An object moves in a straight line, acceleration given by:

$\displaystyle f(t)=\frac{a}{(1+bt)^n}$. The object starts from rest. Find its maximum speed. 

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

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 $q(x)=0$.

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

Identify well-known fractional equivalents of decimals. Convert obscure decimals and recurring decimals into fractions.

Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.

Given five fractions, identify the odd fraction out. The denominators are mainly two or three digits long.

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

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Several problems involving the multiplication of fractions, with increasingly difficult examples, including a mixed fraction and a squared fraction. The final part is a word problem. 

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

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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.

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.

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Addition, multiplication and division of fractions.

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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.

This is a homework assignment. Students may complete this assignment during a maths lesson with the support from the teacher. 

• Passing mark 60%
• Difficulty level 3 Moderat/Average (C+, B-, B Level).

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

Simplify fractions involving the products of factorials.

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them).