Exam-Style Problems

Stage 9 - Q1 - 2 marks

18997

Classify as rational or irrational.

\[\sqrt{226}\]

Hint

Locate the radicand between consecutive squares.

Stage 9 - Q2 - 2 marks

18998

Write in standard form.

\[0.00000031\]

Hint

Count how many places move the decimal to a number from 1 to 10.

Stage 9 - Q3 - 3 marks

18999

Evaluate as an exact fraction.

\[12^{-1}\]

Hint

First write a reciprocal with a positive power.

Stage 9 - Q4 - 3 marks

19000

Write as one power.

\[5^{-4}\div5^{-3}\]

Hint

Subtracting a negative adds.

Stage 9 - Q5 - 4 marks

19001

A square has area 420 square units. Between which consecutive integers is its side length?

Hint

Write area as side squared.

Stage 9 - Q6 - 4 marks

19002

A square has area 12 square units. Between which consecutive integers is its side length?

Hint

Write area as side squared.

Stage 9 - Q7 - 5 marks

19003

Add and normalise your result.

\[2.3\times10^{-3}+1.3\times10^{-4}\]

Hint

Rewrite the first coefficient using the smaller power.

Stage 9 - Q8 - 5 marks

19004

Classify the result and justify it.

\[6+\sqrt{2}\]

Hint

Suppose the sum were rational and subtract the integer.

Stage 9 - Q9 - 5 marks

19005

Find the missing integer exponent.

\[\frac{6^n}{6^{-2}}=6^{1}\]

Hint

Translate the quotient into an equation in indices.

Stage 9 - Q10 - 3 marks

19006

A square has area \(3.24\times10^{-6}\) square metres. Find its exact side length in standard form, then find the reciprocal length in inverse metres to 3 significant figures.

Hint

Take the square root of the coefficient and halve the even exponent.