ACT Math Prep Course

Compute the perimeter of a 100 by 245 rectangle to determine the fence length, totaling 690.

Factor out x from x^2 - 49x to obtain x(x-49)=0, then apply the zero product property to find x=0 or x=49; the trick is factoring.

Distribute the negative four across the equation, simplify to like terms, move the 4x term to 16x, then solve 12x = -24 to find x = -2.

Learn to solve a system of linear equations using the elimination method by comparing two equations for hamburgers and soft drinks, finding H = 2.80 and S = 1.40.

Compute the rental cost by adding a 20 base fee to 0.24 per mile, yielding total cost 20 + 0.24P, which equals 0.24P + 20.

Compute the five-year average profit from six million per year for three years and eleven million per year for two years, totaling 40 million, yielding eight million as the annual average.

Solve the inequality 18 − 7x < 12 by isolating x and dividing by −7, which flips the inequality to x > 6/7. The answer is option B.

Learn to solve exponential equations by rewriting numbers as a common base, adding exponents for like bases and multiplying when constants lack a base, and cross-out to solve for x.

Apply the midpoint formula by adding two points and halving the sum; using -8 and 22 yields 7, so the correct choice is c.

Practice solving a pre-algebra equation by testing rational candidates; verify with the equation |x^2 - 20| - 4 = 0 and confirm x = 4 satisfies it.

Decompose irregular shapes into primary shapes such as rectangles and squares, then calculate and add their areas to solve pre-algebra questions.

Use the mean formula in this pre-algebra question: four numbers average to 30, smallest is 8; the other three sum to 112, so their average is 112/3.

Solve an elementary algebra probability problem by counting red, blue, and white marbles; not white equals red or blue, with 14 of 24 marbles, probability 7/12.

Learn to convert equations to slope-intercept form by isolating y and moving terms, as shown with 9x minus 13 and a parallel case with negative and positive y.

Apply the slots method to count all one junior and one senior committees by multiplying 134 juniors by 100 seniors, yielding 13400 possibilities.

Solve for y to identify the slope and apply it to parallel lines. Extract the slope -8/7 from y equals 5/7 minus 8x/7; parallel lines share this slope.

discover how to find the slope of a line perpendicular to a given equation by applying the negative reciprocal rule. isolate y to determine the slope from the equation and compute the perpendicular slope, such as -5/6.

Differentiate line types by degree: straight lines are degree one, quadratic curves are parabolas, and cubic curves are degree three; the equation with x squared is not a line.

Rearrange the equation to isolate y, turning it into y = (13/7)x + 16/7, and identify the slope as 13/7.

Compute the minute hand’s travel from 2:10 to 5:30: three full revolutions plus a third of a circumference (radius 9 cm), totaling 60 pi cm.

Draw the points (-2, -2) and (4, -7) on the grid, write them down, then form a right triangle and use the Pythagorean theorem to find the distance as sqrt(136).

Identify the greatest common factor of x^2 y^2 and x y^3, pull out x and y^2 to obtain 75, and recognize 25 and 3 as the cofactors.

set the two equations equal to find their intersection, solve for x, and obtain x = 5, which corresponds to choice C.

Solve a straight-line angle problem by using that adjacent angles sum to 180, form 6x+19+3x=180, solve for x, and find the smaller angle 3x = 69 degrees.

Learn how to find the area of a parallelogram using base times height, with base along the x-axis and height along the y-axis, base 8 and height 6, area 48.

calculate the average age of a population by multiplying group sizes (300 males, 200 females) by their ages (26, 21), summing, and dividing by 500.

Solve a cube volume ratio by setting the small cube’s side length to 2 and the large to 6, then compare volumes to obtain a 27 to 1 ratio.

Learn conversions between degrees and radians using 180 degrees equals pi radians, with examples like 30 degrees equals pi/6 and 3 pi radians equals 540 degrees.

Learn to evaluate f(x, y) = y^2 − x, substitute a and b, foil correctly, and avoid miscomputing (a − b)^2; it simplifies to −2ab, giving e as the answer.

Explore a six dollars sixty cents coin problem by linking pennies, nickels, dimes, and quarters: three times as many nickels as pennies, two fewer dimes, and three more quarters.

Solve the exponential equation by rewriting one as a zero exponent to match bases, simplify to B^2 = 6, take ± roots, and identify the solution as choice d.

The circle centered at (6,6) with radius 6 is tangent to both axes, yielding the equation (x-6)^2+(y-6)^2=36.

Determine the y-intercept of the line through the points (5,8) and (3,2) using a quick, common-sense method, showing the intercept is negative, so option A is correct.

Plot (-2,-3) and (-7,-8) as a right triangle with 5-unit legs, use the 45-45-90 rule with Pythagoras, then convert by 10 miles per unit to get the distance.

Compute the midpoint x-coordinate by applying the midpoint formula to the x-values -8 and 4, yielding -2.

Translate the parabola y = x^2 right five units and down three to obtain y = (x - 5)^2 - 3, illustrating that right shifts use x minus h inside.

Apply the midpoint formula to find the x-coordinate in coordinate geometry. With x1 = -13 and x2 = 7, compute (-13+7)/2 = -3; the answer is C.

Compute distance between coordinate points by drawing them, forming a right triangle, and using the 8-15-17 Pythagorean triple to find the hypotenuse efficiently.

Apply the diagonals formula n(n-3)/2 to determine the number of diagonals in a polygon; for n = 7, the result is 14.

Draw a Z between the parallel sides of a trapezoid to use equal Z-angles, apply supplementary angle logic, and find the target angle equals 35 degrees.

Compute the diagonal of the 40 by 75 rectangle using Pythagoras; factor out 5 to reveal the 8-15-17 triple and scale to 85.

Identify the circle’s radius from a scaled 5-12-13 triangle, doubling to get r = 13, then compute area as pi r^2 = 169 pi.

Apply vertical angles and triangle sum reasoning to solve for X. The calculation yields X equals 65, confirming the correct option D.

Calculate the banker’s win probability by comparing the area inside the radius nine region to the total area of the radius fifteen circle, yielding about 36 percent.

solve a plane geometry triangle problem by deducing all interior angles from the 180-degree angle sum, then solving for the unknown side.

Learn to solve a plane geometry question using parallel lines to form a Z, deducing equal angles in an isosceles triangle and finding n = 125.

Visualize the cube as a 3d object and use pythagoras to find the space diagonal. Then apply a second right triangle to get y = 6√3 and the radius 3√3.

Determine the circle's radius from the standard form (x−a)^2+(y−b)^2=r^2 and use r^2 to compute the circumference; for example, r^2=256 gives r=16 and circumference 32 pi.

Apply isosceles triangle marks to deduce equal sides, then use exterior–interior angle relationships via dissection to find 70 and 110 degrees for plane-geometry question 16.

Use radii AC and CB to show equal angles, solve 70 + n + n = 180 to get n = 110, so angle ABC = 55 (option C).

Use the third-side length rule to a triangle with sides 17 and 35, bounding the third side between 18 and 52, excluding endpoints; the only feasible length is 43.

Determine cos theta from sin theta = -3/5 with theta in the fourth quadrant; draw a right triangle with opposite -3, adjacent 4, hypotenuse 5, so cos theta = 4/5.

identify a 3-4-5 right triangle, apply the sine ratio opposite over hypotenuse (3/5), and set up a proportion with 16 to find qr, yielding 12.8.

Master that secant is the inverse of cosine and compute sec r as the reciprocal, using the angle r and the opposite–adjacent relationships shown in the lesson.

Apply log rules to convert log base a of x y into a sum of logs, bring the exponent forward, and substitute log x = m and log y = n.

Analyze angle B in a right triangle using sine rules, noting opposite over hypotenuse, then apply the inverse of sine to reveal the solution D.

Apply the cosine formula to find the distance between two ships as viewed from a lighthouse, using the two known distances and the included eight-degree angle.

Apply soh cah toa to determine which statement about angle b is true. Cosine b equals 12/13, the adjacent over hypotenuse, confirming the correct option.

In this trigonometry question, apply sohcahtoa to relate opposite, adjacent, and hypotenuse; switch the angles, cancel terms, and conclude B is the correct result.

Apply the log rule log_a(a^x)=x to log base seven of seven to the power 15/2, canceling the base and exponent to yield 15/2, between 7 and 8.

Solve for cos theta in a right triangle with adjacent side 8, using a scaled 3-4-5 triple to find the hypotenuse 10, yielding cos theta = 4/5.

Apply exponent rules for dividing like bases by subtracting exponents. Use log base n properties to simplify and cancel terms, yielding minus four.

The lecture shows how to solve the question by using sine and secant beta, noting secant beta equals one over cosine of beta, so sine over cosine equals tangent.

Solve for h in a 45-degree right triangle using sine with opposite over hypotenuse and hypotenuse 16, and act math prep by practicing two practice tests and watching video solutions.

Explore act math questions 12–15 through number line inequalities, proportional reasoning, cross-multiplication, and age-ratio problems to build accuracy and speed.

Apply fractions and common denominators to budget problems, use cross-multiplication to solve for x, compute square and triangle areas, and analyze coordinates within a system of equations.

Solve ACT math questions on a shaded area, adjust red yellow green models to reach a 3/5 red probability, and apply exponent rules with a counterexample for isosceles.

Apply base times height to find parallelogram area, compute distances and slopes in coordinate geometry, and use Pythagorean triples and exponent rules to solve problems 29–33.

Explore ratio and proportion through two-out-of-seven acceptance, cross-multiplication and solving for the unknown; apply logarithmic and fractional power rules; and compute a circle’s central angle from a 360-degree total.

Explore ACT math strategies for interpreting fractions, probability, and tables to determine disapproved responses and how corrected classifications split non-students, high school, and college students.

Learn to compare means when a set's least element changes, test trig expressions with a calculator, and solve volume and tan problems using cylinder formulas and 3-4-5 triangles.

Master ACT math problem solving with calendar arithmetic, angle relationships, gcd and lcm, triangle classification, and probability from the June 2017 questions 45–49.

Interpret a production graph with three machines, outages, and changing slopes through the day, then determine maximum weekly revenue from a price–demand scenario.

convert equations to slope-intercept form to read the slope and y-intercept, identify the graph with a negative slope, and solve a banner fractions problem using copy and flip.

Practice foiling and expanding a cubic with i^2 = -1, analyze graph behavior and zeros, and assess matrix dimension compatibility to identify a not possible product.

Convert a mixed fraction to an improper fraction; identify the numerator. Distribute matrices to compute products, then solve a speed problem and apply the triangle area formula.

Explore matching equations to a table by plugging values, solve a travel-time problem with distance and speed, compute X in terms of Y, and determine parallelogram side lengths from perimeter.

Solve the elimination method on simultaneous equations to determine the large pasta price, then apply the slop method to count order combinations and total costs for pasta, salads, and breadsticks.

Explore solving angles with parallel lines using corresponding angles and linear pairs, calculate ticket pricing from a rental formula, and evaluate a dice probability (nine out of fifty, 18%).

Solve act math problems by forming a width-length equation for a 140-area rectangle, apply the 5-12-13 triangle to distance, and compute circle area from diameter.

Solve ACT questions on least common multiples, quadratic factoring, cylinder volume and percentages, and apply sine, cosine, tangent via Sokoto rules to find unknowns.

This lecture covers ACT math questions 32–36, solving with isosceles triangle properties, angle sums, inequalities, least common denominator, and polygon angle sums.

Explore applying three-dimensional rotation about the x-axis to form a cone, calculate a cube's total and single-face surface area, analyze line intersections, and identify perpendicular slopes.

Explore solving inequalities with absolute value and odd/even powers, compute trapezoid area from bases 8 and 12 with height 6, and distinguish rational versus irrational square roots of primes.

solve probability with and without replacement for red and green balls, and outline shading area and sine x transformations, plus copy-dot-flip and exponent rules.