Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

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For practising how to recognise paired data as the first step to identify a suitable statistical analysis (such as the paired t-test or Wilcoxon test).

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, changes in position, distances are to be calculated.

Use the specific heat capacity of an object and the change in temperature to calculate the heat added to that object.

Uses Custom marking to allow partial credit for common student errors (mal rules).

Thermochemistry Revision Sheet Q 5

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$

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

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

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

More work on differentiation with trigonometric functions

Chain rule

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

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Using BIDMAS rules to solve equations

Simplifying equations/collecting like terms

Rearranging equations/making x the subject

Solving equations for x

Writing equations

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Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

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Integration by susbtitution. Use the letter C for the constant.

Calculate the local extrema of a function ${f(x) = e^{x/C1}(C2sin(x)-C3cos(x))}$

The graph of f(x) has to be identified.

The first derivative of f(x) has to be calculated. 

The min max points have to be identified using the graph and/or calculated using the first derivative method.  Requires solving trigonometric equation

Given mass and volume of an object in SI units, calculate its density. The units are given at different orders of magnitude.