A mass is resting on a rough plane. Given the angle of the plane and the mass of the object, find the normal reaction force and hence the coefficient of friction.

Simple Percentages

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Calculating rates and scaling rates.

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Converting a decimal number to binary.

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Converting a number from binary to decimal.

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Inverse Laplace transform if trig functions.

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Laplace transform of e^{at}

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Find the exVAT price

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Given the cost and profit, find the selling price

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Basic Percentages Question

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Gross wage, tax

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Expansion of two brackets

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Multiplying and dividing decimals

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Arithmetic

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

Indices

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Indices in their simplest form

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Indices in their simples form

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Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.

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Finding areas under graphs using definite integration.

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Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$. Solution involves inverse trigonometric functions.

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Summation Notation

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Solve for x and y on a given triangle and calculate the area

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Pythagoras' Theorem and naming sides of right angled triangle

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Cos, Sin and Tan

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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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