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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Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

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Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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indefinite integration

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

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rebelmaths

Instructions on inputting ratios of algebraic expressions.

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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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rebelmaths

Ratio Questions

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rebelmaths

Split winnings in a ratio

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rebelmaths

Ratio of sides of rectangles

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rebelmaths

Understanding order of operations on a calculator and using power and root keys.

Given amounts of ingredients for n cakes, given list of ingredients for m.

Find the area of a triangle where all three coordinates of the vertices are given.

Calculation of area & circumference of circle, given its radiua.

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

Instructions on inputting ratios of algebraic expressions.

Instructions on inputting ratios of algebraic expressions.

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Add, subtract, multiply and divide numerical fractions.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

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.

Scale a page to some percentage of its original size, then increase/decrease by another percentage. Find the size of the final copy as a percentage of the original.

Based on question 2 from section 3 of the Maths-Aid workbook on numerical reasoning.

Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

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

Instructions on inputting ratios of algebraic expressions.

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Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.