ICSE Class 9 Maths Half Yearly Sample Paper 2025: Download PDF for FREE

Board

ICSE

Class

9

Subject

Maths

Full Marks

80

Total Section

Section A & B

Exam Duration

3 Hours 15 Mins

Q.1

QI. Multiple choice questions (1x15=15)

(1) For two consecutive years a sum of money lent out at C.I. amounts to rupees 2400 and rupees  2760 respectively. The rate of interest is:  

a) 5% 

b) 15% 

c) 18% 

d) 10%

(2) Rates of interest for two consecutive years are 10% and 12% respectively. The percentage increased during the two years.  

a) 22% 

b) 23.2% 

c) 123.2% 

d) 122%

(3) Factorisation of 6xy-4y+6-9x is:  

a) (3y-2)(2x-3) 

b) (3x-2)(2y-3) 

c) (2y-3)(2-3x) 

d) None of the above

(4) Rupees 10 is the difference between compound interest and simple interest in 2 years and 5%  per annum. The principal amount is:  

a) Rupees 4400 

b) Rupees 4100 

c) Rupees 4000 

d) None of the above

(5) The factorisation of 4x2+8x+3 is:  

a) (x+1)(x+3) 

b) (2x+1)(2x+3) 

c) (2x+2)(2x+5) 

d) (2x-1)(2x-3)

(6) One of the factors of (25x2-1)+(1+5x)2 is:  

a) 5+x 

b) 5-x 

c) 5x+1 

d) 10x

(7) If cosB=53, then the value of tanB is:

(a) 4/3 

(b) 3/4 

(c) 4/5 

(d) 5/4

(8) In a quadrilateral ABCD:  

a) AB+BC+CD+DA>AC+BD  

b) AB+BC+CD+DA<AC+BD 

c) AB+BC+CD+DA=AC+BD

d) AB+BC<AC

(9) If each interior angle of a polygon is 1440 the number of sides in it is:  

a) 5 

b) 10 

c) 6 

d) 7

(10) The mean of x-1, x+1, x+3 and x+5 is:  

 a) x+1 

b) x+2 

c) x+3 

d) x+4

(11) In a parallelogram ABCD Angle A – Angle C is equal to:  

a) 90 degree 

b) 120 degree 

c) 0 degree 

d) 180 degree

(12) The median of the data 78,56,22,34,45,54,39,68,54,84 is  

a) 45 

b) 49.5 

c) 54 

d) 56

(13) Point(k,2) lies on the line x-4y=2 the value of k is:  

a) 10 

b) -6 

c) -10 

d) 6

(14) The line 5x-2y-10=0 intersects x-axis at point P. The co-ordinates of point P are:  

a) (0,2) 

b) (0,-2) 

c) (2,0) 

d) (-2,0)

(15) If the mean of x1, x2 is 7.5 and the mean of x1, x2, x3 is 8, find the value of x3.  

a) 9 

b) 8 

c) 7.5 

d) 6

Q.2

a)  AB, BC and CD are the three consecutive sides of a regular polygon. If ∠BAC=150.  Find: [4]  

i) each interior angle of the polygon  

ii) each exterior angle of the polygon  

iii) number of sides of the polygon

b) The diagonals AC and BD of a rhombus ABCD meet at O AC=10cm, BD=24cm. Find   sin ∠OAD. [4]

c) If O is any point in the interior of a triangle ABC, show that OA+OB+OC>2/1(AB+BC+CA).  [4] 

Q.3

a) In triangle ABC , altitudes BE and CF are equal. Prove that the triangle is isosceles. [4]  

b) Solve graphically for x and y: [5]   

(i) 5x+4y=29  

(ii) 8y-3x+7=0 

c) Construct a parallelogram ABCD when Base AB=6.5cm, BC=4cm and the altitude   corresponding to AB=3.1cm [4]

Q.4

a) In triangle ABC, ∠B= 900, AB=40, AC+BC=80 find: [4]  i) sin A ii) cos A iii) tan C  

b) Find the mean of factors of 84. [3]   

c) Factorise (x+4)2 – 5xy -20y -6y2 [3]  

Q.5

a) Two partners A and B together lent rupees 44,200 at 10% C.I. The amount A gets at the end   of 3 years is the same as B gets after 5 years. Determine the share of each in the money   lent. [4]  

b) Factorise (x2+ y2 – z2)2 – 4x2y2 [3]   

c) 2, 4, x-3, x+2,11,15. The median is 7.5 then find its mean. [3]  

Q.6

a) In triangle ABC ∠B=900 and tan A =0.75. If AC = 30 cm find the length of AB and BC. [4]   

b) In the figure given below AD=BD=DC and ∠ACD= 350 Show that: [3]  i) AC > DC ii) AB > AD  

c) Find the sum invested at 10% C.I. on which the sum of interest for first year and third   year amounts to rupees 1768. [3]

Q.7

a) a certain sum of money amounts to ₹57600 in 2 years and ₹65536 in 4 years at   C.I. annually. Find the sum and the rate. [4]   

b) The following data has been arranged in ascending order. If their median is 63, find the value of x. [3]  34,37,53, 55, x, x+2,77,83,89 and 100.  

c) Factorise x(x+z) - y(y+z) [3]

Q.8

a) In a triangle ABC, ∠A=600, ∠C=400 and bisector of angle ABC meets side AC at point P.   Show that BP= CP [4]   

b) Using ruler and compass only, construct a rhombus ABCD, given that AB=5cm, AC=6cm. [3]   

c) Use the information given in the following figure to evaluate: sinθ+cosϕ

Q.9

a) A machine depreciates every year at the rate of 20% of its value at the beginning of the year. The machine was purchased for rupees 250000 when new and the scrap value realized when  sold at rupees 128000 find the number of years of the machine in use. [4]   

b) sin A = cos A. Find tan A + cot A [3]   

c) The given figure shows a rhombus ABCD . Find x and y. [3]

Q.10

a) In triangle ABC, D is a point on BC such that AB=AD=BD=DC. Show that: ∠ADC:∠C = 4:1.  [4]  

b) Factorise (x-1)(x-3)(x-5)(x-7) - 65 [3]   

c) The difference between an exterior angle of (n-1) sided regular polygon and an exterior angle  of (n+2) sided regular polygon is 60. Find the value of n. [3]

CHECK:ICSE Class 9 Maths Half Yearly Sample Paper 2025, Download PDF