Practice rationalising a binomial denominator which contains surds.

Adapted from 'Surds 3' by Joshua Boddy.

Practice rationalising a single-term, surd denominator.

Adapted from 'Surds 2' by Joshua Boddy.

Add, subtract, multiply and divide numerical fractions.

Add, subtract, multiply and divide numerical fractions.

Adapted from 'Algebraic fractions: operations involving algebraic fractions' by Ben Brawn.

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This exercise will help you do advanced mathematical operations using fractions.

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.

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Ratio of sides of rectangles

Ratios used in alloys and mixing paints

Split winnings in a ratio

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Single example with detailed solution for rationalising a binomial denominator which contains surds.

Adapted from 'Surds: rationalising the denominator conjugate' by Ben Brawn.

Simple example with detailed solution for rationalising a single-term, surd denominator.

Adapted from 'Surds: rationalising the denominator simple' by Ben Brawn.

This test will help you with addition, subtraction, multiplication and division of decimals.

Two particles connected by a string which passes over a pulley at the top of an inclined plane. Find the acceleration of the masses and the tension in the string. Can not model the whole system as a single particle.

A box is being pushed up a slope by a horizontal force. Calculate the normal reaction force, and the acceleration of the box up the slope.

Finding the acceleration of a particle on an inclined plane which is at an angle to the horizontal. Smooth then with value for coefficient of friction.

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Instructions on inputting ratios of algebraic expressions. Could link to calculator input.

Ball projected vertically within water of a swimming pool. Finding the acceleration, greatest height above the swimming pool floor reached, speed and time. Uses SUVAT equations and $F=ma$.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Instructions on inputting ratios of algebraic expressions.

Instructions on inputting ratios of algebraic expressions.

Question 5 of CBA1;  Testing vector operations.

Adding several rational functions.

Order of operations

This is a set of questions designed to help you praction adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator