Algebra (10)

Linear Inequations, Quadratic Equations, Ratio and Proportion, Factorisation of Polynomials, Matrices, Arithmetic and Geometric Progression, Co-ordinate Geometry

Solve the following inequation and represent the solution set on the number line
If $ A^2 = 3I $, where I is the identity matrix of order 2, find x and y
Using properties of proportion, solve for x. Given that x is positive
Solve the following Quadratic Equation: $x^2 - 7x + 3 = 0$
Use factor theorem to factorise $ 6x^3 + 17x^2 + 4x - 12 $
The 4th, 6th and the last term of a geometric progression
Find $ A^2 - 2AB + B^2 $
Find the value of p if the lines, 5x - 3y + 2 = 0
Using properties of proportion find x ∶ y, given
What must be added to the polynomial $ 2x^3 - 3x^2 - 8^x $
Prove that $ x^2 - 4ax + 1 = 0 $
If the 6th term of an A.P. is equal to four times its first term
Take 1 cm = 1 unit on both x and y axes
The difference of two natural numbers is 7 and their product is 450
A model of a high rise building is made to a scale of 1 : 50
Solve the following inequation and write down the solution set
Using the factor theorem, show that (x - 2) is a factor of
In an Arithmetic Progression (A.P.) the fourth and sixth terms
Simplify
M and N are two points on the X axis and Y axis respectively
The following numbers, K + 3, K + 2, 3K - 7 and 2K - 3 are in proportion. Find K
Solve for x the quadratic equation $ x^2 - 4x - 8 = 0 $
Take 1 cm = 1 unit along both x and y axis
The first and last term of a Geometrical Progression (G.P.) are 3 and 96 respectively
M is a matrix and I is unit matrix of order 2 x 2
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42
Using properties of proportion solve for x, given
Using the Remainder Theorem find the remainders obtained when
The product of two consecutive natural numbers
Find the value of x and y if
If (k –3), (2k + 1) and (4k + 3) are three consecutive terms of an A.P
If (𝑥 + 2) and (𝑥 + 3) are factors of $𝑥^3$ + 𝑎𝑥 + 𝑏, find the values of ‘a’ and ‘b’.
Solve the following inequation, write down the solution set
If the straight lines 3𝑥 − 5𝑦 = 7 and 4𝑥 + 𝑎𝑦 + 9 = 0 are perpendicular
If the straight lines 3𝑥 − 5𝑦 = 7 and 4𝑥 + 𝑎𝑦 + 9 = 0 are perpendicular to one another
Solve $𝑥^2 + 7𝑥 = 7$ and give your answer correct
The 4th term of a G.P. is 16 and the 7th term is 128
Use graph paper for this question (Take 2 cm = 1unit along both x and y axis)
$x^2 + 4kx + (k^2 -k + 2) = 0$
A (2, 5), B (–1, 2) and C (5, 8) are the vertices of a triangle ABC
₹7500 were divided equally among a certain number of children
Use Remainder theorem to factorize the following polynomial
If A = $ \begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix}, B = \begin{bmatrix} 0 & 4\\ -1 & 7 \end{bmatrix} $
The 4th term of an A.P. is 22 and 15th term is 66