Given a circle equation in the form (x-a)^2+(y-b)^2=r^2, write down the radius and centre coordinates.

Write down the equation of a circle centre C and radius R.

Given a circle with radius between 2 and 6 units, students are given a set of 8 points and asked to identify whether they are on, inside or outside the circle locus.

Given that the circle touches the x-axis at a given point and given a point on the circumference, find the equation of the circle.

Given a circle centre and radius, write an appropriate inequality for the region either inside or outside the circle.

Draw the annulus given by a double inequality. The user moves circles on an interactive jsxgraph.

Este examen se usará para evaluar tus bases matemáticas, en base a mi curso homónimo en Khan Academy. Estas bases serán imprescindibles para tu buen desempeño en la materia que te imparto en la Universidad Politécnica Salesiana.

Inputting algebraic expressions into Numbas.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to rewrite the solution correctly. No variables but this is version 5 of 5 versions of the question. This version uses a much more mangled AI generated solution that the other 4 versions and does not ask for the line with the first error, just for the student to rewrite the solution correctly.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 4 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 2 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is 1 of 5 versions of the question.

Students need to find solution to simultaneous linear equations with randomised coefficients.

This question asks students to find the distance from an aircraft to a given marker. Angle of depression of 2 markers from the aircraft are given and the distance between the markers on the ground (all randomised). Students need to use the sine rule to find the answer. The workding of the question makes googling the answer difficult.

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.

Fixed question: Given two points at opposite ends of a diameter, write down the equation of the circle.

Given a circle centre and a point on the circumference, write down the circle equation.

Determine the radius and centre coordinates of a circle with equation expressed in expanded form.

Given the radius and centre coordinates of a circle write down its equation.

Rearrange a homogeneous circle equation into the form (x-xc)^2+(y-yc)^2=r^2 to find the centre and radius.

Given a graph of a circle, write down its equation.

Two part question, student has to rearrange the parallel resistors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Two part question, student has to rearrange the parallel inductors formula (stated in the question) to make L_1 or L_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Two part question, student has to rearrange the heat flow formula (stated in the question) to make T_1 or T_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

Exercises for HELM Book 2.5.3.

Find the gradient and y-axis intercept of a line through 2 points. The line is not vertical.