5 indefinite integrals containing exponential functions

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Instructions on inputting ratios of algebraic expressions.

rebelmaths

This question tests to see if students can recognise a geometric series and based on its common ratio determine if it is convergent or divergent.

Test whether a student knows the ratio test of a series, and how to use it. Series include those that the ratio test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Writing ratios in the form n:1 or 1:n

Scaling up ratios.

Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

Identifying equivalent ratios

Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.

Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.

Questions about writing simple ratios from raw amounts.

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Ratio Questions

Integration by susbtitution, no hint given

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

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

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

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

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

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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Add, subtract, multiply and divide numerical fractions.

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

Ratio Questions

Rationalising Denominator (complex)

Rationalising the Denominator (Simple)

In this question the student will be asked to manipulate surds and rationalise the denominator of a fraction when it is a surd.

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

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