Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Expanding two linear brackets multiplied together.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

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 a quadratic equation of the form $x^2+bx+c$ with one positive and one negative root.

Factorise a quadratic equation of the form $x^2+bx+c$ with one positive and one negative root.

Factorise a quadratic equation of the form $x^2+bx+c$ with two positive roots

Factorise a quadratic equations of the form $x^2+bx+c$ with 2 negative roots.

Given a number evaluate simple power, negative power, to one half.

Harder inequalities that involve terms like $\frac{1}{x}$ where multiplication by the denominator requires you to split into cases for positive or negative, or you multiply by the square of the denominator.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

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.

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

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

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Question asks student to find zeros of a quadratic equation - disguised as finding time for particle to reach a given position. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance. Coefficients of the quadratic are randomly chosen within linits which give one positive and one negative root.

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

 Question asks student to find zeros of a quadratic equation. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.

Given one of ax^2, ax^3, a/x (where a is a positive integer), calculate f(x+h) and f(x+h)-f(x) 

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.

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.

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.

Calculating the angle between a vector and the positive $x$-axis.