Exercises for HELM Book 2.5.1

Identify the gradient and y-axis intercept of a random non-vertical line.

Given one of ax+b, a/x, x^(1/a), a, is it a straight line.  a is a randomised integer.

State the general form of the equation of a straight line explaining the role of each of the terms in your answer.

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.

Exercises for HELM Book 2.4.3

Characterise the cosh function as continuous, many-to-one, even, and find the limit as x approaches 1. Part of HELM book 2.4.3.

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.

Exercises for HELM Book 2.4.1

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

Given a linear or a quadratic function and asked whether it is continuous. Part of HELM Book 2.4.

The first question from the Numbas tutorial, extended a bit.

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.

This question gives a text encrypted with an affine cipher and asks students to decrypt it.

This question asks students to decrypt a message using a simple Caesar cipher, without giving them the key.

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.

Resolver una ecuación de 1er grado con fracciones

sinB y secA en triángulo rectángulo

Evaluación de una expresión algebraica con dos variables

Exercises for HELM Book 2.2.1