Perfect 36: Math ACT Prep

Learn exponent rules for addition, subtraction, multiplication, and division, including negative exponents. Explore factoring and applying roots, like square roots and cube roots, with variables such as x and y.

Apply the interior angles rule for triangles and quadrilaterals, with sums 180 and 360 degrees. Solve for x by combining 4x+5x+6x to 15x = 180, yielding x = 12.

Use absolute value like parentheses, evaluate inside first, then apply order of operations to compute two times seven minus three times five plus two, which yields negative seven.

Explain how to use arithmetic sequences and the sum formula to compute both the sixth birthday deposit and the total amount deposited in Ricardo’s daughter's account.

Solve this algebra problem by finding the monthly amount X, given a $700 initial payment, 36 equal payments, and a total of $7000, while recognizing fast-paced solution strategies.

Master matrix operations, including addition and subtraction for matching dimensions, and perform multiplication; learn determinants for 2x2 cases for the ACT prep.

Compute subtraction of fractions by converting to a common denominator, illustrated with four gallons minus half and minus one and a quarter gallons, resulting in two and one-quarter.

Use the similarity of right triangles to form a 4 to 5 ratio, link it to the 24-inch hypotenuse, and cross-multiply to find the missing side, which is 30 inches.

Use the Pythagorean theorem to test for a right angle and solve for BD with the given distances. The calculation yields BD = 1500.

Calculate the area by treating the figure as a rectangle with right angles, using length times width, then add the component areas to get the total.

Track a dot on the coordinate plane as it moves right 2 units along the x axis and up 1 unit along the y axis, from (2,3).

Explore percent off concepts by applying a 20% discount to two camp enrollments by May 15, using the 0.8 multiplier to total 720.

Solve a linear relationship between grade and enrollment fee with y = mx + b, deducing slope and y-intercept to determine the grade-zero enrollment (200) and select H.

Compute the probability that both of Miss Chen's children are drawn by multiplying the per-grade chances, 1/20 for grade three and 1/15 for grade four, yielding 1/300 (0.003).

Solve a constant-speed word problem by converting 18 miles in 20 minutes to mph, setting up a ratio, and cross-multiplying with answer choices to find the lowest feasible speed limit.

Apply a quick tip to identify the variable, then isolate I from r = p over I squared until I stands alone, as the problem asks which expression gives I.

Use the least common multiple to solve a word problem with two signs flashing every 8 and 12 seconds, and find the next simultaneous flash after 24 seconds.

Determine the side length of a square with area 900 square inches by taking the square root to get 30, then compute the perimeter as four times 30 equals 120.

Use cross-multiplication on capture-recapture data: 108 deer tagged and released, 54 later captured with 36 tagged, to estimate the county deer population via the DNR proportion.

Convert 3898 steps to feet using 2.25 ft per step, then convert feet to miles with 1 mile equals 505,280 ft. The result is about 1.7 miles.

Learn how to calculate the average of seven numbers and determine how much the sum must increase when the mean rises by four, using simple before-and-after reasoning.

Learn how to write circle equations from center and radius using the standard form (x-h)^2+(y-k)^2=r^2, with examples using centers (4,-3) and (0,-1) and radius 5, including sign changes.

Count how many scores exceed the median in an odd-sized data set. Apply rounding down from 12.5 to compute 12 scores above the median for 25 students with median 80.

Apply a system of two linear equations to solve for x (apples) and y (oranges) using 3x+4y=347 and 12y=636, then compute the maximum apples purchasable with a $10 budget.

From the purchase time of 2:30, subtract 1 hour 15 minutes to the store entry and 25 minutes in the store to find the home departure at 12:50.

Calculate the bag of balloons’ price by removing 6% sales tax from the total using the equation total/1.06 minus 15. Reveal that the balloons cost 2.50 in this example.

Explore a linear graph problem from ACT prep: with a $30 total, marbles cost $2 per bag (x) and cars (y), determine x when y is zero.

Identify angles in 30-60-90 triangle and apply ratios: opposite 30 is x, hypotenuse 2x, opposite 60 is x root three; with x = 10 obtain 20 and 10 root three.

Learn to evaluate and manipulate functions, including f and g, by plugging in x values, composing f with g, and performing addition, subtraction, multiplication, division, and inverse operations.

Analyze how to determine feasible x and y values by plugging in numbers, checking constraints like x+y=0 or x+y=10, and verifying whether x lies between 0 and 5.

Show how to form f(g(x)) by substituting g(x) into f and replacing x with the inner expression. Use examples like x^2+1 and x^2-6x+9+1 to illustrate.

Solve a two-variable system by elimination using x−y=5 and x+y=2, derive x=7/5 and y=3/5, compute x/y=7/3, and verify the final answer matches the question to avoid tricks.

Explore sine, cosine, and tangent equations and graphs, detailing amplitude, period, and shifts; distinguish sine and cosine graphs, and apply formulas for period and left-right and up-down shifts.

Discover how to add fractions by converting to a common denominator, multiplying the top and bottom by a value that acts like one, and combining to obtain (w+2)/w^2.

Identify digits in two three-digit numbers as a, b, c and d, e, f, noting hundreds, tens, and ones, and explain that a difference greater than 100 implies hundreds digits.

Multiply two variables on a number line using A = -0.75 and B = 0.5 to place the product around -0.375, which lies between A and zero.

Compute a weighted average with three tests at 20% and a final at 40% to reach 86. The example shows the final score must be 92.

Calculate the area of a triangle by selecting a base and the corresponding height, determined from coordinates, then multiply one half by base times height.

Apply the pythagorean theorem on the coordinate plane to solve for x from a 1:3 ratio, extend to 4x, and test points to pick C, option D (≈26.8).

Compute the circumference using 2r pi with radius 3 inches to get 6 pi, then add the four spaces where circles do not touch to reach about 42.8 inches (43).

See how multiplying by the conjugate simplifies expressions with imaginary numbers and confirms that rational b stays rational, yielding the conjugate 3 − b i for 3 + b i.

Learn the basics of logarithms by converting between exponential and logarithmic forms, such as log_x 8 = y, where x^y = 8, and identify base and exponent.

Review how multiplying exponents uses addition of exponents, compute x^(1/4+1/6) = x^(5/12), and express the result as the 12th root of x^5.

Convert currencies by setting up ratios between British pounds, US dollars, and Canadian dollars, then use cross-multiplication to determine how much Canadian dollars equal £2.

The lecture explains the law of cosine, shows how three variables determine an unknown, and applies it to a 17,16,15 triangle to identify the smallest angle opposite the shortest side.

Learn to read and classify triangles by angles and sides, apply area formulas and the triangle inequality, and determine right, acute, or obtuse triangles.

Master the standard circle equation, identify the center (h, k) and radius, and apply completing the square to convert to the standard circle equation format and find x-intercepts on ACT.

Explore the ellipse equation (x-h)^2/a^2 + (y-k)^2/b^2 = 1, identify the center (h,k) and radii a and b, and locate the foci along the major axis using the distance sqrt(a^2 - b^2).

Explore parabolas as graphs of quadratics, learn how a determines up or down orientation, and master vertex, standard, and intercept forms with completing the square to convert between them.

Examine polynomial graphs with higher exponents, applying end behavior rules and cross or bounce for roots, and use a five degree example with positive leading coefficient to determine the graph.

Identify vertical asymptotes by setting the denominator to zero, such as x = -2. Horizontal and slant cases depend on degree comparisons: y=0, y=a/b, or y=mx+b.

Explore hyperbolas, their horizontal and vertical forms, and how asymptotes shape their graphs. Learn center, vertices, and foci, with equations and an ACT example to identify the correct graph.

Apply the law of sines to find the missing side and perimeter, using 130 over sine 91 to relate to the 47° side and determine the 42° third angle.

determine the line from intercepts, obtaining slope -a/b and equation y = (-a/b)x + a, then use shading to identify the correct inequality, which is option B.

Discover how to add vectors in ACT prep, using graph form and equation form to find sums and solve for variables by combining like terms.

Explain how a standard deviation graph shows data within ranges from the mean. Note that 68% lie within one standard deviation, 95% within two, and 97.7% within three.

Explore distribution shapes in ACT prep, including bimodal, normal, skewed left and right, and uniform, with examples from random number generation and preschool age data.

Determine the acid concentration in solution x by a mixture equation with 60 ml at 40% acid and 40 ml of solution x to produce 100 ml at 36% acid.

Apply distance equals speed times time to two cars starting at 2 p.m. at 68 and 57 mph to find when their combined distance reaches 240 miles, around 3:55 p.m.