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

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

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

student is to re-arrange the equations $pV=nRT$ and $mgh = \frac{1}{2}mv^2$

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Calculate the marginal and average cost for a given cost function. Find the corresponding startup/shutdown price.
Maximize the profit function at a given price.

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Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

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.

Multiply two numbers in standard form, then divide two numbers in standard form.

This question aims to test understanding and ability to use the laws of indices.

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

Interpreting the minitab output from a logistic regression model of salary against obesity as measured by BMI.

Adaptive marking is in place for Part b), with a small penalty for carry-forward errors from Part a).

Assessment of application of different model selection approaches in multiple regression.

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Find the moment of a couple formed by two equal and opposite forces.

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Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

Encuentra la ecuación de la línea recta que pasa por los puntos $ (a, b) $ y $ (c, d) $.

Crear una tabla de verdad para una expresión lógica de la forma :

                \[(a \ {op1} \ b) \ {op2} \ (c \ {op3} \ d) \ {op4}\ e \]

donde cada una de $a, \; b, \; c, \; d, \; e, \; f $ puede ser una de las variables booleanas \[ p, \; q, \; \neg q, \; \neg p, \]  y cada uno de los operados $\ {op} $  puede ser uno de los operadores $ \lor, \; \land, \; \to $.

Crear una tabla de verdad para una expresión lógica de la forma $ a \ {op} \ b $ donde $ a, \; b $ pueden ser las variables booleanas $ p, \; q, \; \neg p$  y  $\neg q $ y  $\ {op}$ puede ser uno de los operadores $ \lor, \; \land, \; \to $.

Por ejemplo $ \neg q \to \neg p $.

Expresar cada conjunto por extensión.

La derivada de $\displaystyle\frac{ax+b}{cx^2+dx+f}$ es $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$. Encontrar $g(x)$.