Perfect 36 - ACT Math

Learn the basics of right triangles, including the 90-degree angle, identifying the hypotenuse, applying the pythagorean theorem, and using sine, cosine, and tangent.

Explore right triangle concepts through sine, cosine, and Pythagoras to compute heights, distances, and angles, with application examples like ladders, towers, and observer distances.

Explore practical trigonometry problem solving using identities, sine, cosine, tangent, secant, and cosecant, with right triangle reasoning, quadrant signs, and Pythagorean triples to find exact values.

Explore squares and rectangles, their properties, and how to find area and diagonals. Apply the concepts to word problems with quizzes to improve accuracy.

Solve quiz questions on squares and rectangles using area, diagonal, and perimeter formulas, with real-world problems like fencing a rectangle farm and changing dimensions.

Explore the basics of parallelograms, rhombuses, and trapezoids, including properties of opposite sides, diagonals, and area calculations using base and height or the trapezoid formula.

Solve parallelogram, rhombus, and trapezoid quiz questions by applying area formulas, diagonal relations, height and base calculations, and properties like bisecting diagonals and trapezoid similarity.

Learn the fundamentals of angles, including complementary and supplementary pairs and vertical angles. Explore corresponding and alternate angles, straight-line relations, and angle sums in triangles and quadrilaterals.

Learn how to solve angle problems using supplementary and complementary relationships, straight-line sums, parallel lines, bisectors, and vertical angles to ace ACT math questions.

Explore circle basics—radius, diameter, chords, arcs, center, sectors, and segments—and learn arc length and sector area formulas using 22/7 for pi.

Solve circle and mensuration quiz problems focusing on radius and diameter, chords and arcs, segments and sectors, inscribed shapes, and area calculations using pi (22/7).

Explore circle properties by deriving equations from center location (origin, x-axis, y-axis, or general h, k) and radius, and examining tangent, chord, and angle relations.

Explore circle properties through solving quiz-style problems: center and radius, standard form and origin equations, tangent lines, and power of a point with intersecting chords.

Explore basics of cube, cuboid, and sphere, including faces, edges, surface area, and volume. Learn diagonals, radius and diameter, hemisphere, and how changes in side length affect area and volume.

Solve quiz problems on cubes, cuboids, and spheres using volume, surface area, and diagonals, applying radius and dimension relationships from the lecture.

Solve quiz-style problems on polygons and irregular shapes, covering regular polygons, octagons, angle sums (interior and exterior), diagonals, and side lengths.

Explore the four fundamental operators and the modulus and absolute value, and learn how signs change with negative numbers when moving terms across equations.

Solve problems on fundamental operators and absolute values, mastering signs, addition and subtraction, and the modulus operator. Practice evaluating expressions with brackets, including modulus and absolute value applications.

Master the order of operations with PEMDAS, applying parentheses, exponents, and the left-to-right rule for multiplication, division, addition, and subtraction.

master the PEMDAS rule by solving varied expressions from the lecture, applying parentheses, exponents, division, multiplication, and addition/subtraction to achieve quick, accurate results.

Explore basics of decimals and fractions, including proper, improper, and mixed forms; convert between mixed and improper fractions and decimals; perform addition, subtraction, multiplication, and division with decimals and fractions.

Master decimals and fractions with practical problem solving, including converting to improper fractions, finding common denominators, comparing values, and applying percentage conversions.

Explore exponent rules and exponential notation through solving practice problems, simplifying expressions with bases and powers, and applying base equivalence to find unknowns.

Learn the basics of finding the value of a variable by solving equations, isolating the unknown, and moving constants to the opposite side to determine x.

Substitute the given values for x, y, and z into the expression x^2 + 2y - z^3, explain how even and odd powers affect the result, and compute the final value of 39.

Develop fluency in substituting values for variables, evaluating expressions, handling signs and powers like cubes, and solving varied algebra problems with examples.

Explore the basics of polynomials, including algebraic expressions, degree as the highest power, linear, quadratic, and cubic forms, and multiplying binomials via foil.

Explore polynomials by determining degree and type, expanding and factoring, and finding roots using sum and product relationships.

An introduction to simplification in algebra, covering simplifying expressions, exponents, and word problems, with examples and practice quizzes to practice finding values and reducing terms.

Master simplification of polynomials by combining like terms, identifying constants and coefficients, and solving practice quiz questions to improve accuracy and confidence.

Learn to solve word problems by translating text into equations, using variables and algebraic expressions, then substitute values to find solutions, with practice on ACT Math topics.

Master solving word problems by identifying data, forming equations, and applying basic algebra to money, time, speed, and distance scenarios.

Explore the basics of factorization for numbers and polynomials, learn to identify and factor common terms, and apply quadratics and higher-degree factoring to solve problems.

Master factorization techniques for polynomials, solve quadratics by factoring, use identities like a^2+2ab+b^2 and difference of squares to identify factors.

Master the basics of the greatest common divisor by exploring the Euclidean algorithm and prime-factorization methods, with examples like gcd(2,4,6) and gcd(18,24,36) to sharpen problem-solving skills.

Explore greatest common divisor concepts using prime factorization and common factors to solve real problems, from gcd of 96 and 156 to packing boxes and budgets.

Master the basics of the least common multiple, using prime factorization with the highest powers and a fraction method from lcm of numerators over gcd of denominators, including decimals.

Explore least common multiple techniques, including prime factorization, gcd-lcm problems, and practical applications like timing events and fair division, with worked examples.

Explore arithmetic and geometric sequences, identify common difference and common ratio, learn nth-term and sum formulas, and recognize harmonic sequences through reciprocals.

Master arithmetic and geometric sequences by applying common difference and common ratio to solve quiz-style problems, compute sums, and determine terms.

Explore the basics of ratio and proportion, including simplifying ratios, distinguishing ratios from fractions, and recognizing direct and inverse proportionality with real examples like speed, distance, and time.

Master averages as the central value using the sum divided by count formula. Learn to solve for unknowns like X and see how adding or removing data shifts the average.

Master averages for act math through solving quiz questions on scores, prices, weights, and ages, with step-by-step approaches to compute means and understand their applications.

Master percentages by converting fractions to percentages and computing percent of a number using the hundred rule. Explore examples like 75%, 25%, 40% of 500, and 20% of 80.

Learn to solve percentage problems through quiz-style questions, including calculating percentages, discounts, comparisons, and percent increases.

Learn to extract information from data in pie charts, bar graphs, line graphs, and other pictorial forms, then answer interpretation questions on percentages, differences, and totals.

Solve data interpretation questions by extracting data from tables, pie charts, and bar graphs, and calculate percentages, ratios, and interpolation to prepare for the ACT math exam.

Differentiate permutation and combination: order matters in permutations, but only selections count in combinations. Apply factorial formulas for nPr and nCr to count arrangements and selections.

Learn counting techniques for practical problems using combinations, permutations, and the multiplication rule, illustrated with candy, ice cream, gifts, digit codes, train routes, word forms, and team selections.

Learn probability basics, including sample space, outcomes of coin tosses, calculating heads probability 0.5, not getting five 5/6, and distinguishing independent from dependent events with examples of two coins.

Explore probability through diverse examples: drawing from a 52-card deck, identifying diamonds or kings of spades, using combinations, and counting outcomes in coin tosses, multiples of four, and primes.

Explore the types of numbers by solving prime, rational, irrational, and complex-number problems, and classify numbers through examples drawn from ACB Masters quiz questions.

Learn square roots and cube roots by reviewing squares and cubes and identifying perfect squares and perfect cubes. Apply root extraction to simplify expressions with examples.

Solve and simplify square root and cube root problems using prime factorization, identify perfect squares and cubes, and estimate decimal values.

Master basics of time and distance using distance equals speed times time, with unit conversions. Apply the average speed formula and solve boats and streams and trains crossing problems.

Apply speed equals distance over time to solve time and distance questions, compute average speeds, and analyze travel scenarios such as meetings, upstream and downstream movement, and combined distances.

Learn how time and work problems reveal that work is inversely proportional to time and increases with more workers. Master calculating individual and combined work rates using W and time.

Solve time and work problems by calculating individual and combined work rates, using reciprocals and proportions to find days required for tasks across workers, editors, machines, and grazing cows.

Solve function composition and substitution problems using f(g(x)) and f(x) by evaluating polynomials and piecewise definitions, with practical act math practice questions.

Learn to derive equations from graphs using slope, intercepts, and vertex form; analyze lines, quadratics, and absolute value graphs, and verify solutions by substitution.

Explore foundational logarithm identities, including log addition and subtraction with the same base, and apply change-of-base formulas and inverse relationships to simplify problems.

Apply key log identities to solve quiz-style logarithm questions, using base changes, anti-log, and identity properties to compute values.