Solving questions using $F=ma$ and $W=mg$.

This quiz is designed to help you practise your integration techniques.

6 questions on numerical reasoning using percentages and ratios.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

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Find $\displaystyle I=\int \frac{2 a x +b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

Finding areas under graphs using definite integration.

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Integration by Substitution

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Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

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Ratio Questions

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

Simple Linear Equations involving Basic Transposition

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Calculating rates and scaling rates.

Order of precedence for multiplication, division, addition, subtraction.

Finding areas under graphs using definite integration.

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Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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Add, subtract, multiply and divide numerical fractions.

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

Practice rationalising a binomial denominator which contains surds.

Adapted from 'Surds 3' by Joshua Boddy.

indefinite integration

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

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Instructions on inputting ratios of algebraic expressions.

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Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Circumference and area of a circle

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Ratio, working hours

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Ratios used in alloys and mixing paints

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Ratio Questions

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