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.

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Indices

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Multiplication of $2 \times 2$ matrices.

Elementary Exercises in multiplying matrices. 

Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

(Last three parts of original question removed.)

This question aims to test understanding and ability to use the laws of indices.

Integration by Substitution

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15 questions based on module so far. 

Simplifying indices.

Simplifying indices.

Simplifying indices.

Using e to solve equations involving the natural log

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

Finding the stationary points of a cubic with two turning points

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Practice using the log rules to add and subtract logarithms

LSD and Tukey yardsticks on three treatments. Also one-way Anova test on same set of data.

Expand $(ax+b)(cx+d)$.

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Expansion of two brackets

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Substitute values into formulae for the area or volume of various geometric objects.

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Curl of a vector field.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.