Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

The interesting part about the implementation is the way the output is generated for "Advice".

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

This exam includes the formulas students need to memorize for the SAT Math exam.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given a height (in cm) and weight (kg), then need to calculate the BMI given the formula (first converting height to m), then determine the weight range from the table. Weight and height are randomised.

Given th original formula the student enters the transformed formula

Given the original formula the student enters the transformed formula

Given the original formula the student enters the transformed formula

Given the original formula the student enters the transformed formula

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Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

Identify co-efficients, then use quadratic formula to find roots.

All set to be distinct and real. Some can be non-integer (0.5 steps)

Solve quadratic equations (non-simple case, two real, discrete integer roots) using the formula.

Solve quadratic equations (non-simple case, two real, discrete roots) using the formula. Some, random, non integer roots.

Substitute a given value into a formula, and substitute an expression in terms of $x$ into a formula.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Solving quadratic equations using a formula,

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

Substitute values into formulae for the area or volume of various geometric objects.

Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Not randomized because it's the same as in our workbook. But the variables are made in a way that it should be easy to randomise the size of the matrix, and the to change the formula for the input in not too many places.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

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