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MATHEMATICS IB Analysis and Approaches SL (Matura IB 2026)

Prowadzący kurs

Mirosław Malinowski Mirosław Malinowski Prowadzący

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JĘZYK POLSKI online (Matura 2026)
BIOLOGY IB SL&HL (Matura IB 2026)
  • Topic 1: Number and algebra
    • Arithmetic sequences and series. Applications.
    • Geometric sequences and series. Applications.
    • Logarithms and exponents.
    • Proof by contradiction.
  • Topic 2: Functions
    • Concept of a function, domain, range and graph. Odd and even functions. Key features of graphs.
    • Transformations of graphs.
    • Composite functions. Identity function. Finding the inverse function.
    • The quadratic function. Solution of quadratic equations and inequalities.
    • The reciprocal function. Rational functions. Equations of vertical and horizontal asymptotes.
    • Exponential and logarithmic functions and their graphs. Solving equations.
    • Polynomial functions. The factor and remainder theorems. Sum and product of the roots of polynomial equations.
    • Solutions of g(x)≥f(x), both graphically and analytically. Solution of modulus equations and inequalities.
  • Topic 3: Geometry and trigonometry
    • The Sine Rule and the Cosine Rule. Area of a triangle.
    • Solving trigonometric equations in a finite interval. Equations leading to quadratic equations in sinx,cosx or tanx.
  • Topic 4: Probability and statistics
    • Presentation of data (discrete and continuous). Histograms. Cumulative frequency graphs. Box and whisker diagrams.
    • Measures of central tendency. Measures of dispersion. Effect of constant changes on the original data.
    • Linear correlation of bivariate data. Pearson’s product-moment correlation coefficient, r.
    • Equation of the regression line of y on x. Use of the equation of the regression line for prediction purposes.
    • The probability of an event. Calculating probabilities. Combined events. Mutually exclusive events. Independent events. Conditional probability.
    • Discrete and continuous random variables and their probability distributions. Binomial distribution. The normal distribution and curve.
    • Standardization of normal variables (z-values). Inverse normal calculations.
  • Topic 5: Calculus
    • Understanding of limits (convergence and divergence). Definition of derivative from first principles. Higher derivatives.
    • Differentiation of a sum and a multiple of functions. The chain rule for composite functions. The product and quotient rules.
    • Increasing and decreasing functions. Local maximum and minimum points. Points of inflexion with zero and non-zero gradients.
    • Definite integrals. Areas of a region enclosed by a curve y=f(x) and the x-axis. Area between curves.
    • Area of the region enclosed by a curve and the y-axis in a given interval. 
    • Kinematic problems involving displacement s, velocity v, acceleration a and total distance travelled.
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