How to Tackle Year 13 Maths Like a Pro

Year 13 maths is the second year of study of A-level (Advanced level) maths, which is the qualification for further career courses. Year 13 maths is mainly the application of what they have learned in their previous year. It includes advanced concepts such as advanced algebra, advanced binomial theorem, advanced trigonometry, etc. The only way to develop skills in year 13 maths is to improve conceptual understanding and solve more application-based questions.

Developing the skills in the following topics would help them to excel in their future years and courses.

Advanced binomial theorem
The student in year 13 learns the connection between Pascal's triangle and binomial theorem. This helps the students to avoid rote learning and solve the binomial expansions in a much easier way.

• Example: A coin is tossed three times, find the probability of getting exactly 2 tails.

  Solution:

  Using the Pascal triangle formula, the total number of outcomes will be 23 = 8 (1 + 3 + 3 + 1 = 8 )

  Where 3 of them give exactly two tails.

  So the probability of getting exactly two tails is 3/8, or 37.5%

  Answer: The probability of getting exactly two tails is 37.5%

Permutation and combination
This topic is about the number of selections (combinations) and arrangements (permutations). It is the methods employed in counting how many outcomes are possible in various situations.

One can gain command over this topic by first learning it practically for a smaller number of objects. For example, two letters out of three letters a,b,c can be selected in only three ways: ab, bc, ca. But two letters can be selected and then arranged as words from three letters a,b,c in 6 ways: ab, ba, bc, cb, ca, ac.

• Example: Patricia has to choose 5 marbles from 12 marbles. In how many ways can she choose them?

  Solution:

  Patricia has to choose 5 out of 12 marbles. The order doesn't matter here.

  Thus combinations used here. she can choose it in 12C55 ways.

  12C5=12!5!×(12−5)!=12!5!×7!=12×11×10×9×8×7!5!×7!=12×11×10×9×85!=79212𝐶5=12!5!×(12−5)!=12!5!×7!=12×11×10×9×8×7!5!×7!=12×11×10×9×85!=792

  Answer: Therefore there are 792 ways

Integration
Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function.

• Example: Integrate the function f(x)=2x sin(x2+1) with respect to x.

  Solution:

  Observe that the derivative of x2+1 is 2x.

  So, we will proceed with integration by substitution.

  Let x2+1=z

  Then, 2x dx = dz

  ∫f(x)dx=∫2xsin(x2+1)dx=∫sinzdz=−cosz+C=−cos(x2+1)+C∫𝑓(𝑥)𝑑𝑥=∫2𝑥sin⁡(𝑥2+1)𝑑𝑥=∫sin⁡𝑧𝑑𝑧=−cos⁡𝑧+𝐶=−cos⁡(𝑥2+1)+𝐶

  ∴∫2xsin(x2+1)dx=−cos(x2+1)+C

Here are some tips for year 13 students to get good grades.

• Make proper notes of whatever is taught in the school.

• Keep revising the concepts at regular intervals.

• Work on every topic from elementary to hard level.

• Work on previous years' papers and worksheets under exam conditions (like keeping the timing limit).

• Make a note of the mistakes every time and then set up a new plan to avoid the mistakes.

Not know how to best spend the time before an exam? Check out our blog about pre exam ritual!