Foundation Mechanics Question involving a body on a plane

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The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.

The table uses the spreadsheet and JSXgraph extensions.

This question shows how explore mode can be used to loop through several versions of the same question. The variables for each version are stored in a list of "scenarios", and a counter works through that list each time the student moves on to the next part, labelled "try the next version of this question".

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Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

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Given f(x)=1/(a-x)^2, evaluate f(x/z) where a is a randomised constant, and z is a randomised letter.

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) 

Give f(x)=ax^2+b a simple function input (like 6x-3) and evaluate. Constants and variables, and the function input are all randomised.

evaluate a function with randomised alphanumeric expressions as inputs.

Evaluate a linear function at 3 numerical inputs.

HELM book 2.1.2 exercises

Evaluate a given, randomised, linear function at a given, randomised, value.

"Explain what is meant by the argument of a function."

Unmarked: Answer: "The argument is the input."

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Student is shown a simple (randomised) function and asked to describe its behaviour. This is an information only question. Students need to view the advice to check their answer.

Given a function definition in words, evaluate the function with various variable and numeric inputs

A difficult question that involves rearranging a complicated formula, then applying unit conversions to variable values, then evaluating the formula for the selected value. The variable values are randomised.

Rearrange an equation for a variable e in k.1/(1-e) and then evaluate for e, given values for the variables.

Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.

Choice of 2 formulae. The first is a fraction of the form y=(r+x)(1-rx). The second is of the form y=sqrt[(1-x)/(1+x) ]. Rearrange to make x the subject.

Rearrange a formula with a square root to make a variable under the root the subject.

Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

Transpose PV=RT to make a random variable the subject.

Convert a random number of cubic metres into cubic centimetres

Convert a random value in square metres to square centimetres.

Given the formula for a cone or a cylinder, and values for r and h, find the volume.