Calculate a factorial, or the difference of two factorials, or a fraction of two factorials.

Used in HELM Book 5.1.1 Exercises

A BODMAS fraction question. Part of HELM Book 1.1.

Find reciprocals of (a) a proper fraction, (b) an improper fraction, (c) an integer

Rewrite the expression $\frac{c}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

Rewrite the expression $\frac{c}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{c}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{c}{(kx+a)(x+b)}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$.

Simplify (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.

Part of HELM Book 1.2

Use a calculator to evaluate a number to the power of a fractional index. Both the number (a positive integer) and the index (a rational) are randomised.

Part of HELM Book 1.2

Part of HELM Book 1.2

Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.

Part of HELM Book 1.2

Evaluate a simple fraction squared or cubed. Part of HELM Book 1.2

Divisor is single digit. There is a remainder which we express as a decimal by continuing the long division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

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

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

All of these can be done without a calculator.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

This question ensures that students understand that the fraction line means divide. There are 3 versions of the question, for denominators 10, 100 and 1000.

Students are shown one of four containers and asked to convert either one tenth, one hundredth or one thousandth of a litre to millilitres.

Students must match the decimals 0.1, 0.01 and 0.001 to their fraction equivalents. The order in which they appear is randomised but it is always the same three decimals.

Students have to match four receptacles of varying sizes with the following fractions of a litre: 1 whole, 1/10, 1/100 and 1/1000.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

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

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Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given the number of pages read (randomised) and number of pages remaining (randomised), and asked to write the proportion read as a simple fraction.

Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

Find the remainder when dividing two polynomials, by algebraic long division.

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

7 questions on numeric fractions.