Three Topics You Should Nail in Year 10 Maths to Make Maths Advanced Easier

Nervous about studying Maths Advanced next year? No worries!! We’ve got you covered with our recommendations for which topics you should master in Year 10 to make studying Maths Advanced easier. 

Introduction

Maths Advanced might seem a little daunting from the outset. You’ll be introduced to unfamiliar topics such as Calculus and harder applications of Probability. While true, take comfort in knowing that Year 11 Maths Advanced is an extension of what you have already learnt in Year 10 5.2 and 5.3. If you master the topics studied in Year 10, you’ll have a much easier time grasping new concepts in Maths Advanced. 

While all of Year 10 Maths is in some way “important”, we would suggest that you master the following topics in particular:

1. Quadratic and simultaneous equations
2. Linear and non-linear relationships
3. Trigonometry

Let’s dive right in!!

Quadratic and Simultaneous Equations

Both quadratic equations and simultaneous equations feature quite heavily in a number of Maths Advanced topics in ways you couldn’t possibly imagine. In fact, it’s fair to say that solving equations generally is an assumed skill in Years 11 and 12. What makes things a little more challenging is that equations will be seamlessly integrated into other topics such as Functions and 3D Trigonometry, thereby demanding that you know how to solve equations in a variety of contexts. 

Need help solving quadratic and simultaneous equations? All good!! Check out our guides for solving quadratic equations and simultaneous equations. 

Linear and Non-Linear Relationships

Having a solid understanding of linear and non-linear relationships significantly helps when studying Functions and Calculus. The Functions topic in Year 11 Maths Advanced is an extension of what you have already learnt where you review curve sketching and learn about function notation. 

In terms of Calculus, you’ll build on your knowledge of Functions by studying limits and continuity, differentiation, tangents and normals. You’ll also learn how to find stationary points and the nature of the gradient at particular points on your curve. Some of this might involve sketching the curve based on stationary points and your understanding of gradients!! 

In terms of what to know, we’d suggest the following:

• A basic understanding of the general shape of different curves. E.g. y=x; y=x2;y=x3;y=9-x2
• The impact of transformations on particular curves. E.g. What does y=-2(x-1)2-7 look like in comparison to the basic curve y=x2? 
• Domain and range.
• Different “skills” associated with curve sketching: E.g. Finding x and y intercepts.
• Examples of where each type of graph is used in real life. 

The last point is particularly important when completing problem-solving questions. Since problem-solving questions often differentiate the Band 6 students from the rest,  having an idea of where each type of graph is used in practical situations will give you a head start when looking at unfamiliar problem solving questions because you’ll already have some familiarity with which type of relationship needs to be used in a particular situation. 

Trigonometry 

Trigonometry features quite heavily in the Maths Advanced course. Not only do you review the fundamentals of trigonometry (basic trigonometric ratios, bearings, sine rule, cosine rule etc), but you also apply these concepts to harder questions. For example, you will study problem solving questions that involve 3D trigonometry, where you will need to simultaneously apply multiple theorems (sine rule, standard trigonometric ratios, bearings) to solve a problem. 

Final Thoughts

So there you have it: Our suggestion for three topics you should nail to make Maths Advanced easier!! Remember this: The more work you put into Year 10, the easier it will be to pick up concepts in Maths Advanced. Our aim should always be to reduce friction when learning new material and what better way to start doing this when in Year 10!!

Good luck!!