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.

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.

Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.

Determinig the CoG of a composite part

Deducir la ecuación de una recta a partir de su gráfica

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.

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.

Find the gradient of a line through 2 given points. Part of HELM Book 2.5.2.

Deducir la ecuación de una recta a partir de su gráfica

Compare the gradients of 3 lines and choose the steepest. Part of HELM Book 2.5.1.

Find the gradients of 3 lines. Part of HELM Book 2.5.1.

Find the vertical intercept of 4 lines. Part of HELM book 2.5.1

Describe the effect of changing the value of a constant term in a linear function. Part of HELM Book 2.5.1.

Identify whether a function is odd, even or neither from its graph. Part of HELM Book 2.4.3.

Given the period of a repeating function, determine the number of repeats in a given amount of time. Part of HELM Book 2.4.

Given a piecewise function determine whether the limit exists at two points. Part of HELM Book 2.4.1.

A demo of the number entry part and its options.

The student is shown a plot of a mystery function. They can enter values of $x$ check, within the bounds of the plot.

They're asked to give the formula for the function, and then asked for its value at a very large value of $x$.

A plot of the student's function updates automatically as they type. Adaptive marking is used for the final part to award credit if the student gives the right value for their incorrect function.

Compute the inverse of a linear or hyperbolic function. Part of HELM book 2.3.

Find the inverse of a linear function. Part of HELM book 2.3.

Determine whether three graphs are functions or not. Part of HELM Book 2.3.

Given parametric equations, graph the function and obtain an explicit equation. Part of HELM Book 2.2.2.

Use parametric equations to find x for a given value of y. Part of HELM Book 2.2.2.

Graph x^2 - y^2 = 1 from a parametric definition. Part of HELM Book 2.2.2.

Identify the value that is not part of the domain of a function. Part of HELM Book 2.2.1.

Draw a graph of y=x^3 by plotting points. Part of HELM book 2.2.1

Graph a linear or quadratic function and state its domain and range. Part of HELM Book 2.2.1.

Asked to define a function term, e.g. domain, or x(t). Part of HELM book 2.2.1.