ICSE Class 9 Specimen Paper for Mathematics

CLASS IX

MATHEMATICS
(Two hours and a half)
Answers to this Paper must be written on the paper provided separately.

You will not be allowed to write during the first 15 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.

Attempt all questions from Section A and 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 [ ].
Mathematical tables are provided.

SECTION A (40 Marks)
Attempt all questions from this Section.

Question 1

(a) Rationalize the denominator: [3]
14
5√3 − √5

(b) Factorize the given expression completely: [3]
6𝑥 2 + 7𝑥 − 5

(c) 1 22 [4]
In the given figure, AB = 2 BC, where BC = 14 cm (Use π = 7 ). Find:

(i) Area of quad. AEFD
(ii) Area of ABC
(iii) Area of semicircle.
Hence find the area of shaded region.

This paper consists of 7 printed pages.
Mathematics Specimen Paper - Class IX - 2019 Onwards Turn Over

Question 2

(a) Mr. Ravi borrows ₹ 16,000 for 2 years. The rate of interest for the two successive [3]
years are 10% and 12% respectively. If he repays ₹ 5,600 at the end of first year,
find the amount outstanding at the end of the second year.

(b) Simplify: [3]

1 1 1
8 −3 25 2 4 0 125 3
( ) ×( ) ×( ) +( )
27 4 9 64

(c) In the given figure, ABCD is a parallelogram. AB is produced to P, such that [4]
AB = BP and PQ is drawn parallel to BC to meet AC produced at Q. Given AB = 8
cm, AD = 5 cm, AC = 10 cm.

(i) Prove that point C is mid point of AQ.

(ii) Find the perimeter of quadrilateral BCQP.

Question 3

(a) Solve following pairs of linear equations using cross-multiplication method: [3]

5𝑥 − 3𝑦 = 2

4𝑥 + 7𝑦 = −3

(b) Without using tables, evaluate: [3]

sin 31° sec 59° + cot 59° cot 31°
4 tan 60° sec 30° +
8 sin2 30° − tan2 45°

Mathematics Specimen Paper - Class IX - 2019 Onwards 2

(c) Construct a frequency polygon for the following frequency distribution, using a [4]
graph sheet.

Marks 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90 90 – 100
No. of
7 18 26 37 20 6
students

Use 2 cm = 10 marks
2 cm = 5 students

Question 4
(a) Evaluate : [3]

1
3𝑙𝑜𝑔2 − 𝑙𝑜𝑔27 + 𝑙𝑜𝑔12 − 𝑙𝑜𝑔4 + 3𝑙𝑜𝑔5
3
1 1
(b) If 𝑥 − 𝑥 = 3, Evaluate 𝑥 3 − 𝑥 3 [3]

(c) In the given diagram ‘O’ is the centre of the circle and AB is parallel to CD. [4]
AB = 24 cm and distance between the chords AB and CD is 17 cm. If the radius
of the circle is 13 cm, find the length of the chord CD.

Mathematics Specimen Paper - Class IX - 2019 Onwards 3
Turn Over

SECTION B (40 Marks)
Attempt any four questions from this Section

Question 5

(a) Find the coordinates of the points on Y-axis which are at a distance of 5√2 units [3]
from the point (5,8).

(b) In the given figure BC is parallel to DE. Prove that: [3]

area ABE = area ACD

(c) A sum of ₹ 12,500 is deposited for 1½ years, compounded half yearly. It amounts [4]
to ₹ 13,000/- at the end of first half year. Find:

(i) The rate of interest

(ii) The final amount. Give your answer correct to the nearest rupee.

Question 6

(a) Construct a prallellogram ABCD in which AB = 6.4 cm, AD = 5.2 cm and the [3]
perpendicular distance between AB and DC is 4 cm.

(b) Factorize: [3]

4𝑎2 − 9𝑏 2 − 16𝑐 2 + 24𝑏𝑐

Mathematics Specimen Paper - Class IX - 2019 Onwards 4

(c) In the given diagram ABCD is a parallelogram. APD and BQC are equilateral [4]
triangles. Prove that:

(i) PAB = QCD
(ii) PB = QD

Question 7

(a) Solve for 𝑥; where 0° ≤ 𝑥 ≤ 90° [3]

5
sin2 𝑥 + cos2 30° =
4

(b) Evaluate for 𝑥: [3]
𝑥−8
5 27 2𝑥−3
(√ ) =( )
3 125

(c) In the given figure, triangle ABC is a right angle triangle with B = 90o and D is [4]
mid point of side BC. Prove that:

AC2 = AD2 + 3CD2

Mathematics Specimen Paper - Class IX - 2019 Onwards 5
Turn Over

Question 8
(a) In the given figure ABC = 66o, DAC = 38o. CE is perpendicular to AB and AD is [3]
perpendicular to BC. Prove that: CP > AP

P

(b) Mr. Mohan has ₹ 256 in the form of ₹1 and ₹ 2 coins. If the number of ₹ 2 coins [3]
are three more than twice the number of ₹ 1 coins, find the total value of ₹ 2
coins.

(c) Find: [4]
(i) Mean and
(ii) Median
for the following observations:
10, 47, 3, 9, 17, 27, 4, 48, 12, 15

Question 9
(a) Three cubes are kept adjacently, edge to edge. If the edge of each cube is 7 cm, [3]
find total surface area of the resulting cuboid.

(b) In the given figure, arc AB = twice arc BC and AOB = 80o. Find: [3]

(i) BOC

(ii) OAC

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(c) Solve graphically the following system of linear equations (use graph sheet): [4]
𝑥 − 3𝑦 = 3
2𝑥 + 3𝑦 = 6
Also, find the area of the triangle formed by these two lines and the y-axis.

Question 10

(a) Each interior angle of a regular polygon is 135o. Find: [3]
(i) the measure of each exterior angle.
(ii) number of sides of the polygon.
(iii) name the polygon.

(b) If log4 = 0.6020, find the value of log80. [3]

(c) Evaluate 𝑥 and 𝑦 from the figure given: [4]

Question 11.

(a) ABC is an isosceles triangle such that AB = AC. D is a point on side AB such that [3]
BC = CD. Given BAC = 28o. Find the value of DCA.

(b) Prove that opposite angles of a parallelogram are equal. [3]

(c) The cross-section of a 6 m long piece of metal is shown in the figure. Calculate: [4]
(i) the area of the cross-section
(ii) The volume of the piece of metal in cubic centimetres.

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