Mastering AMC 10

Master linear equations with step-by-step solutions drawn from past AMC 10 papers, including creating equations from percentages, variables, and unit digits.

Apply the speed formula distance over time to solve average speed problems using piecewise speeds, mph calculations, and fractions across classic AMC 10 scenarios.

Explore arithmetic sequences by identifying the common difference, counting terms, and using the sum formula; apply these concepts to AMC 10 problems and pattern-based sequences.

Explore mean, median, and mode through AMC 10 problems, using totals and counts to compute averages and compare data sets.

Mastering AMC 10 introduces special calculating, covering powers, factorials, absolute value, and repeating decimals with step-by-step examples from contest problems.

Master basic algebraic expressions by exploring simplifications, cancellations, and reciprocal and ratio concepts through a series of example problems.

Compute quiz solutions for the AMC 10 section, including linear equations, arithmetic sequences, mean/median/mode data, and speed and algebra problem-solving.

Master radical operations for AMC 10, including basic operations, simplifying radicals, rationalizing denominators with conjugates, and applying to geometry like the Pythagorean theorem and similar triangles.

Master special triangles, including 45-degree right triangles and a 30-degree, 50-degree angle, using ratios, similar shapes, height and base to compute equilateral triangle and hexagon areas.

Mastering the art of similar triangles, this lecture explores parallel line constructions, height constructions, right triangle scenarios, and area and ratio problems through AMC 10 examples.

Explore how circles and triangles appear together in right, 45-degree, and equilateral configurations, and compute shaded regions using triangle areas, circle areas, and arc segments from past problems.

Explore circle geometry with radii, tangents, central and inscribed angles, and semicircle properties, showing how central angles double inscribed angles and solving tangent and external tangent problems.

Explore linear functions and their graphs in coordinate geometry, including reflections about y = -x, a 90-degree rotation about (1,5), and AMC 10 style slope-intercept and area problems.

Explore 3d shapes such as cones, pyramids, tetrahedrons, and spheres, and learn to compute surface areas and volumes using base, lateral areas, and formulas.

Explore AMC 10 quiz solutions through geometry-focused problems, including calculating shaded areas in triangles and circles, using heights, similar triangles, coordinates, and 3D surface area and volume reasoning.

Expand and factor using the three key formulas—difference of squares, perfect square trinomial, and square of a binomial—and apply them to solve AMC 10 problems and find minima.

Explore expanding and factoring in AMC 10 problems, solving equations by squaring, and deriving integer pairs from area and perimeter relationships.

Master quadratic equations by factoring, completing the square, and the quadratic formula, with examples that yield two solutions like x = 3 or x = -2.

Develop skill in solving quadratic equations via completing the square, tackle real AMC 10 problems, analyze absolute value cases, find real and integer solutions, and compute A minus B.

Apply the quadratic formula to AMC 10 problems, solving for x and simplifying radicals while connecting area and right-triangle relations to identify the valid positive root.

Explore how to compute the mean, median, and mode using AMC 10 style problems, including finding the median of large lists, and identifying the unique mode.

Explore solutions for quizzes on quadratic equations, factoring, and completing the square, including finding pairs, solving for y and x, analyzing means and medians, and summing possible y values.

master counting by multiplication to solve probability problems, including four-digit numbers with even digits ending in zero, and counting paths across multiple levels.

Master the concept of permutation by counting distinct orders with factorials, handle indistinguishable items by dividing by duplicates, and model problems with grouping blocks as illustrated in AMC-style examples.

explain how combinations differ from permutations by using five choose three, then apply to handshakes, probability with book selection, and parity-based grid problems on AMC 10.

Multiply probabilities to analyze independent events and combine their chances. This lecture uses AMC problems to illustrate multiplying outcomes and simplifying complex probability paths.

Mastering AMC 10 uses two-circle and three-circle Venn diagrams to visualize A and B, A or B, and the areas of combined regions for counting problems.

Explore the stars and bars method for counting distributions. Learn to convert problems into stars and dividers and apply it to advanced combinatorics questions with examples.

Explore probability with geometry by analyzing lattice points, unit circles, and triangles to estimate areas and compute probabilities such as Y>X.

Learn to solve AMC 10 quiz questions using permutations, combinations, probability, and geometry with step-by-step explanations and practical solution strategies.

Explore divisibility rules and prime numbers in number theory, analyzing when one plus n is prime and applying tests like the 11 divisibility rule to digit-based problems.

Master prime factorization and counting divisors using exponent-based methods, with practice on factorial-based powers and AMC 10 style divisor problems, including perfect squares.

Explore prime factorization, count factors, and analyze the ratio of sum of divisors to total divisors in AMC 10 problems on pairwise relatively prime triples and factorial factorization.

Explore the modulo operation, using remainders and pattern recognition to simplify powers. Practice modulo six and five through unit-digit probability problems.

Master base numbers and binary, learn how to convert between bases such as two, seven, ten, and sixteen, and analyze digit sums in base seven for numbers at least 2019.

Tackle the AMC 10 quizzes on number theory, covering sums of four-digit numbers divisible by eight, prime factorization, modular arithmetic, and the least common multiple.

Explore special triangles, including 45-45-90 and 30-60-90, plus equilateral triangles, with area formulas and proportional relationships to solve AMC 10 geometry questions.

Master similar triangles and algebra to solve AMC 10 geometry problems, using area calculations, right triangles, and quadratic equations to find unknowns.

Explore quadratic functions in coordinate geometry, uncover parabola properties, axis of symmetry and vertex, and learn to convert to vertex form using completing the square, with AMC-style examples.

Explore coordinate geometry through circle equations, center-radius form, and completing the square to identify centers and radii, plus circle–parabola intersection problems.

Explore coordinate geometry with absolute value functions and piecewise graphs, solving equations across quadrants, analyzing circles, and area calculations bounded by lines and curves.

Explore how to find the radius of the circle inscribed in a triangle by dividing it into three smaller triangles and using their areas.

Learn the triangle centroid, its two-to-one ratio along medians, and how the centroid traces a circle of radius four when a vertex moves on a circle of radius twelve.

Explore geometry quiz solutions for AMC 10, including area calculations via similarity and Pythagorean ratios, right triangles with diameter, circle by-sector concepts, and quadrilateral area in a circle.

Explore geometric sequences, define a_n = a_1 r^{n-1}, derive S_n = a_1(1 - r^n)/(1 - r) and S = a_1/(1 - r) for |r|<1, with AMC 10 examples.

Explore Vieta's formulas as a method for linking a quadratic's roots to its coefficients, deriving r1 + r2 = -B/A and r1 r2 = C/A, with practical problem examples.

Examine higher degree polynomials through worked examples, exploring roots of cubic and quartic forms, and apply coefficient relationships and remainder calculations to solve problems.

Explore defined functions and the floor function, determine f’s range through patterns and examples from past AMC problems, and inspect prime-based values and related properties.

Mastering AMC 10 explores algebra quiz questions, solving quadratics by discriminant and completing the square to find integer values of a, and counting integers that satisfy a nonpositive condition.

Master AMC 10 combinations through casework and symmetry, count scenarios, and apply triangle counting and binary sequence constraints such as no two consecutive zeros and three consecutive ones.

Explore geometry-based probability in AMC 10, solving obtuse triangle probabilities with x+y>1 and x^2+y^2<1, circle regions, and coin flip and unit-square scenarios.

Explore the stars and bars method for distributing ten identical objects among five people using four bars, and apply it to a 96 counting problem with case analysis.

Explore counting techniques in AMC 10 by counting circle pairings with diagonals, color arrangements on a 3x3 grid with no adjacent same colors, and stand-or-sit configurations in eight positions.

Explore AMC 10 probability puzzles driven by symmetric frog moves, calculating the chance to reach a corner or return to the original position using half and one-fourth probabilities.

Analyze quiz problems on probability and symmetry using rotations and reflections. Explore counting methods for consecutive integers sequences and round-robin team standings in AMC 10.

Master prime factorization and divisor counts through AMC 10 problems, examining factors, squares, and multiples to identify patterns across numbers like 36, 81, 999 and 1000.

Identify the greatest common divisor and least common multiple of two numbers using prime factorization and the rule ab = gcd(a,b) × lcm(a,b); apply to two-number problems and counting pairs.

Explore the modular operation and remainders, using digit-sum divisibility rules for nine and five to solve 2017 AMC 10 problems and relate totals to integer averages.

Explore base-k numbers, including base seven, and master converting between base ten and base seven using place-value. Apply geometric sequences and a quadratic equation to solve related problems.

Mastering AMC 10: explore number theory quiz questions by testing primes, and solve a notes pages problem using divisors of 325 and consecutive sheets.