Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution. Use the letter C for the constant.

Integration by susbtitution, no hint given

Integration by susbtitution

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

A basic introduction to differentiation

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Independent events in probability. Choose whether given three given pairs of events are independent or not.

Ferrous Metals

I created this question, and every other question in Multiple Integration, for my dissertation `Computer-Aided Assessment of Multiple Integration'.

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Substitute given values into formulas.

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Integration techniques for monomials and simple polynomials.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

Students enter equation and turning point

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.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Match up equations with the corresponding lines on a graph.

Match up equations with the corresponding lines on a graph.

A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.