Substitute given values into formulas.

This exercise will help you solve equations of type ax-b = c.

Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.

Small, simple question.

Formative assessment to introduce the concepts of modular arithmetic.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Pythagoras' Theorem and naming sides of right angled triangle

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Draws a triangle based on 3 side lengths.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Draws a triangle based on 3 side lengths.

multiple choice testing sin, cos, tan of  random(30, 45, 60) degrees

Solving quadratic equations using a formula,

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.

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.

Evaluating a function

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

Find the equation of a straight line which has a given gradient $m$ and passes through the given point $(a,b)$.

Practice Questions for Nursing tests

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

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Find the solution of a first order separable differential equation of the form $(a+y)y'=b+x$.

Find the solution of a first order separable differential equation of the form $(a+x)y'=b+y$.

Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.

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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Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

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.

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

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.