Explore every episode of the podcast Exam Prep Rise

Lesson twenty eight builds probability out of counting. It defines probability as favourable outcomes over total outcomes when all outcomes are equally likely, insists that numerator and denominator be counted the same way, and drills the complement rule for at least one questions. It covers the union rule, mutually exclusive and independent events, selection problems built from products of combinations, and the zero to one size check. Lesson 28 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 establishes the two identities that drive this topic, that twice the middle term equals the sum of the outer two in an A.P. and the middle term squared equals their product in a G.P. She covers the AM–GM inequality, inserting k means to build a k plus two term progression, and mixed problems solved with the a minus d, a, a plus d substitution, warning against discarding a valid quadratic root. Lesson 21 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.

Lesson 150 teaches Simpson's rule for MATSEC Paper Two numerical methods. Sarah Mitchell derives the strip width over three times ends, plus four times odd ordinates, plus two times inside evens, and explains why the number of strips must be even. She drills the coefficient check totalling three times the strip count, the exactness for cubics, and layout that protects method marks. Two worked problems follow. Lesson 150 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.

This lesson moves fluently between the point-gradient form, y equals m x plus c, the general form a x plus b y plus c equals zero, and the intercept form. It derives gradients from each, applies the equal-gradient test for parallel lines and the product equals minus one test for perpendicular lines, handles vertical and horizontal special cases, and works a perpendicular bisector and a perpendicular line in full. Lesson 32 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.

Lesson 39 teaches composition of functions for MATSEC Advanced Matriculation Pure Mathematics. It covers the right to left reading of fg of x, forming composites by substituting g of x into f, evaluating from the inside out, the existence condition that the range of g lies inside the domain of f, the resulting composite domain, domain restriction, non commutativity through solving fg of x equals gf of x, and associativity. Lesson 39 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.

This lesson sketches the six trigonometric graphs from memory, covering the periods, zeros and asymptotes of sine, cosine, tangent, secant, cosecant and cotangent. It then explains why sine, cosine and tangent must be restricted to be one to one, states the domain and range of arcsine, arccosine and arctangent, and derives each inverse graph by reflection in the line y equals x, including the arcsine of sine trap. Lesson 46 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 builds the permutation formula from the multiplication principle, showing that n P r equals n factorial divided by the factorial of n minus r, and that arranging all n objects gives n factorial because zero factorial is one. She drills cancelling factorials, the distinctness and no repeats conditions, the n to the power r alternative, circular arrangements using n minus one factorial, and two worked counting problems with their classic wrong answers. Lesson 24 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 derives the three general solution forms for sine, cosine and tangent equations, explaining why sine alternates with minus one to the power n while cosine takes both signs and tangent needs only n pi. She covers principal values, the memorised special cases, multiple angles, and listing solutions inside a stated interval, with two worked radian problems and the marks lost by mixing the forms. Lesson 53 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 teaches arithmetic progressions for MATSEC Advanced Matriculation Pure Mathematics. She covers the nth term formula a plus n minus one times d, both sum formulas, solving simultaneously for a and d from two given terms, proving a sequence is arithmetic, recovering terms from a sum rule by subtracting consecutive sums, and solving quadratics in n for target sums while discarding invalid roots. Lesson 18 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 teaches the three-step method for solving trigonometric equations over a stated interval: isolate the ratio, take the inverse for the principal value, then apply CAST and symmetry. She covers the worked case of two cos theta equals root three, the sine, cosine and tangent symmetry rules, multiple angles, quadratic-type equations, Pythagorean substitution, and why dividing by a trigonometric function destroys marks. Lesson 52 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.

This lesson shows how to locate where two straight lines cross by solving their equations simultaneously, and how to find the acute angle between them using the modulus form of the tangent formula. It covers parallel and identical line cases, the perpendicular breakdown when the denominator is zero, vertical lines handled by inclination angles, angle bisectors from equal perpendicular distances, and testing three lines for concurrency. Lesson 33 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 derives the tangent at a point on a circle from the perpendicular radius property, then finds tangents of a given gradient using the perpendicular distance from the centre and the zero discriminant test. She covers the two equal tangents from an external point, and the tests for external contact, internal contact and orthogonality of two circles. Worked examples cover a tangent line y equals two x plus k and two circles that touch externally. Lesson 37 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 builds the three Pythagorean identities from a unit circle, showing that dividing sine squared plus cosine squared equals one by cosine squared gives one plus tangent squared equals secant squared, and by sine squared gives the cotangent version. She covers the quotient and reciprocal identities, the one side only rule for proofs, difference of two squares factorising, and the conjugate trick, then proves two standard identities. Lesson 48 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 teaches the four transformations of y equals f of x, showing that changes inside the bracket act on x in reverse reading order while changes outside act on y in reading order. She covers translations, the reciprocal horizontal stretch, the vertical stretch that fixes roots, both reflections, and the safe order for a times f of b x plus c plus d, with two worked sketching problems. Lesson 30 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.

An edge-weight lesson on the small angle approximations for sine, tangent and cosine in radians. It states sine x approximately x, tangent x approximately x, and cosine x approximately one minus x squared over two, explains why cosine needs a second order term, applies them to limits such as sine three x over x equals three and one minus cosine two x over x squared equals two, and traces the results to truncated Maclaurin series with rapidly shrinking error. Lesson 55 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.

This lesson derives the repeated object permutation formula, n factorial divided by the factorial of each repetition count, and explains the overcount it removes. It works MISSISSIPPI as eleven factorial over four factorial times four factorial times two factorial, giving 34650, then extends the method to together restrictions, fixed positions, and lattice routes counted as sequences of identical steps. Two worked problems drill the block trap and a four by three grid. Lesson 26 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 teaches the shape and behaviour of exponential and logarithmic graphs for MATSEC Advanced Matriculation Pure Mathematics. She covers why a to the power x always passes through zero comma one, how e to the x and natural log reflect in the line y equals x, the log laws, converting any base to base e, and taking logs to solve for an unknown exponent, with two worked problems and the marks examiners award. Lesson 44 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.

Lesson 148 drills the Newton Raphson iteration, x n plus one equals x n minus f of x n over f dash of x n, for the two iterations allowed. It covers stating x nought from a preceding sign change, differentiating carefully, carrying six decimal places before rounding, the tangent picture behind fast convergence, failure when f dash is zero or tiny, and confirming accuracy by a sign change half a unit either side. Two worked examples, cubic and logarithmic. Lesson 148 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 solves x squared minus four x plus thirteen with a negative discriminant, reading the root of minus thirty six as six i. She then teaches the conjugate root theorem for real coefficients, builds the real quadratic factor from the pair using twice the real part and the modulus squared, divides a cubic by it, and uses Vieta and real-imaginary splitting to recover unknown coefficients. Lesson 59 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 builds the two workhorse formulas of a geometric progression: the nth term a r to the power n minus one, and the sum of n terms a times one minus r to the power n over one minus r, valid when r is not one. She drills the divide-two-equations trick, the r bigger than one rearrangement, log inequalities with a flipped sign, and depreciation as a G.P. in disguise. Lesson 19 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 teaches the modulus function as distance from the origin, defined piecewise as x when x is at least zero and minus x below zero. She covers case-splitting, squaring both sides, checking for false solutions, sketching by reflecting negative parts upward, the V-shaped vertex, and the two standard inequality forms, noting that nested moduli are outside the MATSEC syllabus. Lesson 41 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.

This lesson shows candidates when an inverse function exists, why a domain must be restricted to make a function one-one, and how to find f inverse by setting y equal to f of x, making x the subject and swapping letters. It covers stating the domain and range of the inverse, the verification property, reflection in the line y equals x, completing the square before restricting a quadratic, and the reversed order of a composite inverse. Lesson 40 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 teaches the standard method for square-rooting a complex number: set the quantity a plus b i squared equal to z, expand, and equate real and imaginary parts to get a squared minus b squared and two a b. She works minus eight plus six i, shows why the negative root of the quadratic in a squared is discarded, adds the modulus shortcut, and drills the sign-pairing trap on three plus four i and five minus twelve i. Lesson 58 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.

Lesson 38 defines a function as a rule giving exactly one output per input, distinguishes domain from range, and covers the three notations MATSEC uses. It shows how to exclude zero denominators and negative square roots, test injectivity algebraically and by horizontal line, judge surjectivity against a stated codomain, find a quadratic range by completing the square, and recognise a bijection. Lesson 38 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 teaches the four factor formulae that convert sums and differences of sines and cosines into products, and the reverse identities that turn products back into sums. She covers the half-sum and half-difference setup, the missing minus sign in the cosine difference, evaluating sine seventy-five plus sine fifteen as root six over two, and choosing the right direction for integration versus equation solving. Lesson 51 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 teaches the perpendicular distance formula for MATSEC Advanced Matriculation Pure Mathematics: the modulus of a x-one plus b y-one plus c over the square root of a squared plus b squared. She stresses rewriting the line in general form first, reading the unsigned value to decide which side a point lies on, the origin and parallel-line shortcuts, finding the foot of the perpendicular, and comparing the distance from a circle's centre with its radius. Two worked problems close the lesson. Lesson 34 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 teaches the two equations of a circle for MATSEC Paper One. She moves between centre-radius form and the expanded form with two g x and two f y, reading the centre as minus g, minus f and the radius as the square root of g squared plus f squared minus c. She covers completing the square, the positivity condition, dividing through, the parametric point, three-point fitting and the diameter shortcut. Lesson 36 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 builds the three compound angle formulas for sine, cosine and tangent, stressing that cosine and tangent flip the sign on the right-hand side. She splits fifteen degrees into forty-five minus thirty to get cosine fifteen as root six plus root two over four, works tangent seventy-five and an obtuse-angle sine problem, and explains why tangents multiplying to one mean a right angle. Lesson 49 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 the trapezium rule as h over two times the first and last ordinates plus twice every ordinate between them, with h equal to the range divided by the number of strips and n strips giving n plus one ordinates. She works root one plus x squared over four strips and the natural log of x over five ordinates, and shows how concavity decides over- or underestimation. Lesson 149 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 teaches the standard form a plus i b, the single rule that i squared equals minus one, componentwise addition and subtraction, and full bracket expansion for multiplication. She works three plus four i times one minus two i to eleven minus two i, covers equating real and imaginary parts, the four-step cycle of powers of i, and the trap of leaving i inside an imaginary part. Lesson 56 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.

Lesson thirty one builds the three core coordinate tools. Sarah derives the distance formula from Pythagoras, the midpoint as the average of coordinates, and the gradient as change in y over change in x taken in matching order. She covers undefined and zero gradients, gradient as the tangent of the angle, collinearity by equal gradients, isosceles and parallelogram proofs, and ratio division with swapped weights. Two worked problems drill an isosceles proof and a one to three ratio point. Lesson 31 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.

Lesson 47 drills the radian-only formulas for circular sectors. It covers arc length s equals r theta, sector area one half r squared theta, segment area one half r squared times theta minus sine theta, and the chord two r sine of theta over two. It also covers sector and segment perimeters, degree conversion, the arc-over-area shortcut giving two over r, and shaded-region subtraction problems. Lesson 47 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 works the fixed routine for sketching a polynomial: factorise for the x-intercepts, set x to zero for the y-intercept, then solve the derivative equal to zero for the stationary points, which this syllabus caps at three. She classifies them by second derivative or sign test, reads the arms off the leading term alone, and ties even-only powers to y-axis symmetry and odd-only powers to half-turn symmetry about the origin. A cubic and a quartic are sketched in full. Lesson 29 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 plots complex numbers on the Argand diagram and converts them to polar form. She builds the modulus from Pythagoras, fixes the principal argument in the interval from minus pi to pi, and drills the quadrant adjustments of pi minus alpha, alpha minus pi, and minus alpha. Worked examples cover one plus i, minus one plus root three i, and minus three minus three i, alongside the inverse tangent trap and the conjugate rule. Lesson 60 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 teaches n C r for selections where order does not matter, equal to n factorial over r factorial times n minus r factorial. She separates selections from arrangements, links n C r to n P r over r factorial, multiplies pools such as ten C two times seven C three, uses the symmetry n C r equals n C n minus r, and handles at least and at most by case splits or the complement. Lesson 27 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 teaches radian measure, converting with pi over one hundred and eighty in either direction, and drills the CAST rule for signs in all four quadrants. She covers the memorised exact values for pi over six, pi over four and pi over three, the three reciprocal functions, reference angles for obtuse and reflex angles, periodicity of two pi and pi, and odd and even symmetry. Lesson 45 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.

This lesson teaches counting arrangements under adjacency restrictions. It works the block method, where k objects glued inside n give n minus k plus one factorial times k factorial, then the complement for objects that must not be adjacent, then the gap method, placing restricted objects into the m plus one gaps around m free objects. Two worked problems cover the word number and a shelf of textbooks and novels, with the traps named. Lesson 25 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.

Compresses a cosine theta plus b sine theta into one wave, R cosine of theta minus alpha, where R is the positive square root of a squared plus b squared and alpha is the inverse tangent of b over a. Covers the four equivalent forms, maximum R and minimum minus R, solving by dividing through by R, the no-solution test when the modulus of c exceeds R, and reciprocal expressions. Lesson 54 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 the two counting principles behind every enumeration question on Paper One. She shows the and-then versus or test, multiplies counts from separate pools such as ten choose two times seven choose three, splits at-least conditions into mutually exclusive cases before adding, handles dependent stages with reduced counts, and gives the n to the power r rule when repetition is allowed. Two worked problems name the double-counting trap. Lesson 23 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 classify a function by substituting minus x and comparing with f of x, why even means mirror symmetry in the y axis and odd means a half turn about the origin, and why most functions are neither. She covers period as the smallest positive p, the two pi and pi periods of the trig functions, the modulus of k rule, and the sign algebra of products and sums. Lesson 43 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 extends the binomial theorem to negative and fractional indices, where the expansion never terminates and holds only when the modulus of x is less than one. She shows how to factor a to the power n out of a plus b x, derive the range of validity as the modulus of x less than the modulus of a over b, handle descending powers, expand products, and approximate the square root of one point zero four. Lesson 22 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.

This lesson defines the derivative as the limit, as h tends to zero, of the difference quotient, and identifies that limit as the gradient of the tangent. It differentiates y equals x squared from first principles, then introduces the power rule for every real n, the linearity of differentiation, and the rewriting of roots and reciprocals as powers. Two worked problems cover a first principles proof and a negative power sign trap. Lesson 62 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 teaches when an infinite geometric series has a sum, insisting the modulus of the common ratio be strictly less than one before the formula first term over one minus r is quoted. She derives it from r to the power n tending to zero, sums six plus two plus two thirds to nine, handles a ratio of minus one half, and works a quadratic with a rejected root and a recurring decimal. Lesson 20 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 defines a rational function as one polynomial over another non-zero polynomial, with the domain excluding every zero of the denominator, then separates proper from improper by comparing degrees. She drills polynomial long division beat by beat, insists on zero coefficients for missing powers, checks results by rebuilding the numerator and by the remainder theorem, and reads horizontal, oblique and vertical asymptotes straight off the divided form. Lesson 42 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.

An edge topic on Paper II, taught fast and exactly. Sarah builds the Maclaurin series, then uses the exponential, logarithmic, binomial, sine and cosine expansions to estimate e^0.3 as 1.3498 and ln 1.2 as 0.182 to three decimal places. She states every validity condition, approximates the integral of e^(-x^2) from 0 to 0.2 as 0.1974, and shows how an alternating series bounds its own error. Lesson 151 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.

This lesson shows how to turn counting into probability when every selection is equally likely, dividing favourable combinations by total combinations of the same size. It distinguishes combinations from permutations, builds favourable counts by splitting a pool into categories and multiplying, works the two-aces case as six over one thousand three hundred and twenty-six, and covers stating the randomness assumption and checking plausibility. Lesson 152 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 teaches how multiplication and division behave in polar form: moduli multiply and arguments add, moduli divide and arguments subtract. She covers bringing arguments back into the principal range from minus pi to pi, the stretch-and-rotate picture on the Argand diagram, multiplication by i as a ninety degree turn, reciprocals, De Moivre's result for powers, and choosing between polar and a plus i b form. Lesson 61 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 teaches the complex conjugate as the tool that makes division work. She covers reversing the sign of the imaginary part, multiplying top and bottom by the conjugate of the denominator, the identity that z times its conjugate equals a squared plus b squared, the worked division of one plus two i by one minus i, the modulus formula, the product and quotient rules for moduli, and the real and purely imaginary tests. Lesson 57 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.

Lesson 50 derives every double angle identity from the compound angle formulas, covering sine of two theta, the three forms of cosine of two theta, and tangent of two theta with its denominator condition. Sarah works sine theta equals three fifths through to twenty four over twenty five, rearranges cosine of two theta into the power reduction forms, integrates sine squared x from zero to pi over four, and adds half angle quadrant signs and the t substitution. Lesson 50 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 turn a verbal description of a moving point into an equation by letting the point be x and y, then clearing roots and fractions. She names the standard loci, circle, perpendicular bisector, angle bisectors, the circle of Apollonius, and the circle on a segment as diameter, then eliminates parameters by substitution and by the identity cos squared plus sin squared equals one, and insists on stating restrictions. Lesson 35 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.