Solve a quadratic equation by completing the square. The roots are not pretty!

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Find $\displaystyle\int \frac{a}{(x+b)(x+c)}\;dx,\;b \neq c $.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Finding the stationary points of a rational function with specific features.

Finding the stationary points of a cubic with two turning points

Curl of a vector field.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

This question tests the student's ability to find remainders using the remainder theorem. 

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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Find the first three terms in the binomial series expansion having a non-Natural exponent

Find the first 3 terms of Binomial series having a Natural exponent

Find the binomial expansion of the following:

$X$ is a continuous uniform random variable defined on $[a,\;b]$. Find the PDF and CDF of $X$ and find  $P(X \ge c)$.

Find the sum of the first n terms of a Geometric progression

Find the sum of the first n terms of a Geometric progression

Find the nth term of a Geometric progression

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Find the sum of the first n terms of an arithmetic progression

Find the nth term of an Arithmetic progression