1st Year Maths — The Ultimate Guide

1st Year Maths Overview

Ah, 1st year……..where the innocence and joy of entering ‘big school’ is slowly ebbed away by the sheer volume of homework and information overload of the secondary school system.

God, I am some miserable character.

Let’s keep this topline here — 1st year Maths is straightforward. It’s not too complex. You are introduced to Algebra in the middle part of the year. This often causes some confusion for students, but it’s manageable. It’s really in 2nd year when the pain of Maths starts, when it starts to get very complex.

Here’s the spinning wheel of the overall breath of topics your child will cover in 1st year.

The Good News

The good news is that I am going to break these topics down into bite sized chunks for you to help your child.

I’ll help you recognise when to spot a particular topic. I’ll stick in relevant examples at the end. I’ll lay down what the Christmas and Summer exams will look like.

So, grab some paper and follow along – you will thank me when your child goes to revise their Maths!

The Christmas Test

This usually takes place at the end of November in most schools. Typically, it’s straightforward enough as your child is just adjusting to secondary school. Expect to see on the exam –

  • Calculations
  • Factors
  • Integers
  • Word problems
  • Fractions – decimals – percentages

And to be honest, that’s the most of what they will ask you in the Christmas exam in 1st year.

The Summer Test

A big step-up here from Christmas. Expect to see almost everything you have done at Christmas-time and more complex topics like Algebra. It’s Algebra that cause the biggest issues.

It often feels like a foreign language for students. The ‘X’s and ‘Y’s…. they just turn into mush for some students. And If you miss any parts of Algebra in 1st year, it is very difficult to do well in the summer test – Algebra is key.

So the overarching advice in summer is to nail down your Algebra. Practice all the revision questions at the end of the chapter. Be fluent with them. Constantly test yourself again and again.

Natural Numbers


Basic stuff here that is mostly a follow on from Primary School maths.. Be able to perform operations with exponents and square roots, as well as addition, subtraction, multiplication, and division on natural numbers.


1.) 3² = ?

2.) √(9+5) = ?

3.) 20 / (2 + 2) = ?

4.) (3 * 6)² = ?

5.) (20 – 2) = ?


Calculate and interpret factors, multiples, and prime numbers.


1.) What are the factors of 10?

2.) What is the highest common factor of 8, 12, and 36?

3.) What is the lowest common multiple of each of the following?

4.) What is the lowest prime number?


Perform operations of addition, subtraction, multiplication, and division on integers.


1.) 11 – 8 = ?

2.) -5 + 7 = ?

3.) (-9) * (-9) = ?

4.) 50 / 5 = ?

5.) [(15 + 3) / 9] / [(2 * 8) – 7] = ?

Order of Operations

Be able to perform operations of addition, subtraction, multiplication, and division, in the correct BEMDAS order.


1.) (11 – 8) * (2 + 2) = ?

2.) -5 + 7 / 7 = ?

3.) (-9 + 3 / 2) * (-3) = ?

Percentages, Decimals and Fractions

This is mostly a follow on from what your child would have completed in primary school. Routine enough questions, your child should be comfortable moving between percentages, fractions, and decimals.


1.) 2/5 = ?/20

2.) 3/21 = ?/7

3.) (2/3) * (6/8) = ?

4.) (6/9) / (3/5) = ?

4.) (6/9) – (4/18) = ?


Set’s always come up. They will invariably always ask for stuff like the intersection of two sets.

Have them well-prepared. Here is an example of a sets question:


Data can be quite word heavy. Students can get quite lost in some Data questions. The Maths are often easy — but the English can be complex. Help your child to SLOW DOWN here.

Here is an example question:


Students get very confused here. Algebra is what they are looking for in the 1st year summer exam. It’s by far and away the hardest topic in the summer test.

If you can do the questions below, you are in good order:


This is mostly a follow on from what your child would have completed in primary school. Routine enough questions, your child should be comfortable answering. A good understanding of fractions and percentages is essential.

Here’s an example question:


This is all about angles. Perpendicular angles, parallel angles. Guaranteed questions on the summer test, and they should provide easy marks for most students.

Try these questions:

Perimeter and Area

Perimeter, Area, and Volume are guaranteed questions at both the Christmas and Summer exams. It’s a good test of a students’ ability to problem-solve.

Test yourself — can you do this question out fully:

These topics should cover you for the majority of 1st year Maths questions on both your Christmas and summer exams.

Still Confused?

No problem. Watch this 40-second video.

Hope that helps.

TJ— CEO of Breakthrough Maths.

Need help in Maths? Contact the Breakthrough Maths team here.

Send article to a friend 👇