Rational and quotient functions
Chapter 20 of 5 strong
RESTS ONMultiply polynomials using complete distribution and exponent laws, then collect equal powersFOUNDATIONSAdd or subtract polynomials by aligning equal powers and combining their coefficients, including zero coefficients for missing powersFOUNDATIONSSolve a pair of simultaneous linear equations for the shared (x, y)FOUNDATIONSConstruct direct, contrapositive and contradiction arguments with justified stepsCH 1Calculate second derivatives and analyse concavity,inflections and linked derivative graphsCH 4Identify the numerator and denominator, apply (v u' − u v')/v², preserve the squared denominator, and state the non-zero denominator conditionFOUNDATIONSRecall and apply the natural-logarithm derivative in its base forms — d/dx log_e(kx) = 1/x and d/dx log_e(g(x)) = g'(x)/g(x) — identifying the inner function g, using log laws first where that simplifies, and stating the domain on which the rule appliesFOUNDATIONSIdentify the asymptotes, excluded domain and range values, branch orientation, intercepts and end behaviour of a translated and dilated reciprocal functionFOUNDATIONS
Partial fractions and rational structure
Quotient curve sketching