## Math AA SL Spring Group Course

7 Max. Students

NY: 08:00-12:30, UK: 13:00-17:30, Dubai: 16:00-20:30 (4.5 Hours a day incl. 1/2 an hour break) Join our expert tutor, Susovan as he provides you with Math AA SL Spring Revision Tuition. See our detailed Curriculum breakdown below.

For problems using several concepts (e.g. integral of trig functions), they can be covered in either of the three days!

Important: The lesson will solve a lot of actual IB problems!

a^n is a to the power n, e.g. 2^3 = 8

**Day 1:**

- Introduction: Revision of prerequisites: number systems, integers, positive and negative integers, fractions and their decimal representations, rational and irrational numbers, and their symbols wherever needed. Modulus of a number. Examples.
- Number and Algebra I:

* Laws of exponents with integer exponents, rational exponents

* Laws of logarithms.

* Solving exponential equations, including using logarithms.

*Operations with numbers in the form a × 10^k where 1 ≤ a < 10 and k is an integer. - Number and Algebra II:

*Arithmetic and Geometric sequences and series with finite numbers of terms: Use of the formulae for the n-th term and the sum of the first n terms of the sequence. Use of sigma notation for sums of arithmetic sequences. Applications - compound interests.

* Sum of infinite convergent geometric sequences - Number and Algebra III:

Permutations, Combinations, and the Binomial Theorem with integer indices: expansion of (a + b)^n, n ∈ ℕ - Number and Algebra IV: Familiarity with the existence of equation x² + 1= 0 and its solution as the complex number i or -i.
- Number and Algebra V:

*Simple deductive proof, numerical and algebraic; how to layout a left-hand side to right-hand side (LHS to RHS) proof. The symbols and notation for equality and identity. - Number and Algebra VI: Basic familiarity with the fact that there are systems of linear equations.

**Day 2:**

- Functions I:

*Concept of a function, domain, range, and graph. Function notation.

*The graph of a function, Determine key features of graphs, transformations of graphs.

*Composite functions, identity functions, inverse functions. - Functions II:

*Linear functions and straight lines: Different forms of the equation of a straight line. Gradient; intercept

*The quadratic function f(x) = ax² + bx + c: its graph, y-intercept (0, c). Axis of symmetry. The form f(x) = a(x − p)(x − q), x-intercepts (p, 0) and (q, 0). The form f(x) = a (x − h)²+ k, vertex (h, k). Solution of quadratic equations and inequalities. The quadratic formula. The discriminant Δ = b²− 4ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots. - Functions III: The reciprocal function f(x) = 1/x , x ≠ 0: its graph and self-inverse nature. Rational functions and their graphs. Equations of vertical and horizontal asymptotes.
- Geometry and trigonometry I:

*Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere, and combinations of these solids. The size of an angle between two intersecting lines or between a line and a plane. - Geometry and trigonometry II:

*Use of sine, cosine, and tangent ratios to find the sides and angles of right-angled triangles. The sine rule, cosine rule, area of a triangle.

*Applications of right and non-right angled trigonometry, including Pythagoras’s theorem. Angles of elevation and depression.

*The circle: radian measure of angles; length of an arc; area of a sector.

*Definition of cosθ, sinθ in terms of the unit circle. Definition of tanθ as sinθ/cosθ. Exact values of trigonometric ratios of 0, π/6 , π/4 , π/3 , π/2, and their multiples. Extension of the sine rule to the ambiguous case.

*The Pythagorean identity cos² θ + sin² θ = 1. Double angle identities for sine and cosine. - Geometry and trigonometry III: Basic concept of what a vector is.

**Day 3:**

- Statistics and Probability:

*Concepts of population, sample, random sample, discrete and continuous data. Outliers.

*Presentation of data (discrete and continuous): frequency distributions (tables). Histograms, cumulative frequencies. Median, quartile, percentiles etc. Box and whisker plots.

*Measures of central tendency (mean, median, and mode).

*Measures of dispersion (interquartile range, standard deviation, and variance).

*Linear correlation of bivariate data. Pearson’s product-moment correlation coefficient.

*Scatter diagrams; lines of best fit, by eye, passing through the mean point

*Regression, regression lines, and their use for prediction purposes. Interpretation of parameters of regression lines.

* Probability, random samples, conditional probability, independent events, discrete random variables, binomial distribution, its mean, and variance.

*Normal distribution, its curve, normal and inverse normal calculations. - Calculus I:

*Limits and continuity.

*Derivatives, derivatives of power functions, and polynomials. Product, quotient, chain rules.The second derivative.

*Increasing and decreasing functions. Graphical interpretation of f ′(x) > 0, f ′(x) = 0, f ′(x) < 0.

*Tangents and normals at a given point, and their equations.

* Local maximum and minimum. - Calculus II:

*Indefinite integrals. The indefinite integral of x^n (n ∈ ℚ), sin x, cos x, 1/x, and e^x. *Definite integrals, including analytical approach.

*Areas of a region enclosed by a curve. Areas between curves. - Calculus III: Basic knowledge of what a differential equation is.

**Full past paper practice**