Model Test Paper മാതൃകാ ചോദ്യപേപ്പർ
A full paper in the Kerala pattern. Work on paper, with a timer, before you look at the solutions.
Standard IX · Mathematics
Chapter 10 · ബഹുപദങ്ങൾ · Polynomials
Instructions: Answer all questions. Show your working. Draw diagrams where they help; write every polynomial with the highest power first. Marks for each question are shown on the right.
SECTION A8 × 1 = 8 marks
1.
The degree of the polynomial 5x3 − 2x + 7 is .
(1)2.
If p(x) = 3x + 4, then p(2) = .
(1)3.
Which of these is a polynomial?
(1)(a) x + 1/x(b) √x + 2(c) x2 + √3 x(d) 2/x
4.
The coefficient of x2 in 4x3 − 7x2 + x − 9 is .
(1)5.
For any polynomial p(x), p(0) equals .
(1)6.
A square has side x + 1. Its perimeter, written as a polynomial, is .
(1)7.
(x + 2)(x + 3) = .
(1)8.
The general form of a second degree polynomial is .
(1)SECTION B5 × 2 = 10 marks
9.
p(x) = 2x2 − 3x + 1. Find p(0), p(1), p(−1) and p(2).
(2)10.
A rectangle has sides 4 cm and 6 cm. Every side is increased by x cm. Write the perimeter p(x) of the new rectangle and find p(2½).
(2)11.
Squares of side x cm are drawn. Is each relation a polynomial? Give the reason. (i) The side and the length of the diagonal. (ii) The side and the area of the square drawn on the diagonal.
(2)12.
Show that (x + √x)(x − √x) is a polynomial, and find its degree.
(2)13.
p(x) = x3 + 2x2 + 5x + 3. Find p(1) and p(10). What pattern do you see?
(2)SECTION C4 × 3 = 12 marks
14.
A rectangle has sides 5 cm and 3 cm. Every side is increased by x cm. (i) Write the area a(x) of the new rectangle as a polynomial. (ii) Find a(1) and a(2). (iii) Draw the area model.
(3)15.
Rectangles are made with a loop of string 60 cm long. One side is x cm. (i) Write the area a(x). (ii) Show that a(10) = a(20) and explain why. (iii) When do two different values of x give the same area?
(3)16.
For p(x) = ax3 + bx2 + cx + d find p(0), p(1) and p(−1). Use them to find p(0), p(1), p(−1) for p(x) = 2x3 − x2 + 4x − 5.
(3)17.
Which of these are polynomials? Give reasons. (i) 3x2 − √5 x + ½ (ii) x2 + 2/x (iii) √(x2 + 1) (iv) (√x + 1)2
(3)SECTION D2 × 5 = 10 marks
18.
From a card 12 cm long and 8 cm wide, squares of side x cm are cut from the four corners and the sides are folded up to make an open box. (i) Write the length, width and height of the box. (ii) Write its volume v(x) as a polynomial. (iii) What is its degree? (iv) Find v(1) and v(2). (v) Which values can x take?
(5)19.
A rectangular block has edges 1 cm, 2 cm and 3 cm. Every edge is increased by x cm. (i) Find the volume v(x) by multiplying out. (ii) Find v(1) in two ways. (iii) Write the total surface area s(x) as a polynomial. (iv) Find s(1).
(5)