Essential Mathematics: should I choose it?

What will I learn?

How will I be assessed?

Progression and companion subjects

No complete companion or exclusion review is attached to this profile. Check the official course-entry conditions, language eligibility and your school’s sequence before enrolling. Links between resource hubs show related learning; they do not establish a compulsory prerequisite.

Will I find it hard?

Difficulty depends on your experience, interests, teaching and assessment. These are our reflection prompts, not an official difficulty rating.

• How do you feel about explaining a method and working through unfamiliar multi-step problems?
• Try the sample without looking at a worked answer, then check the steps you need to practise.

Does it scale up or down?

Use applicable SATAC evidence. Vocational certificate credit is not automatically an ATAR input.

Scaling is not a measure of difficulty or a guaranteed bonus. Prioritise content you can engage with and required subjects for courses you are considering.

Try a little of the subject

Calculations, time, and ratio

Most practical problems in Essential Mathematics come down to adding, subtracting, multiplying and dividing whole numbers, fractions and decimals. You are expected to do the core calculations by hand first, because a tradesperson quoting a job, a nurse checking a dose or a shop assistant counting change often has no device in hand. This includes square roots of perfect squares (√49 = 7, √144 = 12) and moving between index form and ordinary numerals (2⁵ = 32, 10⁴ = 10 000, 81 = 3⁴). Order of operations. Evaluate brackets first, then indices and roots, then multiplication and division working left to right, and finally addition and subtraction working left to right. For example 20 − 2 × 3² = 20 − 2 × 9 = 20 − 18 = 2. Doing the subtraction first would give 18 × 9 = 162, which is wrong. Place value after the decimal point. In 4.375 the 3 means three tenths, the 7 means seven hundredths and the 5 means five thousandths. Place value lets you compare decimals (0.45 is larger than 0.405 because both have 4 tenths, but 0.45 has 5 hundredths and 0.405 has 0 hundredths) and turn fractions into decimals by dividing the numerator by the denominator: 5/8 = 5 ÷ 8 = 0.625, and 2/3 = 0.666…, which is 0.67 to two decimal places. Multiples of ten. Multiplying by 10, 100 or 1000 moves every digit one, two or three places to the left; dividing moves them to the right. To multiply by 300, multiply by 3 and then by 100: 2.4 × 300 = 7.2 × 100 = 720. To divide by 400, divide by 4 and then by 100: 1800 ÷ 400 = 450 ÷ 100 = 4.5. Using technology discerningly. A calculator is the sensible tool for longer multi-step work with fractions, decimals, roots and indices, but you still need to enter it correctly. Use brackets and the fraction key, and write down the calculation you entered so a reader can

Original practice question: Evaluate 18 − 3 × 4 + 2² without a calculator.

This is ATARMAxxing’s original sample learning material. It is not an official assessment task or a prediction of your school’s workload.

Explore the resources

Open the Essential Mathematics subject hub and free preview (opens in a new tab)

• Essential Mathematics — SACE Stage 2 (opens in a new tab)

Core subject information and planning are free. Full study resources are optional.