Factorise the difference of two squares, t^2-number^2. Number is a random perfect square, or 1 over a perfect square.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Expand (a+b)(c+d). a,b,c,d are random terms that can be +ve or -ve, and can consist of a number and/or a letter.

The answer must contain no brackets but will be accepted if it is not simplified from there.

Part of HELM Book 1.3

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given a proportion of students who DO speak a language other than English at home, and are asked to find the percentage who do NOT. The fraction denominator is either 20 or 25, and the numerator is randomised.

A graph (of a cubic) is given. The question is to determine the number of roots and number of stationary points the graph has. Non-calculator. Advice is given.

Write a large number and a small number in scientific notation. (Numbers contain 5 digits). Indices range from -7 to +7, excluding 0 and 1

Part of HELM Book 1.2

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised positive numbers.

Part of HELM Book 1.2

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Compute the modulus of either (a) a signed decimal, or (b) a sum or difference of two decimals.

Used in HELM Book 1.1.5 Exercises

Divide two numbers, at least one of which is negative. The answer is always an integer.

Multiply two numbers, at least one of which is negative.

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

Round a number to $n$ significant figures. Part of HELM Book 1.1

Round a number to $n$ decimal places. Part of HELM Book 1.1

Find reciprocals of (a) a proper fraction, (b) an improper fraction, (c) an integer

Compute the modulus of (a) a positive rational, (b) a negative rational, (c) 0

Calculate the product of two randomised scientific notation numbers and give the answer in scientific notation.

Part of HELM Book 1.2

Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Use a calculator to evaluate a number to the power of a fractional index. Both the number (a positive integer) and the index (a rational) are randomised.

Part of HELM Book 1.2