4 questions on integrating by parts.

Three items of work done on a car. Given total price, and a couple of ratios of prices between pairs of items, work out the cost of one of the items.

Based on question 4 from section 3 of the Maths-Aid workbook on numerical reasoning.

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.

Based on section 3 of the maths-aid/mathcentre workbook on numerical reasoning.

Questions about percentage and ratio, applied to finance.

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

4 questions testing the precedence of operations applied to integers. In other words testing BIDMAS: Brackets, Indices, Division/Multiplication and Addition/Subtraction.

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5 questions on using substitution to find indefinite integrals.

4 questions on integrating by parts.

4 questions on using partial fractions to solve indefinite integrals.

Instructions on inputting ratios of algebraic expressions.

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

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

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Step by step solving for integration by substitution

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Three items of work done on a car. Given total price, and a couple of ratios of prices between pairs of items, work out the cost of one of the items.

Based on question 4 from section 3 of the Maths-Aid workbook on numerical reasoning.

Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$. 

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Given that $\displaystyle \int^i_j x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $