Quotient and remainder, polynomial division.

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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

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 $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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

Add, subtract, multiply and divide algebraic fractions.

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.

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

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

More work on differentiation with trigonometric functions

Chain rule

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

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.

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