Additional Mathematics Overview (OCR)

This syllabus consists of 4 main topics:

 

Algebra

Linear expressions are a key basic to this topic; this includes the simplification and factorisation of linear expressions and equations involving brackets and fractions. Quadratic expressions should be familiarized, and you need to know the 3 main ways of solving them (completing the square, factorization and using the equation). You will be expected to understand simultaneous equations in both elimination and substitution, and how to incorporate them into graphs. Inequalities (linear and quadratic), working with surds and polynomials are standard, as are the factor and remainder theorems. Binomial expansion and distribution should be understood, especially in terms of probability.

 

Co-ordinate Geometry

gradients, and how they relate to perpendicular lines (such as a line and its normal at a given point) is a key area.  You should also know about the Midpoint and length of a line, as well as its equation and how it can be drawn on a graph. Conversely, you need to be able to find the equation of a line, and find points of intersection between lines. Equations relating to the circle are also of crucial importance in this topic.

 

Trigonometry

This involves the study of applications to right-angled triangles (namely, Pythagoras' Theorem), sin and cosine rules, the cos sin and tan graphs, the CAST diagram and trigonometrical identities. The area of a triangle, and knowing how to solve three dimensional problems are also reviewed in this section.

 

Calculus

the gradient of a curve, stationary points, tangents and normals (which are all related to differentiation) are expected to be known and familiarized here. Additionally, integration is also met in this topic, where the area between curves and lines is concerned. Kinematics is briefly discussed in relation to constant acceleration and variable acceleration.

 

Test Yourself

If you think that you are familiar with all of these topics, see if you can answer the questions below. The mark scheme of these topics can be found here, in which you can identify if and where you went wrong, and what topic should be your main cause for concern.
Q1. Factorise 84a⁵b⁴ - 96a⁴b⁵
Q2. Simplify 2x/3y - 3x/2y
Q3. Find x by all possible means in the equation 7x = 12 + x²
Q4. What is the point of intersection between these two lines?

Q5. Solve for x in the inequality 12x² + 3x ≥ 24 - 3x.
Q6. Simplify √12/√6
Q7. is x + 2 a factor of f(x) = x³ + 5x² + 7x + 2?
Q8. expand (1 - 2x)¹⁰, and identify the co-efficient of each term.
Q9. 5 friends each roll an unbiased die. What is the probability that
       i) all of them roll a 6
       ii) two of them roll more than 2
Q10.i) Give the equation of line AB, given that the co-ordinates of A and B are (-3,-1) and (3,5) respectively.

       ii) hence or otherwise, find the area of the triangle formed by the line AB and the x and y axes.
       iii) What would be the equation of the normal to the line AB at the point B?
Q11.i) A circle with origin (0,2) has a point A on its circumference. What is the equation of the circle?
       ii) point A has co-ordinates of (-4, 1). Does it lie within the circle?
Q12. What values of x satisfy x² + 10y + 25 > 0?
Q13. Triangle ABC is a right angled triangle, where hypotenuse AC = 10 and AB = 6. What is angle BCA?

Q14. Find x using the sine rule

 

Q15. Find angle CBA

Q16. i) Prove that 2sin²θ = 3cosθ is equivalent to 2cos²θ + 3cosθ = 2
       ii) solve the equation 2cos²θ + 3cosθ = 2  for 0 ≤ θ ≤ 360
Q17. What is the equation of line BC, given that the curve has an equation of y = x² + 1

Q18. i) A curve has the equation 0 = 4x³ + 6y +25. What are the co-ordinates of the stationary point(s).
         ii) determine if these points are maximum or minimum points
Q20. Line AC is the normal to a curve at its stationary point. The curve has the equation y = 3x² + 4. What is the gradient of line AC?
Q21. Find the area S, given that a =2, b = 10 and f(x) = 2x³ + 9

Q22. a car has a constant acceleration of 3 m/s², and it moves from rest to a velocity of 10 m/s. In what distance does this happen?
Q23. During braking, the speed, v m/s of a car is given by v = 30 - 5t, where t seconds is the time since the brakes were applied.
       i) sketch a graph of v, on the vertical axis, against t.
       ii) how long does the car take to stop?
       iii) how far does it travel while breaking?

Click here for mark scheme
want to test yourself further? You can get free exam papers and mark schemes here.

Welcome to the GCSE Overviews blog!

I am a secondary school student living in London, and the purpose of this blog is really to consolidate my own knowledge on certain GCSE topics, simply for my own development. However, if you are (like me) a GCSE student who may be struggling with certain topic areas, I hope you find my materials worthy of review, and that you find them useful. Yes, there are millions of websites, online resources and books you can read on this topic, but the aim of this blog is to provide (hopefully) a unique method of revision, whereby each subject has a quick 'overview' which you can read over and see if you understand it. If it happens that you don't understand the overview, or parts of it, you can read a more comprehensive analysis specifically relating to certain issues you may have.

Just to give you a perspective of my educational background, and how I am actually able to do this blog to a good standard (and thus not give you any false information, which could completely screw you over for the coming exams), I am a top achieving student in my school. For all of my subjects, my predicted grades are A*'s, with the exception of Chemistry and Physics (predicted A for both). I achieved an A in statistics in year 9, an A in biology last year, an A* in Maths last year as well as an A* in English Language. This year, I will be doing Additional Mathematics (which, as far as I know, isn't an actual 'GCSE', but a bridge between A level and GCSE), Chemistry, Physics, English, History, Music, Resistant Materials and Spanish.

It does sound rather cocky, but it's only there so you know that it's coming from a decent source. I hope you find this useful to read, and please leave some comments if you find any errors in my writings or anything you think can be added/improved.