Singapore Math GCE O Level Additional Math: Complete Course

Explore the shape of a quadratic graph, a parabola with a vertex, showing a minimum when a is positive and a maximum when a is negative.

Learn to complete the square for a quadratic by converting ax^2+bx+c into a(x+g)^2+h, with g=b/(2a) and h=c - b^2/(4a).

Explore the discriminant of ax^2+bx+c: if b^2-4ac>0 there are two real roots and two x-intercepts; if =0 there is one tangent root; if <0 there are no real roots.

Master rationalize denominators with surds: apply conjugates for single-term and two-term quotients, using difference-of-squares to obtain clean, simplified results.

Master adding and subtracting polynomials by combining like terms. Recognize that unlike terms cannot be combined, and practice adding and subtracting terms like x^3, x^2, x, and constants.

This lecture covers division of polynomials, using long division with descending powers and zeros for missing terms, and coefficient comparison, to obtain the quotient and remainder.

Sketch cubic curves with y = a(x - f)(x - g)(x - h) from x-intercepts f, g, h and y-intercept to find a, noting a's sign shapes the max/min order.

Solve cubic equations by factoring, using roots to form factors like x minus alpha, apply the factor theorem, and decompose into a linear times a quadratic by comparing coefficients.

Decompose a polynomial fraction into partial fractions by factorising the denominator into non repeated linear, repeated linear, and non repeated quadratic factors, then solve for the constants.

Learn factorial, denoted by the exclamation mark, where n! equals n×(n−1)×...×1, with examples like 3! and 7!, and using the x! function on scientific calculators.

Learn how to identify bases and exponents, use zero and negative powers, apply fractional exponents and roots, and combine indices when bases or exponents match for multiplication and division.

Explore logarithms by converting between exponential and logarithmic forms, using base a, exponent x, and examples like 3^2=9 and log_3 9=2 to evaluate x.

Explore natural log, or ln, as log base e, and learn that e equals 2.71828; use calculators to compute ln and e^x, and apply ln e^x = x.

Learn to solve equations with unknown exponents by separating terms, applying logarithms, and bringing the exponent down to solve for x, for single-term and multi-term cases.

Learn to solve trig equations by using inverse functions to find the basic acute angle in sine, cosine, or tangent forms, identify quadrants, and compute all degree and radian solutions.

Explore trigonometric identities, including sine, cosine, and tangent sum and difference formulas, with plus minus patterns and practice applying these identities to questions.

Explore double angle identities for sine, cosine, and tangent, including sin 2a = 2 sin a cos a and cos 2a = cos^2 a − sin^2 a.

Compute AB as sqrt(32) units, find the midpoint M(1,7), and determine the gradient -1 for AB.

Understand gradient from y = mx + c; it measures steepness and whether the function increases or decreases, with parallel lines sharing the gradient and perpendicular lines multiplying to -1.