Maths4U Original · Short practice

Use \(\displaystyle a=6\). Work with real numbers; no calculator is needed.

Which of these numbers is irrational?

Choose one answer.

Maths4U Original · Short practice

Use \(\displaystyle a=7\). Work with real numbers; no calculator is needed.

Which of these numbers is irrational?

Choose one answer.

Maths4U Original · Short practice

Use \(\displaystyle a=7\). Work with real numbers; no calculator is needed.

Find the square of a.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Use \(\displaystyle a=8\). Work with real numbers; no calculator is needed.

Find the square of a.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Use \(\displaystyle a=8\). Work with real numbers; no calculator is needed.

Find the reciprocal of −a.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Use \(\displaystyle a=9\). Work with real numbers; no calculator is needed.

Find the reciprocal of −a.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Use \(\displaystyle a=9\). Work with real numbers; no calculator is needed.

Find the cube root of 1331.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Use \(\displaystyle a=3\). Work with real numbers; no calculator is needed.

Find the cube root of 125.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=144\) and \(\displaystyle M=1080\).

Find the exponent of 2 in the prime factorisation of N.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=864\) and \(\displaystyle M=32400\).

Find the exponent of 2 in the prime factorisation of N.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=864\) and \(\displaystyle M=32400\).

Find the HCF of N and M.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=12\) and \(\displaystyle M=90\).

Find the HCF of N and M.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=12\) and \(\displaystyle M=90\).

Find their LCM.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=72\) and \(\displaystyle M=2700\).

Find their LCM.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=72\) and \(\displaystyle M=2700\).

Find M divided by their HCF.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle N=432\) and \(\displaystyle M=3240\).

Find M divided by their HCF.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=10\) and \(\displaystyle b=7\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle a^{2}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=11\) and \(\displaystyle b=2\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle a^{2}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=11\) and \(\displaystyle b=2\). Apply the stated brackets and root conventions.

Calculate the principal square root of 121.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=12\) and \(\displaystyle b=3\). Apply the stated brackets and root conventions.

Calculate the principal square root of 144.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=12\) and \(\displaystyle b=3\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle (-b)^{3}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=3\) and \(\displaystyle b=4\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle (-b)^{3}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=3\) and \(\displaystyle b=4\). Apply the stated brackets and root conventions.

Calculate the real cube root of -64.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Let \(\displaystyle a=4\) and \(\displaystyle b=5\). Apply the stated brackets and root conventions.

Calculate the real cube root of -125.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.