Beat the SAT Math

Factor out the common term to rewrite 3x+3y as 3(x+y), use x+y=4 to get 12, and explore plug-in test-taking tricks for choosing values.

Students learn to simplify a, b, and c fractions using given ratios c/b = 1/2 and b/a = 4, deducing a/b = 1/4 and arriving at 7/4.

The lecture shows how squaring x+2y=5 yields x^2+4xy+4y^2=25, and reinforces this with a quick check using x=1, y=2.

Factor out common x and y terms to simplify algebraic expressions, then solve for xy by division and substitution, and verify with distribution.

Foil the expression x plus one over 2x, square it, and compare to nine; subtract the extra 1 revealed by squaring to obtain x^2 + 1/(4x^2) = 8.

Demonstrates expanding x and y with binomials, uses foil on (a+b)^2 and (a-b)^2, and applies the difference of squares to relate x^2 - y^2 to ab.

Identify that 64 equals k squared, so k equals 8, and compare x^2+16x+64 to the form x^2+kx+64 to solve for l=2, yielding k+l=10.

Solve two absolute-value equations by splitting into two cases. Maximize the product x times y by choosing negative x and y, yielding 13.

Solve a system of equations by adding to cancel a variable, using the sum (three) and difference (two) of numbers to find x and y, then compute their product.

Beat the sat math course presents a problem where one number is three times another and their sum is -16; solving yields the smaller number -12.

Solve a three-variable linear system with two equations using elimination to find y, then substitute to obtain x and z, yielding 8x minus 4z equals 48.

Use base-3 exponent rules to turn the equations into a+b=12 and a−b=4. Solve the linear system to find a=8 and b=4, then compute a times b equals 32.

Apply exponent rules to solve 5^x × 5^y = 125 by equating bases to 5^3, deducing x+y=3 and 3x+3y=9.

Apply the exponent rule by rewriting the expression as five to a over five squared, then substitute the given values to compute 50/25 equals 2.

Apply exponent rules to transform 5^x times 5^y = 1/125 into x+y = -3, then multiply by -2 to get -2x - 2y = 6.

Determine that if x^2 = y^2 and x ≠ y, then x = -y, making x*y < 0 and |x| = |y| in all valid cases.

Find the smallest three-digit number whose digits multiply to zero, with distinct digits and not divisible by 5. Set B = 0, A = 1, C = 2, yielding 102.

Identify the smallest perfect square divisible by both 6 and 8 by testing squares, with 144 as the answer.

Analyze a number-line based SAT math question to identify which statement is not true by comparing fractions and signs of coordinates A, B, C, and D.

Beat the SAT Math section 4B question 7, explores choosing the greatest value under x < y with negative numbers, identifying positive candidates and evaluating x times y.

Identify equal corresponding angles formed by two parallel lines cut by a transversal, set up 10x+6y=180 and 5x+3y=90, and conclude x+y from these relations.

Solve section 6a problem by recognizing that equal angles imply equal sides in a triangle with sides 4, 4, and 5, and compute the perimeter as 13.

Identify the 45-45-90 triangle inside the circle, deduce the radius is 12, and compute the circumference as 24π.

Apply the triangle area formula and the 45-45-90 property to set base equals height, solve x^2/2=16 to get x=4 sqrt 2, and the hypotenuse is 8.

Analyzes a 30-60-90 triangle, showing x = 6 from the long leg 6√3 and yielding the hypotenuse 12 for the answer.

Solve a 30-60-90 triangle problem by deriving y=12, recognizing the side ratio x, x√3, 2x, and identifying the opposite angle as 30 degrees.

Apply the triangle inequality to sides 5 and 7 to show the third side must lie between 2 and 12, with eight as a valid example, answer B.

In section 7A question 8, central angles 130° and 50° yield an arc length ratio of 13:5; arc length is directly proportional to the angle, scaling the circumference accordingly.

Section 7A, question 9 analyzes a semicircle with arc length four to find the distance across, using half the circumference to yield the diameter, 4 + 4 pi.

In a circle, partition the semicircle into four 45-degree sectors to relate arc measures and distances; conclude that BC equals 6 pi.

Compute the shaded region by subtracting the total area of nine identical small circles from the large circle area, yielding 64π.

Determine circle area from circumference 7π using r = C/(2π) and A = πr², giving 49π/4.

Compare a large circle of radius 3 and a small circle of radius 1, using circumference 6 pi and area pi r^2 to determine radius difference and the correct choice.

Convert dimensions from centimeters to meters, compute the rectangle's area as 0.005 m², then divide one by that area to find 200 rectangles per square meter.

Compute the perimeter of a circle segment with radius 10 and central angle 120°, adding two radii and one-third of the circumference to obtain 20 + 20π/3.

Identify the shaded region as one eighth of a circle with radius 8, corresponding to a 45-degree angle, confirming the angle measure.

Identify the shaded sector of a circle with radius sqrt(800) and 45-degree central angle, and compute its area using the sector formula.

An inscribed square of area 50 yields a diagonal equal to the circle's diameter; from this, the diameter is 10, the radius 5, and the circle area is 25 pi.

Solve a section 8a question in Beat the SAT Math by computing the 3-d distance using the 3-d pythagorean theorem with components 6, 6, and 3, yielding 9.

Determine the radius of a sphere inscribed in a cube with volume 125, giving an edge length of 5. The diameter equals the cube edge, so the radius is 2.5.

Determine AB in a rectangular prism with volume 24 by using base sides 2 and 3 and half the height 2; apply the three-dimensional Pythagorean formula 2^2+3^2+2^2 to get sqrt(17).

Use rise over run to find the ramp slope; the slope is negative, -5/2, verified by reading left to right along the line.

Learn to find the slope of a line in a circle problem by using rise over run and radius symmetry, yielding -2/5 and verifying slope invariance across the line.

Use the line y = 3x + 2 with slope 3 to move 3 units across and 9 units up, yielding distance sqrt(90) = 3 sqrt(10) and option C.

Determine which option yields a valid point among three on the same line by using rise over run to compute the slope from the given coordinates.

Compute the coordinates by comparing the horizontal distance between points and applying a vertical shift, given AB is twice BC, to find k; conclude k equals 2.