Students are given a diagram with 2 triangles. They are given 2 randomised lengths, and a randomised angle of depression.

They need to compute an angle by subtracting the angle of depression from 90°. Then they need to use the sine rule to calculate a second angle. Then they need to use the alternate angles on parallel lines theorem to work out a third angle. They use these to calculate a third angle, which they use in the right-angle triangle with the sine ratio to compute the third side. They then use the cos ratio to compute the length of the third side.

Student is given a triangle with the value of 2 sides and 1 or 2 angles and asked to find the value of the third side using the cosine rule. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Student is given a triangle with the value of 3 sides and asked to find the value of an angle. Triangle can be acute or obtuse.

Side and angle lengths are randomised. Units are randomised.

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x  \right) }+V $ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

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.

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. 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. The word problem is about the costs of sweets in a sweet shop. The quantity of each type of sweet is randomised.

This question was modified from a Newcastle University question.

Finding the cost including VAT

rebelmaths

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\cos(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\cos(\theta)-B\sin(\theta)$ to $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Rewriting a trigonometric expression of the form $A\sin(\theta)+B\cos(\theta)$ to $R\sin(\theta+\alpha)$ by calculating $R$ and $\alpha$.

Simplifying the trigonometric expression $\frac{\sin^2(x)}{1\pm \cos(x)}$ using the trigonometric identity $\sin^2(x)+\cos^2(x)=1$.

Calculating the integral of a function of the form $a \cos(bx)$ using a table of integrals.

Calculating the integral of a function of the form $\frac{\cos(x)}{\sin(x)+a}$ using integration by substitution.

Calculating the integral of a function of the form $\cos(x) \sin^2(x)$ using integration by substitution.

Calculating the integral of a function of the form $ax \cos(x^2+b)$ using integration by substitution.

Calculating the integral of a function of the form $\frac{\cos(x) \sin(x)}{(\sin(x)+a)^2}$ using integration by substitution.

Calculating the integral of a function of the form $e^{ax} \cos(x)$ using integration by parts.

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $(a+bx)\cos(x)$ using integration by parts.

Calculating the integral of a function of the form $ax \cos(bx)$ using integration by parts.

Calculating the area enclosed between a cosine function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Calculating the derivative of a function of the form $\frac{a\sin(x)}{bx+c \cos(x)}$ using the quotient rule.

Calculating the derivative of a function of the form $\ln(ax) \cos(bx)$ using the product rule.