RI C1 Basics Lect Notes

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 ________________________________ Chapter 1: Assumed Knowledge Page 1 of 37 Chapter 1: Basics CONTENT FROM O LEVEL ADDITIONAL MATHEMATICS The following content is stated as assumed knowledge in your 9758 H2 Mathematics syllabus document: ALGEBRA A1, A2 Quadratic functions; equations and inequalities • Finding the maximum or minimum value of a quadratic function using the method of completing the square • conditions for a quadratic equation to have: – two real roots, two equal roots, no real roots • conditions for ax2 + bx + c to be always positive (or always negative) • solving simultaneous equations in two variables by substitution, with one of the equations being a linear equation A3 Surds • four operations on surds, including rationalising the denominator • solving equations involving surds A4 Polynomials and partial fractions • multiplication and division of polynomials • use of remainder and factor theorems • partial fractions with cases where the denominator is not more complicated than: – (ax + b)(cx + d) – (ax + b)(cx + d)2 – (ax + b)(x2 + c2) A6 Exponential and Logarithmic functions • Exponential and logarithmic functions ax, ex, loga x, ln x and their graphs, including – laws of logarithms – equivalence of y = ax and x = loga y – change of base of logarithms • Simplifying expressions and solving simple equations involving exponential and logarithmic functions

Raffles Institution H2 Mathematics 2025 Year 5 ______________________________________________________________________________________________ ________________ Chapter 1: Basics Page 2 of 37 GEOMETRY AND TRIGONOMETRY G1 Trigonometric functions, identities and equations • six trigonometric functions, and principal values of the inverses of sine, cosine and tangent (which will be discussed in the chapter on Functions) • trigonometric equations and identities (see Formulae List) • expression of in the forms and . G2 Coordinate geometry in two dimensions • coordinate geometry of the circle with the equation in the form CALCULUS (We will revisit this section in Chapters 5 and 8) C1 Differentiation and Integration • derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point • derivative as rate of change • derivatives of xn for any rational n, sin x, cos x, tan x, ex and ln x, together with constant multiples, sums and differences • use of Chain Rule • derivatives of products and quotients of functions • increasing and decreasing functions • stationary points (maximum and minimum turning points and points of inflexion) • use of second derivative test to discriminate between maxima and minima • connected rates of change • maxima and minima problems • integration as the reverse of differentiation • integration of xn for any rational n, ex, sin x, cos x, sec2 x and their constant multiples, sums and