Sec 4 IP Finals Math Summary (2023 batch)

Update: we got A2 for math CONTENTS Surds Inequalities Simultaneous inequalities Indices and Exponential Functions Solving Graphs Logarithms Solving Proving not defined Graphs Discriminant and Roots Prove there are no real roots. For y to be always increasing/decreasing. To find values where (expressions) have no intersection Find range of values of k for which f(x) is always positive/negative Probability Polynomials and partial fractions Factor and remainder theorem Splitting into partial fractions Improper fractions Special methods of substitution Circular Measure Circle properties Circle angle properties Proving circles (do not) intersect Trigonometric Functions and Graphs Drawing parabola Finding asinbx+c Transformation Translation Scalling // Reflection (Further) Trigo identities and equations

Proving equations General steps General methods Finding cosb given cosa Diagrams Solving Bearings Solving Modulus Solving (Further) Differentiation and Applications Solving Finding minimum/maximum area/volume Finding change over time (Further) Integration and Applications Solving Proving an integral is not defined (i.e has an asymptote) Special methods Tangents and Normals Find equation of tangent at x=k Kinematics Linear Law Binomial Theorem The General Term Finding unknowns given first few terms Vectors Surds Always rationalise denominator. CHECK VALIDITY FOR ALL EQUATIONS especially when there is x 2 or y 2 . Inequalities Simultaneous inequalities 1) Solve separately 2) Both solutions are related by ‘and’ not ‘or’

3) Use number line to find common values. 4) Check Validity (LHS=RHS) Indices and Exponential Functions Solving 1) e |x| < 2 a) |x| < ln2 b) x < ln2 or x > -ln2 c) -ln2 < x < ln2 2) Replacing ln(f(x)), log(f(x)), x y with k to solve quadratically. Graphs Logarithms Solving 1) Use properties of log/ln to simplify. a) log (ab) = loga + logb b) log (a/b) = loga - logb c) log a b = lgb/lga d) alogb = logb a 2) Equate both sides to a single log/ln 3) Equate one side to log/ln.

Proving not defined 1) Since (expression) is not defined when (denominator) = 0, 2) (expression) is not defined when (solve denominator). 3) Since (equation) is not continuous at (solved value in denominator), 4) It is not possible to evaluate … Graphs Discriminant and R