Mathematics IX - First Term Practice Paper

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Questions and Answers

What is the total cost of two pencils if a pen and two pencils cost 17 rupees and a pen and a pencil cost 13 rupees?

8 rupees (correct)

6 rupees

5 rupees

4 rupees

If the perimeter of a square is 4 centimeters, what is the length of one side of the square?

1 centimer (correct)

4 centimeters

3 centimeters

2 centimeters

In an equilateral triangle, if the perpendicular distance from a vertex to the opposite side is 4 centimeters, what would be the side length of the triangle?

5.76 centimeters

6.93 centimeters (correct)

4 centimeters

8 centimeters

When counting 5-rupee and 10-rupee coins that total 80 rupees, what is a possible incorrect total that could have been calculated?

70 rupees (C) Signup and view all the answers

What is the expansion of the expression $(x + y)^2$?

$x^2 + 2xy + y^2$ (D) Signup and view all the answers

If a point divides the median of a triangle in the ratio 2:3, what is the special name of this point?

Centroid (C) Signup and view all the answers

What would be the area of an equilateral triangle with a side length of 6 cm?

12√3 cm² (D) Signup and view all the answers

What is the length of the diagonal of a square with a side length of 1 centimeter?

√2 cm (B) Signup and view all the answers

What is the total amount when counted correctly?

70 rupees (C) Signup and view all the answers

When the sum of two odd numbers is equal to which of the following values?

Even number (C) Signup and view all the answers

If three squares with areas of 9 cm², 16 cm², and 25 cm² are joined to form a triangle, what are the lengths of the sides?

3 cm, 4 cm, 5 cm (A) Signup and view all the answers

If the perimeter of an equilateral triangle is 6 centimeters, what is the length of each side?

2 cm (B) Signup and view all the answers

The two-digit number has digits that sum to 7 and becomes 27 more when reversed. What is the correct equation representing this?

10y + x = 10x + y + 27 (A), x + y = 7 (B) Signup and view all the answers

What would be the result of the product of two natural numbers if their sum is 15?

45 (B) Signup and view all the answers

If 'x' and 'y' are consecutive natural numbers, what is the difference between them?

1 (C) Signup and view all the answers

If the lengths of the diagonals of a parallelogram intersect at point O, what can be inferred about triangles AOB and COD formed at the intersection?

They are congruent (A) Signup and view all the answers

What is the relationship between speed and time for an object moving in a straight line with an initial speed?

Speed increases at a constant rate over time. (D) Signup and view all the answers

In a triangle, if a point is the midpoint of a side, how does it relate to the opposite vertex?

It divides the triangle into two equal areas. (A) Signup and view all the answers

What will be the area of a square if the length of one side is given as $5$ meters?

$25$ m² (D) Signup and view all the answers

If the perimeter of a regular hexagon is $30$ cm, what is the length of one side?

$5$ cm (B) Signup and view all the answers

What is the relationship between the diagonals of a square?

They are equal and bisect each other at $90$ degrees. (A) Signup and view all the answers

What is the Pythagorean theorem used for in right triangles?

To relate the lengths of the sides to the hypotenuse. (C) Signup and view all the answers

In a triangle with midpoints on two sides, how would one express the sides in relation to a given measurement?

The lengths are half of the original triangle's sides. (B) Signup and view all the answers

What is the calculated value of the hypotenuse if one side of a right triangle is $3$ cm and the other side is $4$ cm?

$5$ cm (A) Signup and view all the answers

Study Notes

Mathematics IX - First Term Sample Practice Paper

Time: 2 hours and 30 minutes
Score: 80
Instructions: Answer any 3 questions for 2 marks each. Answer any 4 questions for 3 marks each. Answer any 8 questions for 4 marks each. Answer any 6 questions for 5 marks each.

Question 1

Cost of pen and two pencils: 17 rupees
Cost of pen and one pencil: 13 rupees
Find: Cost of one pencil and cost of one pen

Question 2

Perimeter of square: 4 cm
Find: Length of side and length of diagonal

Question 3

P divides AB in the ratio 1:2
BC and PD are parallel lines
Find: AD:CD and AC if AD = 5 cm

Question 4

Integers x and y are related as: 𝑥 + 𝑦 = 12 and 𝑥𝑦 = 11
Find: Expansion of (x + 1)(y + 1) and the actual value of (x + 1)(y + 1)

Question 5

Three equations: 𝑥 + 𝑦 = 7, 𝑦 + 𝑧 = 4, 𝑥 + 𝑧 = 3
Find: 𝑥 + 𝑦 + 𝑧 and 𝑥, 𝑦, and 𝑧

Question 6

Perpendicular distance of equilateral triangle: √3 cm.
Find: length of its side and the area of the triangle.

Question 7

Point G divides the median AD in the ratio 2:1
Line PQ is parallel to BC
Find: G's special name in the triangle, AP : PB, and AQ if AC = 21 cm

Question 8

Expansion of (x + y)(u + v)
Express (x + 3)(y + 4) as a sum of four terms

Question 9

x and y are small angles of a right-angled triangle
Find: x + y and individual values of x and y if xy = 10

Question 10

Draw an equilateral triangle with a perimeter of 11 cm.

Question 11

Pattern: 0.111..., 1/9 , 2/19, 0.222... , 3/29, 0.333,...
Find: Next line and decimal form of 0.444... in fraction form

Question 12

Coin counting with 5-rupee and 10-rupee coins
Number of coins and total amount
Find: The number of coins of each denomination.

Question 13

Sum and Product of two odd numbers
Find: Expansion of (x + 2)(y + 2) and value of (x + 2)(y + 2) if x and y are odd numbers with a sum of 24 and product of 143.

Question 14

Parallelogram ABCD
Midpoints: M of AB, N of CD.
Is the shaded part a parallelogram? Why?
Prove: AP = PQ = QC if PQ = 4 cm, find AC

Question 15

Sides of a triangle
Find and calculate the approximate and perimeter of the triangle using the given values.

Question 16

Consecutive natural numbers (a, b, c, d): if a = x
Express: b, c, and d in terms of x
Find: The difference between bc and ad, if be = 72

Question 17

Parallelogram ABCD and intersection at O: OD = x + y, OC = x + 3y
Find: x, y, and the diagonals

Question 18

Square on equilateral triangle altitude:
Perimeter of triangle is 6 cm.
Find: sides of triangle, area of square, altitude of triangle

Question 19

Isosceles triangle with a perimeter of 13 cm: The equal sides are 1/2 the length of the shortest side.

Question 20

Pattern: 1² + 1² = 2 , 2² + 1² = 5
Write 11 as the difference of two perfect squares
If N = a² – b² where a and b are consecutive natural numbers and N is odd, what is 𝑎 ₊ 𝑏

Question 21

Two-digit number: The sum of the digits is 7. The new number formed by reversing the digits is 27 more than the original number.
Find: Equations and the original number

Question 22

Product and sum of two natural numbers : Product is 70, sum is 17.
Find: Expanding (x -1)(y – 1) where (x > y)
Calculate (𝑥 - 1)(𝑦 -1)

Question 23

Object's increasing speed Initial speed 'u' , acceleration '𝑎'
Using given data (speed v at t=6s and v at t=10s), calculate u and a
Find: speed after 12 seconds

Question 24

Midpoints in triangles ABC and BOC: P is midpoint of AB, Q is midpoint of AC, R is midpoint of OC, S is midpoint of OB
Find: PQ, SR, PS, QR, suggest a name for PQRS

Question 25

Rectangles with equal areas: Equations and calculations for x and y, and sides of middle rectangle

Question 26

Right triangles in a figure: hypotenuse of first triangle, sides of second triangle, perpendicular sides of 10th triangle, area of square on hypotenuse of 10th triangle

Question 27

Regular hexagon with perimeter of 20 cm.

Question 28

Square with removed right triangle
Find: Hypotenuse, diagonal, perimeter.

Question 29

Pythagorean triplets for 4n, 4n² – 1, 4n² + 1 for n = 1,2,3....
Find: Triples for n = 1, smallest side of right triangle with hypotenuse 17, largest number if middle number in triplets is 399

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Description

Test your understanding of key mathematical concepts with this First Term Sample Practice Paper for Mathematics IX. This quiz includes various problems related to cost, geometry, ratios, and equations, designed to enhance your problem-solving skills.