school.

Height(in cm) No.of students

160-162 15

163-165 118

166-168 142

169-171 127

172-174 18

Find the modal height of students.

........End of Paper........

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X Maths SQP1 QP