Description
Math tutoring and Math problem solving for curriculums of elementary, middle and high school.- EXAMPLES: Number – Core curriculum : 1.1 Vocabulary and notation for different sets of numbers: natural numbers k, primes, squares, cubes, integers w, rational numbers n, irrational numbers, real numbers o, triangle numbersk = {0, 1, 2, ...} 1.2.- Use of the four operations and brackets 1.3 Highest common factor, lowest common multiple 1.4 Calculation of powers and roots 1.5 Ratio and proportion including use of e.g. map scales 4.51.61.7 Equivalences between decimals, fractions, ratios and percentages 1.8 Percentages including applications such as interest and profit excluding reverse percentages includes both simple and compound interest 1.9 Meaning of exponents (powers, indices) in Standard Form a x 10n where 1 ≤ a < 10 and n∈w Rules for exponents.- .- Quadratics: carry out the process of completing the square for a quadratic polynomial ax2 + bx + c and use this form, e.g. to locate the vertex of the graph of y = ax2 + bx + c or to sketch the graph•find the discriminant of a quadratic polynomial ax2 + bx + c and use the discriminant, e.g. to determine the number of real roots of the equation ax2 + bx + c= 0•solve quadratic equations, and linear and quadratic inequalities, in one unknown• solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic• recognise and solve equations in x which are quadratic in some function of x, e.g. x4 – 5x2 + 4= 0.Differentiation: understand the idea of the gradient of a curve, and use the notationsf’(x), f’’(x), xydd and 22 ddxy • use the derivative of xn (for any rational n), together with constant multiples, sums, differences of functions, and of composite functions using the chain rule• apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (including connected rates of change)• locate stationary points, and use information about stationary points in sketching graphs (the ability to distinguish between maximum points and minimum points is required, identification of points of inflexion is included)