By powers of ten I mean a 1 followed by some 0s. The scientific notation questions will take care of the power of ten notation.

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

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Issues: alignment in columns in the working - not sure what to do about it

Decimal divided by a decimal. Multiply by a power of ten to get an integer divisor. Long and short division process. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to some number of decimal places.

Some students believe a decimal is larger if it is longer, some believe a decimal is larger if its first non-zero digit is larger.

Decimals addition algorithm. 2 and 3 digit numbers. Carrying.

Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.

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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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Friction

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."

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

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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