5 questions on using substitution to find indefinite integrals.

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

Practice dividing polynomials using the long division method.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

Practice using the log rules to add and subtract logarithms

Example of displaying a randomly chosen image.

Introductory exercise about subsets using custom grading code.

Introductory exercise about subsets using custom grading code.

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.

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.

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.

Using e to solve equations involving the natural log

Practice using the log rules to add and subtract logarithms

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A (quadratic) function is skethed sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

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. 

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Solving arithmetic progressions using simultaneous equations

Solving arithmetic progressions using simultaneous equations

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

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