Given a point and a line, determine the distance between them.

Calculate the moment of a force.  Must calculate perpendicular distance based on simple geometry, and recognize direction.

Pulley supported by a cable, so the tension in the rope is constant.    Advice is a youtube video showing how to solve the problem.

Using the unit circle definition of sin, cos and tan, to calculate the exact value of trig functions evaluated at angles that depend on 0, 30, 45, 60 or 90 degrees.

Homework set.  Calculate Moment of Inertia for I beams, channels, angles, etc.

Determine the resultant of three random 2-D vectors.  

Find the magnitude and direction of a force given its scalar components.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Student must calculate distance swum in km given number of laps of 50m pool, days of week and weeks in term. These variables are randomly selected.

Taken from question 37 of the book Problem Solving in GCSE Mathematics by Daniel Griller.

Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.

A Eukleides diagram shows the setup visually.

Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .

Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .

Find the number of people with heights greater then mean plus two times the standard deviation.

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Tests understanding of scatter plots and related concepts.

Calculations involving Standard form.

Convert numbers between 0 and 1 intro standard form/scientific notation.

Convert numbers greater than 1 into standard form/scientific notation.

State the Upper and lower bound of a distance that has been rounded to either the nearest 10 or 100 miles.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Identify the truth value of an inequality (T/F) between two numbers

Find the diagonal or one side of a rectangle using Pythagoras' theorem.

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

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Match the relevant graph (sin, cos, tan) with its equation. 

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Calculate the centroidal moment of intertia of a rectangle with a excentric rectangular hole.

Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or y-axis.  Parallel axis theorem is often required.