Vectors, lines and planes
Chapter 70 of 15 strong
RESTS ONRepresent directed plane vectors and solve component linear combinationsFOUNDATIONSCalculate exact plane-vector magnitudes directions and unit vectors with nonzero conditionsFOUNDATIONSCalculate signed scalar and vector projections and perpendicular decompositionsFOUNDATIONSSolve a pair of simultaneous linear equations for the shared (x, y)FOUNDATIONSConstruct direct, contrapositive and contradiction arguments with justified stepsCH 1Calculate the determinant of a 2 × 2 matrixFOUNDATIONSSolve a non-singular system of three or four linear equations by exact elimination or substitution, preserving variable order and checking every original equationFOUNDATIONSIdentify the inner and outer functions of a composite, differentiate each, multiply the outer derivative evaluated at the inner function by the inner derivative, and write the result in the requested factorised formFOUNDATIONSIdentify the numerator and denominator, apply (v u' − u v')/v², preserve the squared denominator, and state the non-zero denominator conditionFOUNDATIONSConvert Cartesian,parametric and polar conic forms retaining restrictionsFOUNDATIONSState the complete anti-derivative family with one arbitrary additive constant, and verify that the constant disappears under differentiationFOUNDATIONSCalculate relative velocity future coincidence and closest approach under constant motionFOUNDATIONS
Three-dimensional vector algebra
Cross products and geometric proof
Lines and planes
Parametric paths and vector calculus