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SL 1.1—Using standard form
SL 1.2—Arithmetic sequences and series
SL 1.3—Geometric sequences and series
SL 1.4—Financial apps – compound interest, annual depreciation
SL 1.5—Intro to logs
SL 1.6—Simple proof
SL 1.7—Laws of exponents and logs
SL 1.8—Sum of infinite geo sequence
SL 1.9—Binomial theorem where n is an integer
AHL 1.10—Perms and combs, binomial with negative and fractional indices
AHL 1.11—Partial fractions
AHL 1.12—Complex numbers – Cartesian form and Argand diag
AHL 1.13—Polar and Euler form
AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers
AHL 1.15—Proof by induction, contradiction, counterexamples
AHL 1.16—Solution of systems of linear equations
SL 2.1—Equations of straight lines, parallel and perpendicular
SL 2.2—Functions, notation domain, range and inverse as reflection
SL 2.3—Graphing
SL 2.4—Key features of graphs, intersections using technology
SL 2.5—Composite functions, identity, finding inverse
SL 2.6—Quadratic function
SL 2.7—Solutions of quadratic equations and inequalities, discriminant and nature of roots
SL 2.8—Reciprocal and simple rational functions, equations of asymptotes
SL 2.9—Exponential and logarithmic functions
SL 2.10—Solving equations graphically and analytically
SL 2.11—Transformation of functions
AHL 2.12—Factor and remainder theorems, sum and product of roots
AHL 2.13—Rational functions
AHL 2.14—Odd and even functions, self-inverse, inverse and domain restriction
AHL 2.15—Solutions of inequalities
AHL 2.16—Graphing modulus equations and inequalities
SL 3.1—3d space, volume, angles, distance, midpoints
SL 3.2—2d and 3d trig, sine rule, cosine rule, area
SL 3.3—Angles of elevation and depression, bearings
SL 3.4—Circle, radians, arcs, sectors
SL 3.5—Unit circle definitions of sin, cos, tan. Exact trig ratios, ambiguous case of sine rule
SL 3.6—Pythagorean identity, double angles
SL 3.7—Circular functions, graphs, composites, transformations
SL 3.8—Solving trig equations
AHL 3.9—Reciprocal trig ratios and their pythagorean identities. Inverse circular functions
AHL 3.10—Compound angle identities
AHL 3.11—Relationships between trig functions
AHL 3.12—Vector definitions
AHL 3.13—Scalar (dot) product
AHL 3.14—Vector equation of line
AHL 3.15—Classification of lines
AHL 3.16—Vector product
AHL 3.17—Vector equations of a plane
AHL 3.18—Intersections of lines & planes
SL 4.1—Concepts, reliability and sampling techniques
SL 4.2—Histograms, CF graphs, box plots
SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
SL 4.4—Pearsons, scatter diagrams, eqn of y on x
SL 4.5—Probability concepts, expected numbers
SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
SL 4.7—Discrete random variables
SL 4.8—Binomial distribution
SL 4.9—Normal distribution and calculations
SL 4.10—X on y regression line
SL 4.11—Conditional and independent probabilities, test for independence
SL 4.12—Z values, inverse normal to find mean and standard deviation
AHL 4.13—Bayes theorem
AHL 4.14—Properties of discrete and continuous random variables
SL 5.1—Introduction of differential calculus
SL 5.2—Increasing and decreasing functions
SL 5.3—Differentiating polynomials, n E Z
SL 5.4—Tangents and normal
SL 5.5—Integration introduction, areas between curve and x axis
SL 5.6—Differentiating polynomials n E Q. Chain, product and quotient rules
SL 5.7—The second derivative
SL 5.8—Testing for max and min, optimisation. Points of inflexion
SL 5.9—Kinematics problems
SL 5.10—Indefinite integration, reverse chain, by substitution
SL 5.11—Definite integrals, areas under curve onto x-axis and areas between curves
AHL 5.12—First principles, higher derivatives
AHL 5.13—Limits and L’Hopitals
AHL 5.14—Implicit functions, related rates, optimisation
AHL 5.15—Further derivatives and indefinite integration of these, partial fractions
AHL 5.16—Integration by substitution, parts and repeated parts
AHL 5.17—Areas under curve onto y-axis, volume of revolution (about x and y axes)
AHL 5.18—1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx
AHL 5.19—Maclaurin series
Show that b1−a1a1+b1=a−ba+b, for a,b=0 and a=b.
[2]Show that x+h1−x1=−x(x+h)h, for x=0 and x+h=0.
[2]Show that (1+x1)2−(1−x1)2=x4, for x=0.
[3]Prove that a−b=a+ba−b, for distinct positive real numbers a,b.
[3]Prove that x+2x2+x+1=x−1+x+23, for x=−2.
[2]Prove that x−11−x+11=x2−12, for x=±1.
[2]Verify that 1−x1+x−1+x1−x=1−x24x, for x=±1.
[3]Show that x+y1+x−y1=x−y2x, for x=y, x,y>0.
[2]Prove that x−yx3−y3=x2+xy+y2, for x=y.
[2]Prove that n!(n+1)!=n+1, for integer n≥0.
[2]Prove that m+11+m2+m1=m1, where m=0,−1.
[3]Show that a−ba2−b2=a+b, for a=b.
[2]