(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.

Prove that in an isosceles triangle the altitude from the vertex will bisect the base.

In ΔABC, AB = AC. D is a point in the interior of the triangle such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ΔABC.

O is any point in the ΔABC such that the perpendicular drawn from O on AB and AC are equal. Prove that OA is the bisector of ∠BAC.

In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.

ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.

Prove that 
(i) BG = CH
(ii) AG = AH

In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.

Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.

PQRS is a quadrilateral and T and U are points on PS and RS respectively such that PQ = RQ, ∠PQT = ∠RQU and ∠TQS = ∠UQS. Prove that QT = QU.

In the given figure, AB = DB and AC = DC. Find the values of x and y.

The mark obtained by the students in a class test are given below: 
31, 12, 28, 45, 32, 16, 49, 12, 18, 26, 34, 39, 29, 28, 25, 46, 32, 13, 14, 26, 25, 34, 23, 23, 25, 45, 33, 22, 18, 37, 26, 19, 20, 30, 28, 38, 42, 21, 36, 19, 20, 40, 48, 15, 46, 26, 23, 33, 47, 40.

Arrange the above marks in classes each with a class size of 5 and answer the following:
(i) what is the highest score?
(ii) What is the lowest score?
(iii) What is the range?
(iv) If the pass mark is 20, how many students failed/
(v) How many students got 40 or more marks?

The runs scored by a cricket player in the last 30 innings are:

75, 125, 36, 89, 154, 56, 12, 28, 96, 142, 78, 54, 30, 88, 116, 104, 55, 84, 10, 29, 31, 08, 24, 136, 117, 22, 99, 80, 112, 35.

Arrange these scores in an ascending order and answer the following:

1. Find the highest score.
2. Find the number of centuries scored by him.
3. Find the number of times he scored over 50.
4. Find the number of times he failed to score a 50.

Construct a grouped frequency table from the following data of the daily wages earned by 60 labourers in a company. Take each class size as 7.

25, 26, 34, 48, 39, 16, 55, 28, 37, 42, 45, 55, 28, 54, 53, 18, 35, 47, 44, 28, 55, 45, 39, 54, 21, 49, 45, 38, 29, 53, 48, 44, 15, 28, 14, 32, 15, 44, 14, 15, 16, 41, 33, 52, 29, 34, 51, 22, 19, 37, 44, 25, 48, 38, 24, 52, 51, 42, 32, 27.

Construct a rectangle ABCD, when AD = 3.2cm and diagonal BD = 5.5cm. Measure CD.

Construct a rectangle ABCD, when AB = 5cm and BC = 6.2cm.

Construct a rectangle ABCD with one diagonal AC = 5.8cm and the acute angle between the diagonals is equal to 45°.

Construct a rectangle ABCD with perimeter 18cm and AB = 6cm.

Construct a rectangle ABCCD, AB = 6cm. ∠CAB = 30°.

Construct a rectangle PQRS, when its Area = 21 cm² and length = 4.2cm

Construct a rectangle PQRS, when its Area = 33.8cm² and breadth = 6.5cm