Indices - Changing the Base WORKSHEET
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Indices - Changing the Base WORKSHEET DESCRIPTION
Once your learners are confidently working with positive and negative integer and fractional indices they are ready to change the base in problems involving indices.
Section A asks pupils to fill in the missing indices in statements such as ⅟9 = 3^?, which involves changing the base. The section begins with integer indices and progresses to include negative, fractional and finally negative fractional indices.
In section B, there are 9 terms with varying bases that are to be rewritten in the form 2ⁿ. Here n is sometimes an algebraic expression such as 6q + 6.
Section C sees students solving equations based on indices and different bases. The first two questions are scaffolded to aid learners.
Are your students in need of a challenge? Section D requires them to solve two further equations simultaneously.
