Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Evaluate a decimal: either 0.1,0.2,0.3,0.4,0.01,0.02,0.03,0.04 squared or cubed. Part of HELM Book 1.2

Evaluate a simple fraction squared or cubed. Part of HELM Book 1.2

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

A chi-squared test for proportions. Would be  a difficult A-level question or a fairly simple university level. 

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Statistical notation including mean, standard deviation, probability, correlation coefficient, chi-square and others.

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Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Educational calculation tool rather than "question".

This allows the student to input a square matrix (max rows 5). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a "calculator". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.

It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.

It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.

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Calculating the square root of a complex number using De Moivre.

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. NC = Non Calculator. A diagram of a shape on a 5mm grid is shown, and students are asked the area in square centimetres. There are six different diagrams.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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Write the expression $ax^2+bx+c$ in completed square form $a(x+p)^2+k$.

Given vector $\boldsymbol{v}$  find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.

Given vector $\boldsymbol{v}$  find the norm. Since putting in square roots is tricky, actually input the square norm, so it's an integer.

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Ask for the squares of five randomly-chosen numbers between 0 and 15.

The shuffle function puts a list in random order.

Find a matrix whose associated linear map maps the unit square to the shown parallelogram. Match figures "of linear maps" with matrices.