Sequences and series notes
Below are some sequences and series notes. They should help when working with sequences and series. A series of numbers following a set rule is called a sequence. [IMAGE] …is an example of a sequence Each number in a sequence [...]
Sketching curves notes
This document contains sketching curves notes. Below are some of the standard graphs that you should be able to recognise. [IMAGE] [IMAGE] [IMAGE] Transforms [IMAGE] …is a translation of –a in the x-direction. [IMAGE] …is a translation of +a in [...]
Algebra and functions notes
Here are a few notes that are useful when working with algebraic expressions and functions. Remember you simplify an expression by collecting like terms You can also simplify expressions by using rules of indices (powers) [IMAGE] [IMAGE] [IMAGE] To expand [...]
Equation of a line
This chapter explores equation of a line. It covers understanding that y – y = m(x = x1) is the equation of a straight line, finding the equation of a line using gradient and one point, finding the equation of [...]
Integration: Negative areas
This chapter explores negative areas. It covers understanding that areas below the x axis are negative, calculating areas under a curve, some or all of which may be under the x axis. Before attempting this chapter you must have prior [...]
Tangent graphs
This chapter explores graphs. It covers sketching the tangent graph and solving simple equations such as tan x = 0.2. Before attempting this chapter you must have prior knowledge of basic trigonometry and sine and cosine graphs. What is the [...]
Sine and Cosine Graphs
This chapter explores sine and cosine graphs. It covers sketching sine and cosine graphs, finding angles which have same sine or cosine values, and solving simple equations such as sin x = 0.6 You must have prior knowledge of basic [...]
Trigonometric Equations 2
This chapter explores trigonometric equations. It covers solving harder trigonometric equations using identities. Before attempting this chapter you must have prior knowledge of solving trigonometric equations and must go through trigonometric equations 1 Solving sin x = 1/4 Suppose we [...]
Solving Equations With Algebraic Fractions
This chapter explores solving equations with algebraic fractions. It covers understanding how to solve equations involving fractions, working with denominators with either constants or linear factors. Before attempting this chapter you must have prior knowledge of expanding brackets and factorising [...]
Solving equations using logs
This chapter explores solving equations using logs. It covers solving equations and inequalities usig logs, fiding intersection s of exponential graphs uing logs. Before atempting this chapter you must have prior knowledge of logs basics. Solve equations using logs on [...]