This question allows you to practice working out a fraction of an amount.

It is designed for you to complete without a calculator.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide numerical fractions.

Pratice of dividing by a fraction.

Practice of adding fractions.

Cancelling to reduce a fraction to its lowest terms.

Practice of multiplying fractions (without a calculator).

Subtracting fractions.

Finding the numerators & denominators of 4 equivalent fractions.

Converting a fraction to a percentage by cancelling (without a calculator).

8/9/15

Practice of cancelling a fraction, where the denominator will reduce to either 5,10, 20, 25, or 50 and then multiplying numerator and denominator by either 20, 10, 5, 4 or 2 respectively, to represent the fraction as a percentage.  A helpful strategy in the QTS test...

Tweaked the variables to avoid duplicate fractions in the 2 parts & make the second slightly more tricky, on average.  Used the Testing facility to prevent 100 or 200 appearing in the denominators.

Integrate various functions by rewriting them as partial fractions.

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min? 

 Basics, percentage of an amount, converting to fractions and decimals.

Add, subtract, multiply and divide numerical fractions.

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

7 questions on numeric fractions.

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4 questions on using partial fractions to solve indefinite integrals.

13 questions on combining algebraic fractions. An area in which students often need practice. 

Customised for the Numbas demo exam

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.

Simplify fractions involving the products of factorials.

More work with dividing and multiplying algebraic fractions

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Practice with fractions

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Split $\displaystyle \frac{b}{(cx + d)(px+q)}$ into partial fractions.