GCSE Maths: Past Papers and Sample Questions

As of 2017, the GCSE exams have adapted a new grading structure. Students taking the GCSEs this year and onwards will no longer receive letter grades in the form of A–G, but rather numerical grades ranging from 9–1. More significantly, the structure of many of the GCSE subject exams have also undergone changes, including the GCSE Maths exam.

The two tiers in the Math GCSE consist of a Maths foundation level (1–5) and a Maths higher level (4–9). The new structure has resulted in the following reforms:

• A stronger emphasis has been placed on mathematical reasoning and problem solving.
• The content has increased in volume, meaning teachers now need to dedicate more time to teaching it.
• In addition to the increased content, the content itself has grown in difficulty, which means pupils will need more study time.
• The number of papers students must sit has increased from two to three.
• Pupils will be provided with fewer formulas at the exam. Correspondingly, they will have to memorise and master more formulas.

To access practice tests and sample questions for the new GCSE, visit our GCSE Teacher’s page. Read on to learn more about the test structure in each tier of the GCSE Maths exam. For a more extensive list of the GCSE reforms in general, visit our GCSE Past Papers page.

The most significant change to the GCSE Maths foundation tier is the new subject matters that were once part of the higher tier. Some of these subject matters include numeric and algebraic index laws, vectors, linear equations, mensuration problems, and trigonometric ratios, amongst others. The breakdown of content domains have also been altered to include the following:

• 15% Geometry and Measures
• 15% Statistics and Probability (which has decreased in emphasis since the 2010 foundation tier papers)
• 20% Algebra
• 25% Ratio, Proportion, and Rates of Change—an entirely new subject matter introduced to the foundation tier papers
• 25% Number

Due to these reforms, more pupils have been entered for the foundation tier Maths GCSE instead of the higher tier papers. Teachers have been dedicating more time to the foundation tier curriculum as a result. Visit our GCSE Past Papers page and gain access to sample questions and practice tests equipped to prepare you for the foundation tier Maths GCSE papers.

Like the foundation tier, the GCSE Maths higher tier has adapted to new subject matters. The GCSE now includes expanding the products of binomials, completing the square, calculating conditional probabilities, and more. With these additions have also come omissions of topics that were previously part of the higher tier GCSE Maths papers. These topics include isometric grids, 3D coordinates, and imperial units of measure, amongst others.

Below is a breakdown of content domains making up the new higher tier GCSE Maths papers:

• 20% Geometry and Measures
• 15% Statistics and Probability
• 30% Algebra
• 20% Ratio, Proportion, and Rates of Change
• 15% Numbers

This new structure places less of an emphasis on the once stressed Statistics and Probability domain and more of a stress on Algebra. The Ratio and Proportion domain has also been adapted to its own content area, whereas it was previously intertwined with various other content areas.

These reforms have all been made with the intention of creating a more challenging exam for the more academically gifted pupils. Those who choose to sit the higher tier papers should receive excellent preparation for A Level Mathematics.

The following problem is an example of a foundation tier Maths GCSE problem.*

*Note: You must answer this question without a calculator.

Exam Mark Scheme

The following is an example of a higher tier Maths GCSE problem.*

*Note: You must answer this question without a calculator.

Exam Mark Scheme

Student Explanation

For Lucy to pick one card of each colour, she either has to choose a red then a black or a black then a red.

You must consider both of these options when calculating the probability. Remember that in probability:

AND means  x

OR means  +

So, to find probability of a red AND then a black, you must multiply the probabilities.

Use the probability formula to correctly write your expressions:

Now, consider the second option, which was picking a black card and then a red. Notice, the denominators have switched as there are always 11 cards at the start and then 10 after she has made her first selection.