Exam Prep Rise

Derives the polar area formula, one half the integral of r squared with respect to theta from alpha to beta, and shows how to pick limits that sweep a region exactly once. Covers the double angle substitutions, symmetry shortcuts, outer squared minus inner squared between two curves, intersections by equating radii, and the hidden intersection at the pole. Worked examples cover one petal of a four petal rose, and a circle minus cardioid area of pi. Lesson 132 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise. Watch the video course: https://exampreprise.com/courses/mt-matsec-am-pure-mathematics-fundamentals Free practice questions: https://exampreprise.com/practice/mt-matsec-am-pure-mathematics Always confirm the current test plan, eligibility rules, fees and scheduling details with the official test provider before you register.

Sarah Mitchell shows how to move a curve between Cartesian and polar form using x equals r cos theta, y equals r sin theta and x squared plus y squared equals r squared. She derives the polar equation of a general line, the special cases x equals k and theta equals a constant, and the multiply-by-r trick that turns r equals two a cos theta into a circle of radius a centred at a comma zero, plus the pole and extra-branch traps. Lesson 131 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise. Watch the video course: https://exampreprise.com/courses/mt-matsec-am-pure-mathematics-fundamentals Free practice questions: https://exampreprise.com/practice/mt-matsec-am-pure-mathematics Always confirm the current test plan, eligibility rules, fees and scheduling details with the official test provider before you register.

Sarah shows how to sketch r as a function of theta from a table of values taken every thirty or forty five degrees, and how to halve that work using symmetry in the initial line for cosine and in theta equals pi over two for sine. She covers pole angles and tangents, maximum and minimum r, restricted domains, the circle, cardioid, limacon and rose, and choosing the tracing interval. Lesson 130 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise. Watch the video course: https://exampreprise.com/courses/mt-matsec-am-pure-mathematics-fundamentals Free practice questions: https://exampreprise.com/practice/mt-matsec-am-pure-mathematics Always confirm the current test plan, eligibility rules, fees and scheduling details with the official test provider before you register.

Sarah teaches how to plot a point given as r and theta by turning anticlockwise from the initial line, then converting with x equals r cosine theta, y equals r sine theta, r equal to the square root of x squared plus y squared, and tangent theta equal to y over x. She drills the inverse tangent quadrant trap, the principal range, negative radii, and the pole. Lesson 129 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise. Watch the video course: https://exampreprise.com/courses/mt-matsec-am-pure-mathematics-fundamentals Free practice questions: https://exampreprise.com/practice/mt-matsec-am-pure-mathematics Always confirm the current test plan, eligibility rules, fees and scheduling details with the official test provider before you register.

Sarah derives reduction formulae with integration by parts, relating I sub n to I sub n minus one or n minus two, and stresses computing the base case I sub zero or I sub one separately. She contrasts the vanishing definite boundary term with the surviving indefinite one, uses the Pythagorean peel for trig powers, and works two examples ending at three pi over sixteen and e minus two. Lesson 128 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise. Watch the video course: https://exampreprise.com/courses/mt-matsec-am-pure-mathematics-fundamentals Free practice questions: https://exampreprise.com/practice/mt-matsec-am-pure-mathematics Always confirm the current test plan, eligibility rules, fees and scheduling details with the official test provider before you register.