Evaluate pi / (2r+s) given values for r and s (r>0, s positive or negative)

evaluate sqrt(x/z) where x and z are random positive decimals.

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

Compute P = 3/(QR) given values for Q and R.

Calculate R = ap^2 for given positive values of a and p.

evaluate the function y=ax+b for given values of a,b and x, each of which may be positive or negative.

HELM Book 1.5.2 Task 1. This is a fixed question, asking you to rearrange an equation.

HELM Book 1.5.2 Task 2. This is a fixed question, asking you to rearrange an equation.

HELM Book 1.5.1: using formulae and substitution: task 1

Add two algebraic fractions with coprime denominators. Part of HELM Book 1.4.3.

HELM Book 1.4.3 Exercises: addition and subtraction of algebraic fractions

There are two parts: 

(3x)/4-x/5+x/3 and (3x/4)-(x/5+x/3).

The numbers are randomised to small, coprime, positive integers.

This is a fixed, unmarked, question:

Show that (x1)/((1/x3)-(1/x2))) = (x1x2x3)/(x2-x3)

Given 2 or 3 fractions such as A/(2x+5), add them.

There are 5 possible versions.

Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(rx+b)^2

x is a randomised variable. a,b,c,d,q,r are randomised integers.

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.

Simplify ax/b +/- cx/d, where x is a randomised variable, and a,b,c,d are randomised integers.

Add two algebraic fractions. Part of HELM Book 1.4.3.

6 Exercises from HELM Book 1.4 Part 2: Multiplication and Division of Algebraic Fractions.

Part of HELM Book 1.4.2

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html  CC-0

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.

Shows how to switch to the 3D graphics view of a geogebra applet using an extension function.

Given a graph of the form either a.cos(bx) or a.sin(bx), identify the amplitude and period.

Should not be used: this relies on a custom JavaScript which is not guaranteed to continue working.

Wrap the student's answer in set() so it's marked as a set.

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Drag points on an axis to plot a linear graph (integer gradient and intercept only)