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

Simplify (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.

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

Part of HELM Book 1.2

Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.

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 and can be positive or negative numbers.

Part of HELM Book 1.2

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Part of HELM Book 1.2

Given an arbitrary polynomial, identify its degree. Part of HELM Book 1.2

Is this polynomial a quadratic, linear or constant? Part of HELM Book 1.2

Part of HELM Book 1.2

Simplify n1.v^k1.(n2.v^k2), where n1, n2 are positive integers, v is a random letter variable, and k1 and k2 are nonzero integers.

The answer should be expressed as n.v^k

Part of HELM Book 1.2

Remove the brackets from (na)^k, or from n(a)^kwhere n is a number and a is a variable.

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2

Evaluate a simple fraction squared or cubed. Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Asks students to compute (base)^index without a calculator for two simple questions. Part of HELM Book 1.2

Part of HELM Book 1.2

Part of HELM Book 1.2

Part of HELM Book 1.1

Part of HELM Book 1.1

Two BODMAS questions. Part of HELM Book 1.1.

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 reciprocal. Find a modulus. Find a factorial. Part of HELM Book 1.1

Part of HELM Book 1.1

Part of HELM Book 1.1

Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.

Note that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.

Part of HELM Book 1.3

Part of HELM Book 1.3