Evaluate J = (1/2)Ma^2 for random values of M and a.

convert a random length in m to centimetres

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

Multiplication algorithm with integers

Multiplication algorithm with integers

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.

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.

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

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

Examples of the following custom part types: Yes/no, List of numbers, Give a numerical input for an expression, Number entry modulo.

This question shows a JSXGraph diagram above a mathematical expression input, containing a plot of the expression the student enters.

Directional derivative of a scalar field.

Basic fraction arithmetic, giving answers in lowest form.

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.