Gcse Maths - My Revision Guide

1) The Number Line I believe that is the best place to start for students who are not very confident with their maths. Good knowledge of the number line will help you to add, subtract, multiply and divide both negative and positive numbers. This skill will also help you prepare for algebra and solving for unknowns in more advanced topics. Every student must learn that every number has a positive or negative sign on its left which describes the position of the number on the number line (just like every object has a shadow). The sign on the right of a number does not describe that number. It indicates what action we need to take. For example -3 + 4 tells us we need to add 4 to the number negative 3. We can also swap these numbers. Remember each number must move with its sign just like you always move with your shadow. The expressions, therefore, becomes +4-3. Since we normally do not show positive signs of a number, the expression becomes 4-3 which is easy to solve. The answer is 1. Learning how to manipulate expressions can go a long way in improving a student's maths skills.

2) Numbers Before learning about numbers, students must be confident with multiplication and division of numbers. Learning about different numbers such as Prime Numbers, Even Numbers, Odd Numbers, Factors, Multiples and the characteristics of different numbers will help you to prepare for topics on fractions, decimals, percentages, ratios and proportions. Many D grade students are surprised to learn that fractions, decimals and percentages are just the same only "dressed in different clothes". Since a big proportion of the problems in Foundation Level Maths is on Numbers, when D grade students learn this topic they increase their grades quickly. Understanding numbers also helps the student to solve problems on series, train time tables, speed, distances and business transactions. Ability to solve many of the number problems can help a student to earn high marks.

Once a student is comfortable, it becomes easy to handle Higher Level maths problems such as; Standard Form, Surds, arithmetic series and geometric series.

3) Algebra Simple algebra is another important topic but many students who have not mastered the number line and numbers find it difficult. I have noted that mastering the number line and numbers helps the student to solve algebraic problems quickly and efficiently. Most important, knowledge of algebra helps a student to solve problems on unknowns and prepare a student for Higher Level exams. I have noted with equal excitement how excited many students become when they learn how to solve equations with an expression which says "I didn't know I can solve this". I normally introduce graphs at this point to make sure the student appreciate the different axes and the dependent and independent variables. Higher Level students must also learn how to factorise more complex equations such as the quadratic equation in the form ax2 + bx + c. At this point, one of the most important skills at the Higher Level is to change the subject of a formula. By understanding how to change the subject of a formula, the student can solve many different types of problems which involve solving the unknown.

4) Space Before learning problems on space, it is a good thing for students to learn the different types of units and how to convert them. Memorising a simple conversion table is appropriate at this point. It is also very important for students to know the difference between perimeter and area. Perimeter is simply the length of outer edges of a shape. I ask students to imagine the fence of their back garden. If the student were to stretch the fence into a straight line, he or she would get the perimeter. On the other hand, area is like the number of little squares that fit into a surface such as a carpet or the garden. The squares could be of any unit as long as the units are appropriate. Since the area of any square is in square units, the area of any shape is also in square units. Students then progress towards volume, angles, transformation, and simple trigonometric ratios in preparation for the Higher Level papers.

For Higher level students it is critical to learn trigonometry at a deeper level and how and when to use different formula such as the Pythagora's Theorem, Sine Rule, Cosine Rule, and most important how to obtain the inverse Trigonometric Ratios using their calculators and how to get them. At this point, the student must also understand and be comfortable in using their calculator. I know of a student who failed his exams because his calculator was in the radian (A Level maths) mode which means the answers to his trigonometric problems were wrong. Although it was not his fault, it was very unfortunate.

Students must also learn apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

5) Data handling As a statistician, this is my favourite topic. Although many students, including higher Level students, find statistics and probability too abstract, it is possible to explain abstract concepts using simple examples using real life application of data and information. At Foundation Level, students need to learn how to identify means, modes and medians.

Although students at Higher Level are not expected to solve problems on distributions, they are expected to understand box plots, spread (range, including consideration of outliers, quartiles and inter-quartile range) and simple regression analysis using the line of best fit.

In my next article, I will discuss one of these topics in brief but in more detail.