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• Question
This is a new and easy way for solving quadratic equation. It is based on the property that the roots are equidistant from the average.
• Question

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

• Question

A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

• Question

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

• Question

Some quadratics are to be solved by factorising

• Question

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

• Question

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

• Question

A quadratic function is given. The graph of the function is drawn with three coordinates on the graph, without any x or y ticks.  The $x$ coordinate is given for a couple and $y$ coordinate given for the third, and coordinates are asked for.

• Question

Some quadratics are to be solved by factorising

• Question

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

• Question

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

• Question
Solving 1 linear and 1 quadratic simultaneous equations
• Question

Quadratic factorisation that does not rely upon pattern matching.

• Algebra 1
Exam (3 questions)
In this practice test you can work on simple equations and also solving quadratics using the formula. You should give all answers to 2 decimal places.
• Question

No description given

• Question

No description given

• Question

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.

• Question in Demos

Give the student three points lying on a quadratic, and ask them to find the roots.

Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.

Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

• Question

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Version II. Graph is horizontal

Version III. Graph is cubic

Version IV. Graph is sinusoidal

Question

Quadratic factorisation that does not rely upon pattern matching.

• Conditional visibility
Question in How-tos

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

• Question in How-tos

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

• Question in How-tos

Student is asked whether a quadratic equation can be factorised. If they say "yes", they're asked to give the factorisation.

• Question

Some quadratics are to be solved by factorising

• Question

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

• Question

Approximating integral of a quadratic by Riemann sums . Will include an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

• Question

No description given

• Question

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

• Question

Given one solution of the quadratic equation in $\mathbb{Z}_n$ where $n=pq$ is a product of two primes find the other 3 solutions.

• Question

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.