Represent a given probability to a decimal, fraction or percentage.

Inputting ratios of algebraic expressions.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

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Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

Basic Percentages Question

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Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Represent a given probability to a decimal, fraction or percentage.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

Simplifying indices.

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.

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.

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find negative powers of the complex numbers.

Manipulation of algebraic fractions

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Integrate various functions by rewriting them as partial fractions.

Find the integral of an improper fraction.

4 questions on using partial fractions to solve indefinite integrals.

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Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$. Enter the constant of integration as $C$.