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9math PW

This document contains a mathematics practice worksheet for 9th standard students. It includes 14 problems related to topics like geometry, trigonometry, factorization, and speed-time-distance calculations. The problems involve finding lengths, areas, radii, and costs using information given in various shapes like triangles, circles, and fields.

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623 views2 pages

9math PW

This document contains a mathematics practice worksheet for 9th standard students. It includes 14 problems related to topics like geometry, trigonometry, factorization, and speed-time-distance calculations. The problems involve finding lengths, areas, radii, and costs using information given in various shapes like triangles, circles, and fields.

Uploaded by

Desert Eagle
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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SRI SRI RAVISHANKAR VIDYA MANDIR, MULUND

FIRST TERM (2022 – 23)


MATHEMATICS PRACTICE WORKSHEET
STD.: IX DATE: 30.04.22
DATE OF SUBMISSION :08.06.22

1. A car travels 1 km distance in which each wheel makes 450 complete


revolutions. Find the radius of its wheels.

2. The base of a triangular field is three times its altitude. If the cost of sowing the
field at ₹ 58 per hectare is ₹ 783, find its base and height.

3. Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length.
Hence, find the height corresponding to the longest side.

4. The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 :
12. Find the area of the triangle. Also, find the cost of ploughing the field at ₹
18.80 per 10 m2.

5. Simplify:

i.

ii.

6. The area between two concentric circles is 770 sq.cm.


If the radius of the outer circle is 21 cm,
find the radius of the inner circle.

7. The wheel of a car is making 5 revolutions per second. If the diameter of the wheel
is 84 cm, find its speed in km/hr. Give your answer correct to nearest km.

8. The outer circumference of a circular race track is 528 m. The track is everywhere
14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per
square meter.

9. Show that :
10. In the adjoining figure, ∠𝐴𝑂𝐵 = 90°, 𝐴𝐶 = 𝐵𝐶 = 𝑂𝐶 = 6.5 𝑐𝑚.

Find the area of ∆ AOB.

11. Factorize:
i. 27a3b3 − 45a4b2
ii. 2a(x + y) − 3b(x + y)
iii. 2x(p2 + q2) + 4y(p2 + q2)
iv. x(a − 5) + y(5 − a)

v. 8(3a − 2b)2 − 10(3a − 2b)

vi. x3 + 2x2 + 5x + 10

vii. 27a3 + 64b3

viii. 16x4 + 54x

12. In the adjoining figure, PS = QR,


∠SPQ = ∠RQP. Prove that
i. ∆ PQS ≅ ∆ QPR
ii. PR = QS

13. In the adjoining figure, ∆ ABD and ∆ CBD are


Isosceles triangles on the same base BD.
Prove that ∠ABC = ∠ABD.

14. In right triangle ABC, right-angled at C,


M is the mid-point of hypotenuse AB.
1
C is joined to M and produced to a point D such that DM = 2CM.
Point D is joined to point B (see fig.).Show that : (i) ∆AMC ≅ ∆BMD (ii) ∠DBC =
1
90° (ii) ∆DBC ≅ ∆ACB (iv) CM = 2 AB

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