GOKULDHAM HIGH SCHOOL &JUNIOR COLLEGE
SECONIDARY SECTION(2024-2025)
I TERMINAL EXAMINATION
SUBJECT: MATHEMATICS
GRADE: 10 MARKS: 80
DATE: 02.09.2024 TIME: 2 hours 30 minutes
> Answers to this Paper must be written on the paper provided separately.
> You wvillnot be allowed to write during first 1S minutes.
º 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.
Attempt all questions from Section Aand any four questions from Section B.
All working, including rough work, must be clearly shown, and must be
done on the same sheet as the rest of the answer.
> Omission of essential working will result in loss of marks.
> The intended marks for questions or parts of questions are given in brackets I
> Mathematical tables are provided.
> This paper consists of9 printed pages and a blank page.
SECTION A
(Atempt all questions from this section)
Question 1
Choose and write the correct answers to the questions from the given options: [15|
[Do not copy the question.]
() Which term of the A.P: 21,42, 63---. is 210?
a) 9th
b) 10th
c) 11h
d) 12h
(ii) The point (3,0) is invariant under reflection in
a) origin
b) x-axis
c) y-axis
d) line y =3
(ii) When 2x3 x23x +5 is divide by 2.r + Ithen the remainder is
a) 6
b) -6
c) -3
d) 0
1
GRAD1E
GRADE 10
(IV)
Ir xA= hen the order of matrix Ais MATIHENMN (x)
a) 2 x 2
b) 1x 2
c) 1x 3
d) 2x 1
(V)
lf the circumference of the base of acylindrical vessel is 132 cm and its height i
25 cm then its radius is
a) 20 cm
b) 22cm
c) 21 cim
d) 14 cm
(vi) In the adjoining figure of AABC, DE is
parallel to
such that AD =3 cm, DB=4 cm AE =6cm then ECBC is
a) 8 cm
b) 12 cm D
c) 6 cm
d) 4 cm
(vii) Ifx E W, then the solution set of equation
-x> 7is
a) {8,9,10 ---}
b) {0,1,2,3,4,5,6}
c) {0,1,2,3 -----}
d) }
(viii) ASSERTION (A):Mode can be calculated by plotting a less than ogive for a
grouped frequency distribution.
REASON(R): A less than ogive is constructed on the basis of cumulative
frequencies being in ascending order.
a) A is true, R is false
b) A is false, R is true
c) Both A and R are true
d) Both A and R are false
(ix) Allletters of words MATHEMATICS &MATTER are written on cards and put
in a bag. What is the probability of getting letter T', if one card is taken out
from the bag?
a) 2/11
b) 2/3
c) 4/17
d) 4/33
2
GRADE 10 MATHEMATICS
(X) What is the product of the mean proportion of I8 and 32 and the third
proportional of 12 and 5
a) 24
b) 25
c) 50
d) 100
(X) The roots of the quadratic cquation x+ 2x +1=0are
a) Real and distinct
b) Not real
c) Real and cqual'
d) None
% per
(xii) A man deposited? 1200 per month in a recurring account for lyear at 5
annum.The interest earned by him on maturity is
a) 14790
b) 390
c) 780
d) 500
=130°
(xii1) In the given figure, O is the centre of acircle and LPQR
Then, the value ofx is
a) 50°
b) 65°
c) 100°
d) 130°
(xiv) V1+ tan²0 is equal to
a) cote
b) cos
c) sec²0
d) seco
= 0, then the value ofk is
(XV) If is a root of the equation x + kx 4
a) 2
b) -2
c) 3
d) 4
3
GRADE I0
Question 2
incquation:
(i) Solve the given linear 2r-5< 5.x+ 4< 1 each
represent the solution set on number line in
Write the solution set and
case vhen
(a)x E Z 14|
(b) x E R
(ii)
65°
diameter,
In the adjoining fgure of acircle with centre O, BA is a
ZADE = 65° and ZBCD = 135°, then find
(a)zABC
(b)LACB
(c)BAC
(d) zDAC |4|
(ii) Vimal has a recurring deposit account in a bank and he deposited Rs. 500
per month for a period of 4years. If he gets Rs. 28410 on maturity, find the
rate of interest. |4|
Question 3
(i) A cylinder with capacity 7392 cm' is filled with water such that the cylinder
is empty 2 cm from the top. Ifthe volume of water in cylinder is 6160 cm.
find the radius and the height of the cylinder. |4|
(ii) Prove : sec A(1- sin A )-2 tan² A=| 14|
4
GRADE 10
(u1) The following frequency MATHEMATICS
students in an
distribution table shows the marks obtaincd by 200
examination:
Marks Number of
Students
0-10 5
10-20 11
20-30 10
30-40 20
40-50 28
50-60 37
60-70 40
70-80 29
80-90 14
90-100
Draw an ogive by taking 2cm = 10 marks on one axis and
2cm =20 students on the other axis. Using the graph estimate
(a) the median marks.
(b) the number of students who scored more than 85.
(c) lower quartile.
SECTION B
(Attempt any four questions from this section)
Question 4
(i) A bag contains 3 White, 4 Red and n Black balls. If probability of picking a
1
white ball is of probability of picking ablack ball when aball is drawn at
random. Find:
(a) total number of balls in the bag. |3|
(b) probability of picking a black ball.
(ii) Solve the following quadratic equation:
x?- 10x +6 = 0
Give your answer correct to three significant figures. [3|
(i) If(x-2) is a factor oftheexpression 2x + ax? + bx -14 and when the
expression is divided by (x-3),it leaves a remainder 52, find the values of
a and b
|4|
GRADE 10 MATHEMATICS
Question5
(1)
Find a, b and c Where A + B= AB (3
(1)
D
In the given figurc, O is the centre of a circle and LOAB =50°, BC IS a
diameter. Find:
(a) z AOC
(b) ZADC (3|
(c) Z BDA
(1i) Using properties of proportion, find a: b if (a' +
3ab² )(62)= (b'+ 3a'b )(63) (4|
Question 6
() Prove the following trigonometrical identity:
(cosec A sin A) (sec A - cos A) sec' = tan A
[3|
(ii) Factorize x 7x2 + 14x-8 completely using factor theorem.
[3|
(iii) Sum of first three terms of an arithmetic progression is 13.5 and the
of first and third term is 14. Find:
product
(a)the common differcnce
(b)first term
(c)sum of first 21 terms of this progression. 14]
6
MATIHEMATICS
(GRADE I0
Question
()
perpendicular to
ofAABC, ZB 90° and DE is
In the above given figure
AC.
(a)Prove that AADE ~AACB
AC= 13cm, BC = 5 cn, AE = 4 cm, find AD
(b)lf
(c)Find area(AADE):area(quadrilateral BCED)
paper to answer the following questions.
(ii) Use graph axes]
[Use scale: 2cm = l unit on both
2)
(a) Plot the point P (3, 5) and Q (1, x axis. Write down
coordinates of
when reflected in
(b) P is the image of P
P' Write down
of Q when reflected in the line PP',
(c) Q is the image
coordinates of 0'.
special geometrical name.
(d) Join POP'Q and write its Q0"? [5|
under reflection in
(e) Is the point (4, 2) invariant
Question 8
jug of radius 8 cm and height 10 cm is filled with juice. It is
Acylindrical Find the |31
(i)
poured into small conical cups of radius 2 cm and height 6 cm,
then
number of cups that can be filled.
(ii) Prove the following identity (3|
cot A + tan A = cosec A sec A
[4)
(m) IA-and
1
I-| find A -5A +71
7
GRADE 10
Question 9
I3)
60 cm
Find the totalsurface arca of toy, if the radius of cone is 10 cm and its
height is 24 cm, the total height of toy is 60 cm and radius of base of cone is
twice the radius of base ofcylinder.
(i) The toy nnodel of atruck and realtruck are in the ratio 1:60
(a) Calculate the length of truck, in metres, if the length of the model is 25
CIm.
(b) If the open area of truck is 90 m², find the open area of the model in cm.
(c) If the volume of the model is 7500 cm', find the volume of truck in m'. 3|
(ii) Rs. 480 can be divided cqually among .x children. If thenumber of children is
increased by 20 then each child would receive Rs. 12 less than the initial
amount. Find the number of children by framing and solving a quadratic
equation. [4)
Question 10
|3)
B
ABCD isa cyclic parallelogram. Show that it is a rectangle.
(ii) Prove that:
secA-1 secA+1 2cosecA [3)
V secA+1 VsecA-1
8
HEMATICS
13]
GRADE 10
(iii) There are 20 cards
picked up randomly has
(a) a prime number
numbered 1 to 20, MATHEMATICS
What is the probability that a card |4|
(b) a number
between 2 and 7
(c) a cube number
(d) a number divisible by 3
and 5
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