How to Ace your GCSE Maths!

In year 11 maths, some topics like estimating the square roots and cube roots, quadratic inequalities, types of functions, the law of sines and law of cosines are newly introduced. Further, statistics and probability is also extended by a few topics like IQR (Inter Quartile Range), conditional probability etc. Though these new topics are at the introductory level in year 11 maths, learning them to the core would be very helpful for students when they go to their further classes.

Relations and functions: In this topic, the students of year 11 learn different types of functions, their domain and range, and graph them. The graphing part of functions is very crucial to understand, as a student can understand "what a particular type of function stands for" only through graphing.

• Example: For the given functions f(x) = 3x + 2 and g(x) = 2x - 1, find the value of fog(x).

  Solution:

  The given two functions are f(x) = 3x + 2 and g(x) = 2x - 1.

  We need to find the function fog(x).

  fog(x) = f(g(x))

  = f(2x-1)

  = 3(2x - 1) + 2

  = 6x - 3 + 2

  = 6x - 1

  Answer: Therefore fog(x) = 6x - 1

Advanced trigonometry: In the previous year, students have already learned how to apply trigonometry to right-angled triangles. But this year, trigonometry related to non-right triangles is introduced, which involves the sine rule, cosine rule, and bearings. Advanced trigonometry has more application-based type questions.

• Example: Find the area of triangle ABC, given that the sides AB = 5 units, BC = 8 units and ∠ABC = 60°.

  Solution

  Length of AB = c = 5 units, Length of BC = a = 8 units
  Angle between AB and BC = ∠B = 60°
  Area ΔABC = 1/2 × a × c × sin(B)  = 1/2 × 5 × 8 × sin60º  = 10 √ 3 square units 

  Answer: Area of triangle ABC = 10√3 square units

Equations and Inequalities: In previous years, students already have experience with linear equations and simple quadratic equations. But in year 11, they will learn to solve the linear and quadratic inequalities and graph them as well. Also, in "sequences", they will learn how to find the general term of a sequence and how to find its sum, etc.

• Example: What will be the 15th term of the arithmetic sequence -3, -(1/2), 2…. using sequence and series formula?

  Solution: Given a = -3, d = -(1/2) -(-3) = 5/2, n = 15

  Using the formula for nth term of an arithmetic sequence:
  an = a+(n-1)d

  Putting the known values:

  a15 = -3 +(15-1) 5/2

  a15 = 32

  Answer: The 15th term of the given arithmetic sequence is 32.

Here are some tips and tricks that are helpful for year 11 students to excel in maths.

• Build a strong foundation of basics to make life easier.

• Keep revising the basics.

• Work hard, and practice as many questions as possible from each topic.

• Then solve exam-style questions in an exam type environment (by setting a time limit).

• Keep noting the topics/problems that are difficult and keep visiting them.

• Keep the year 11 maths curriculum in hand to know how many topics are left for practice.

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