Mathematics IX - First Term Practice Paper

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