REVISION FOR SECOND TERM MATHEMATICS (CLASS IX)

REVISION FOR SECOND TERM MATHEMATICS (CLASS IX)

Q 1: Classify the following as linear, quadratic and cubic polynomial :x2 + x

a) cubic b) quadratic c) linear

Q 2: Line segment joining the centre to any point on the circle is a radius of the circle.

a) True b) False

Q 3: Of all the line-segments that can be drawn from a point to a line not containing it, the perpendicular line-segment is the shortest.

a) True b) False

Q 4: Given statement is true or false? Give reason : Every natural number is a whole number.

a) True b) False

Q 5: The triangle formed by joining the mid-point of the sides of an isosceles triangle is ______

a) an isosceles triangle b) obtuse triangle

Q 6: Find : 321/5

Q 7: Find the value of the polynomial 5x – 4x2 + 3 at x = 0

Q 8: Use the factor theorem to determine whether g(x) is a factor of p(x) in the following cases : p(x) = 2x3 + x2 - 2x - 1, g(x) = x + 1

Q 9: AD is the bisector of ∠A of ABC, where D lies on BC. Prove that AB > BD and AC > CD. Q 10: Find the mean and median of first ten prime numbers . <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 11: The class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102 Determine the class size, the class limits and the true class limits. Q 12: Write four solutions for the following equation : x = 4y <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 13: Find the value of the following equation for x = l, y = l as a solution. ax – 2y = 10 Q 14: Factorise : 3x2 - x - 4 Q 15: Is (x + 1) is a factor of given polynomial ? x4 + 3x3 + 3x2 + x + 1 Q 16: Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x. Q 17: Evaluate the following product without multiplying directly : 104 × 96 Q 18: Given two points A and B and a positive real number k. Find the locus of a point P such that ar( PAB) = k. Q 19: A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs. 50 per metre, the sheet being 2 m wide. Q 20: A room is 5 m long, 3.5 m wide and 3 m high. Find the cost of cementing the inner portion of the walls at Rs. 20 per square metre. Q 21: The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Q 22:Prove that diagonals of a parallelogram divides it into four congurent triangles. <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 23: A powder tin has a square base with side 8 cm and height 13 cm. Another is cylindrical with the radius of its base 7 cm and its height 15 cm. Find the difference in their capacities. Q 24: A conical pit of top diameter 3.5 cm is 12 m deep. What is its capacity in kilolitres ? Q 25: Two chords PQ and RS of a circle are parallel to each other and AB is the perpendicular bisector of PQ. Without using any construction, prove that AB bisects RS. Q 26: In the following figure, D, E and F are respectively the mid-points of sides BC, CA and AB of an equilateral triangle ABC. Prove that DEF is also an equilateral triangle. Q 27: The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of leveling at the rate of Rs. 25 per square metre. Q 28: The diameter of the base of a right circular cylinder is 28 cm and its height is 21 cm. Find its (i) curved surface area (ii) total surface area and volume. Q 29: If the radius of a sphere is halved then what is the decrease in its surface area ? Q 30: An exterior angle of a triangle is 115o and one of the opposite angles is 35o. Find the other two angles. Q 31: Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any common such solution? 3x + 2y = 6 and 5x + 2y = 10 Q 32: Factorise : x3 + 13x2 + 32x + 20 Q 33: Given below are the seats won by different political parties in the polling outcome of a state assembly elections: <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Political party A B C D E F Seats won 75 55 37 29 10 37 (i) Draw a bar graph to represent the polling results. (ii) Which political party won the maximum number of seats? <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 34: Give the geometric representation of 2x + 9 = 0 as an equation in one variable.  Q 35: If the work done by a body on application of a constant force is directly proportional to the distance traveled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance traveled by the body is 2 units.