# Bombay Scottish School, Mahim PRELIMINARY ASSESSMENT MATHEMATICS

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Bombay Scottish School, Mahim

PRELIMINARY ASSESSMENT

MATHEMATICS

Grade : 10

Date

: 16.02.2022

Duration : 1 ½ hrs

Max. Marks

: 40

No.of Questions : 06

No. of printed sides: 09

Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 10 minutes. This time is to be spent in reading the question paper.

The time given at the head of this Paper is the time allowed for writing the answers.

Log tables and graph paper will be provided

Attempt all questions .from Sectio n A and any three questions from Section B.

The intended marks fo1questions or parts of questions are given in brackets [j.

- - - -- - - ---·--· · ·-·- --·-·- - - - -- - ~ - - - - - - - - - - - -

SECTION A

(lit1:em.pi a.ll questions from this Section.)

Question 1

Choose the correct answers to the questions from the given options. (Do not

copy the question,write the correct answer only.)

[10]

i) The reflection of point A(-5,4) in the x-axis is

a) (5,4)

b) (-5,4)

c) (-5,-4)

d) (-5,0)

ii) If a card is drawn from a well shuffled pack of cards, then the probability that the card drawn is a red and a king is

7

a) 13

b) O

1

c) 26

1 d) 13

iii) A right angled triangle ABC with 3iries Scrn, 12cm and 13cm is revolved about the side of 12cm,the volurr1e of the solid s o formed is

a) 300n

b) 240n c) 100n

d) 720n iv) The slope of a line parallel to x-axis is

a) 1

b) 0 c) -1

d) not defined

v) In the figure given below, if AB is the diameter of a circle with centre 0,

LBCD = 130°, then LDBA is equal to

a) 50° b) 40° c} 30° d) 60° vi) sec 8 - tan8 sin0 is equal to a) sec 0 b) tan 8

c) 1

d) cos 8

vii) In the figure given below, if the lines AB and CD are equally inclined to th coordinate axes and passing through the point (0,-2)

B

then the equation of line CD is

a) y = 2x + 1 b) y + x + 2 = 0

c) y-x + 2 = 0 d) y-x-2 = 0

viii) If point P(3,a) divides the segment joining the points A(7,l) and B(0,8) in the ratio 4 : 3, then the value of a is

a) 5 b) -4 c) -5 d} 4

ix) Which of the following cannot be the probability of an event?

b) 43%

c) 0.25 d) 2.7

x) From the histogram given below, the modal class is y

.50 '.

f 40

f so :

:a

r«: 2100---.1-vi-'l-.

-40

- ._JM,_l

01•- ~iF""""w+,- ' f >X

5 a10a1.5 -2.0 35

a) 10-15

b) 5-10

c) 20-25 ' d) 15-20

SECTION B

{Attempt any th•.,.,e questionsfirom this Section.)

Question 2

a) Find the equation of a line whose i·nclinat·ion is 60° and y-intercept

is -4

(2

b) A bag contains twenty 5 coins, fifty 2 coins and thirty { 1 c~ins. If it i~ equally likely that one of the coins will fall down when the bag 1s turned

upside down, what is the probability that the coin i) will be a~ 1 coin?

ii) will not be a 2 coin?

[2]

c) Prove that (1 + cot A - cosec A)( 1 + tan A+ sec A) = 2

[3)

d) In the figure given below,from an external point P,tangents PA and PB

are drawn to a circle. CE is a tangent to the circle at D.If AP= 15cm, find

the perimeter of the triangle PEC.

[3]

Question 3

a) Calculate the ratio in which the line joining A(6,5) and B(4 _ ) . . .

b -2

.

yy -

' 3 is d1v1ded [2]

b) Find the value of p for which the lines 6x + Sy - 7 = O and

2px +Sy+ 1 = 0 are parallel to each other.

[2J

c) Use graph paper for this question. Marks obtained by 100 students in an examination are given below:

Marks obtained

No.of students

0-10

8

10-20 10

20-30 22

30-40 40

40-50 20

Draw an ogive for the given distribution taking 2cm = 10 marks on one

axis and 2cm =10 students on the other axis. Using the graph, determine

the median marks.

[3]

d) From a solid cylinder of height 12 cm and diameter 10 cm, a conical

cavity of the same base radius and of the same height is hollowed out.

Find

the

total

surface

area

of the

remaining

solid.(Take

n

=

2 })

[3]

Question 4

a) AB is the diameter of a circle with centre (2,-1). If A(-2,5),find the

coordinates of B.

[2]

b) In the figure given below, 0 is the centre of the circle, LBCE = 30° and

AB is a tangent to the circle at C.

B A

Find

i) LACD

ii) LCOE

[2]

c)

If the

mean

of the

following

d.1stn.bu f10n

1.s

24 '

find

the

value

of a.

[3]

Marks

0-10

10-20

20-30

30-40

40-50

Number of

7

a

8

10

5

students

d) The point Pis the foot of a perpendicular from A(-5,7) to the line

2x -3y + 18 = 0

Find:

i) the equation of the line AP.

ii) the coordinates of P.

[31

Question 5

a) A cylindrical container of radius 6cm and height 15cm is filled wit h ice

cream. The whole ice cream is to be distributed to 5 children in equal

cones.The height of the cone is 12 times the radius at the base of the

cone. Find the radius of each cone.

[2

b)

+ = Prove that:t-an-A-sec A-1

tan A sec A+ 1

2 cosec A

[2j

c) In the adjoining figure,diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD= 7.8 cm, PD= 5cm ,PB= 4cm.Fin

i) AB ii) the length of tangent PT.

d) Use graph paper for this question. Take 1cm = 1 unit on both the axes· Plot the points A(3,5) anf B(-2,-4)

i) Reflect A in the x-axis to get the image A' and reflect Bin the y-axis,followed by reflection in the origin to get the image B'.Write dow n

the coordinates of A' and B'.

ii) Write down the geometrical name of the figure M'BB'.

iii) Name one invariant point under the reflection in the x -axis.

[3 ]

Questh.:iiu 6 a) The coordinates of two points P and Q are (2,6) and (-3,5)

respectively. Find:

i) the equation of PQ.

ii) th e coordinates of the point where PQ intersects the x-axis.

[2 ]

b ) Tv.·c, dice 2se rolled together. Find the probability of getting

i) the ,.r:.1.~-r1 of the n umb ers on the upper-most faces between 5 and 8.

ii) a prirne n u rnber on each dice.

[2]

c) A pHot seated in an aircraft at an altitude of 250m, observes the angle of

depression of two boats on the opposite banks of a river to be 45° and

60° respectively.Find the width of the river.Give your answer correct to

3 significant figures .

[3 ]

d) Use graph paper for this question.

Using an appropriate scale on both axes, estimate the mode of the given distribution by plotting a histogram. [3]

Expenditure (~) 20-25 25-30 30-35 35-40 40-45 45-50

No.of girls

4

7

23

18

6

2

PRELIMINARY ASSESSMENT

MATHEMATICS

Grade : 10

Date

: 16.02.2022

Duration : 1 ½ hrs

Max. Marks

: 40

No.of Questions : 06

No. of printed sides: 09

Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 10 minutes. This time is to be spent in reading the question paper.

The time given at the head of this Paper is the time allowed for writing the answers.

Log tables and graph paper will be provided

Attempt all questions .from Sectio n A and any three questions from Section B.

The intended marks fo1questions or parts of questions are given in brackets [j.

- - - -- - - ---·--· · ·-·- --·-·- - - - -- - ~ - - - - - - - - - - - -

SECTION A

(lit1:em.pi a.ll questions from this Section.)

Question 1

Choose the correct answers to the questions from the given options. (Do not

copy the question,write the correct answer only.)

[10]

i) The reflection of point A(-5,4) in the x-axis is

a) (5,4)

b) (-5,4)

c) (-5,-4)

d) (-5,0)

ii) If a card is drawn from a well shuffled pack of cards, then the probability that the card drawn is a red and a king is

7

a) 13

b) O

1

c) 26

1 d) 13

iii) A right angled triangle ABC with 3iries Scrn, 12cm and 13cm is revolved about the side of 12cm,the volurr1e of the solid s o formed is

a) 300n

b) 240n c) 100n

d) 720n iv) The slope of a line parallel to x-axis is

a) 1

b) 0 c) -1

d) not defined

v) In the figure given below, if AB is the diameter of a circle with centre 0,

LBCD = 130°, then LDBA is equal to

a) 50° b) 40° c} 30° d) 60° vi) sec 8 - tan8 sin0 is equal to a) sec 0 b) tan 8

c) 1

d) cos 8

vii) In the figure given below, if the lines AB and CD are equally inclined to th coordinate axes and passing through the point (0,-2)

B

then the equation of line CD is

a) y = 2x + 1 b) y + x + 2 = 0

c) y-x + 2 = 0 d) y-x-2 = 0

viii) If point P(3,a) divides the segment joining the points A(7,l) and B(0,8) in the ratio 4 : 3, then the value of a is

a) 5 b) -4 c) -5 d} 4

ix) Which of the following cannot be the probability of an event?

b) 43%

c) 0.25 d) 2.7

x) From the histogram given below, the modal class is y

.50 '.

f 40

f so :

:a

r«: 2100---.1-vi-'l-.

-40

- ._JM,_l

01•- ~iF""""w+,- ' f >X

5 a10a1.5 -2.0 35

a) 10-15

b) 5-10

c) 20-25 ' d) 15-20

SECTION B

{Attempt any th•.,.,e questionsfirom this Section.)

Question 2

a) Find the equation of a line whose i·nclinat·ion is 60° and y-intercept

is -4

(2

b) A bag contains twenty 5 coins, fifty 2 coins and thirty { 1 c~ins. If it i~ equally likely that one of the coins will fall down when the bag 1s turned

upside down, what is the probability that the coin i) will be a~ 1 coin?

ii) will not be a 2 coin?

[2]

c) Prove that (1 + cot A - cosec A)( 1 + tan A+ sec A) = 2

[3)

d) In the figure given below,from an external point P,tangents PA and PB

are drawn to a circle. CE is a tangent to the circle at D.If AP= 15cm, find

the perimeter of the triangle PEC.

[3]

Question 3

a) Calculate the ratio in which the line joining A(6,5) and B(4 _ ) . . .

b -2

.

yy -

' 3 is d1v1ded [2]

b) Find the value of p for which the lines 6x + Sy - 7 = O and

2px +Sy+ 1 = 0 are parallel to each other.

[2J

c) Use graph paper for this question. Marks obtained by 100 students in an examination are given below:

Marks obtained

No.of students

0-10

8

10-20 10

20-30 22

30-40 40

40-50 20

Draw an ogive for the given distribution taking 2cm = 10 marks on one

axis and 2cm =10 students on the other axis. Using the graph, determine

the median marks.

[3]

d) From a solid cylinder of height 12 cm and diameter 10 cm, a conical

cavity of the same base radius and of the same height is hollowed out.

Find

the

total

surface

area

of the

remaining

solid.(Take

n

=

2 })

[3]

Question 4

a) AB is the diameter of a circle with centre (2,-1). If A(-2,5),find the

coordinates of B.

[2]

b) In the figure given below, 0 is the centre of the circle, LBCE = 30° and

AB is a tangent to the circle at C.

B A

Find

i) LACD

ii) LCOE

[2]

c)

If the

mean

of the

following

d.1stn.bu f10n

1.s

24 '

find

the

value

of a.

[3]

Marks

0-10

10-20

20-30

30-40

40-50

Number of

7

a

8

10

5

students

d) The point Pis the foot of a perpendicular from A(-5,7) to the line

2x -3y + 18 = 0

Find:

i) the equation of the line AP.

ii) the coordinates of P.

[31

Question 5

a) A cylindrical container of radius 6cm and height 15cm is filled wit h ice

cream. The whole ice cream is to be distributed to 5 children in equal

cones.The height of the cone is 12 times the radius at the base of the

cone. Find the radius of each cone.

[2

b)

+ = Prove that:t-an-A-sec A-1

tan A sec A+ 1

2 cosec A

[2j

c) In the adjoining figure,diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD= 7.8 cm, PD= 5cm ,PB= 4cm.Fin

i) AB ii) the length of tangent PT.

d) Use graph paper for this question. Take 1cm = 1 unit on both the axes· Plot the points A(3,5) anf B(-2,-4)

i) Reflect A in the x-axis to get the image A' and reflect Bin the y-axis,followed by reflection in the origin to get the image B'.Write dow n

the coordinates of A' and B'.

ii) Write down the geometrical name of the figure M'BB'.

iii) Name one invariant point under the reflection in the x -axis.

[3 ]

Questh.:iiu 6 a) The coordinates of two points P and Q are (2,6) and (-3,5)

respectively. Find:

i) the equation of PQ.

ii) th e coordinates of the point where PQ intersects the x-axis.

[2 ]

b ) Tv.·c, dice 2se rolled together. Find the probability of getting

i) the ,.r:.1.~-r1 of the n umb ers on the upper-most faces between 5 and 8.

ii) a prirne n u rnber on each dice.

[2]

c) A pHot seated in an aircraft at an altitude of 250m, observes the angle of

depression of two boats on the opposite banks of a river to be 45° and

60° respectively.Find the width of the river.Give your answer correct to

3 significant figures .

[3 ]

d) Use graph paper for this question.

Using an appropriate scale on both axes, estimate the mode of the given distribution by plotting a histogram. [3]

Expenditure (~) 20-25 25-30 30-35 35-40 40-45 45-50

No.of girls

4

7

23

18

6

2

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