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.

Rewrite the product (3x+2)(3x-2) with foil to get 9x^2-4, then set equal to the problem value and find 9x^2 = 36.

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.

Use the difference of squares identity (x+y)(x−y)=x^2−y^2 to simplify and substitute, concluding that the expression equals −2k.

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.

Apply the difference of squares by writing a^2 - b^2 as (a+b)(a-b), set (a+b)(a-b) = 40 with a+b = 10, then divide to find a-b = 4.

Rewrite using (x - y)^2 to expand x^2 - 2xy + y^2, then solve for x^2 + y^2 by moving terms to get x^2 + y^2 = 5xy.

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.

Subtract the equations to eliminate y and quickly obtain the target value 5x+1, avoiding solving for x and y while preparing you for more elimination practice, including multiplication.

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.

Solve a pair of equations in three unknowns by multiplying the bottom equation, subtracting to eliminate variables, and solving for x; the result is x = 200.

Solve for k by squaring both sides of (sqrt(5))^k = 15 to cancel radicals, yielding 5^k = 15 squared.

Derive x < 3 and y < 2 from the inequalities, then analyze possible x + y values, with sums near four and approaching five.

Solve a three-equation system with three unknowns using substitution, finding X, Y, and Z, and compute X times Y times Z as 40.

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.

Apply exponent rules to simplify expressions with powers, such as multiplying exponents when raising a power, yielding x^6 from (x^2)^3 and x^12 from (x^4)^3, and noting 3^3 = 27.

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.

Beat the SAT math, section 3A question 11, shows solving negative x times negative y equals 1/60 by using a common base and negative exponents, then finding x plus y.

practice solving two-equation systems by rewriting one equation to substitute into the other, demonstrating how rewriting x^6 enables substitution and yielding x^2 y = 100, avoiding decimals.

Solve a section 3a sat math problem by factoring out 3^n, applying exponent rules to simplify terms, and isolating k. Learn the plug-in numbers option as an alternative test-taking trick.

Apply exponent rules to simplify x^(-2) / x^(-5) to x^3 and y^3 / y^4 to y^-1, illustrating subtraction of exponents and reciprocals.

This lecture demonstrates two methods to solve an exponent equation for x: raise both sides to the fourth power or take the eighth root of 3 to the fourth.

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.

Apply the rule to break down A plus two and A plus one, divide by 20, substitute for A plus three, and obtain the final answer 16/5.

Apply modular arithmetic by choosing x that leaves remainder 2 when divided by 7, then observe x+5 is a multiple of 7, yielding remainder 0 in all tested cases.

Analyze how negative integers interact in addition and multiplication to find expressions that are always negative. Apply negative times negative becoming positive and C squared positive to determine correct choice.

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.

Use sign analysis with a positive b and a negative c to determine expression positivity; show that b−c is positive and c^2 is positive, avoiding ambiguous numerical guesses.

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.

Consider any B between 0 and 1; the square root of B is larger than B. Observe that B^2 exceeds B^3, and dividing by a fraction increases a positive number.

Use isosceles triangle reasoning: two equal sides imply equal base angles of 40°, so the third angle is 100°, and all angles sum to 180°.

Apply the triangle angle sum by noting the three angles add to 180 degrees; solving with the given 18-degree relation yields the missing angle as 54 degrees.

Express all angles in terms of x using y = 3x and z = 6x, then 30 + x + 3x + 6x = 360 to solve x = 33.

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.

Learn to solve a geometry angle problem from section 5b question 9 by setting up angle relationships, using 180-degree sums, and solving for x, yielding 38.5.

Set angle a as x, angle b as 3x, and angle c as 2b; use the triangle's 180-degree sum to find x and B equals 54 degrees.

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.

Compute the diagonal of a square from its area by applying 45-45-90 triangle properties. This yields the diagonal sqrt(20), which simplifies to 2 sqrt(5).

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.

solve a 30-60-90 triangle problem by identifying the side opposite 30 as 6√2, double it to 12√2, and select choice B as the answer.

Evaluate a triangle with sides five and twelve and an angle B under ninety to find the third side; it lies below thirteen, so possible values are nine to twelve.

Determine AB as the distance from the circle center to the tangency point using a radius-1 circle and a right triangle with legs 2 and 3, giving AB = sqrt(13).

A square inscribed in a circle has its diagonal equal to the circle's diameter. Diameter is 4√2, so the radius is 2√2, and the area is 8 pi.

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.

Calculate the shaded sector area of a circle with radius 30 by using a central angle of 120 degrees, which is one third of the full circle.

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

Compute the shaded region by taking the total area 192 and subtracting the three circles' area, yielding 192 minus 40 pi.

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.

Apply the Pythagorean theorem to the right triangle formed by splitting the base, calculating legs 3 and 5 to find the hypotenuse as sqrt(34).

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.

Rotate the trough to minimize base area to six square inches; with seven cubic inches of liquid, the water height becomes seven-sixths of an inch.

Determine the cube edge from a volume of 125 by cube root, which equals five, then compute the surface area of three faces as 75.

Compute AB in a square-based pyramid with base side ten and height six by forming a right triangle with legs 5 and 6; apply the Pythagorean theorem to obtain sqrt(61).

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.

Use the 3D Pythagorean theorem on a cube with edge 12 to find AB, giving d^2 = 6^2 + 12^2 + 6^2 and d = 6√6.

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).

Compute ab in a pyramid with a square base side 8 and height 3 by using half the base diagonal 4√2, giving ab = √41.

A cube with edge length 4 sits inside a sphere, whose diameter equals the cube diagonal of 4√3; thus the radius is 2√3.

Use the slope formula with points (3,2) and (5,B) to set (B−2)/(5−3) = 3/2. Solve to find B = 5.

Three collinear points share the same slope between any two points. Use the slope formula to set pairs equal and solve for the unknown, yielding p = 11.

Find the line perpendicular to y = (2/3)x − 4 that passes through (2, −1) using the negative reciprocal slope of −3/2, giving y = −3/2 x + 2.

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

Determine point d with x = -4 so the slope from a(-4,3) to d(-4,-1) is -1/2; deduce d = (-4,-1) and compute the distance from a to d as 4.

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.

Explore finding the slope of a line using rise over run, identify perpendicular lines, and apply the negative reciprocal to determine the slope for section 9A question 13.

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.

Explore circle geometry strategies for SAT: use congruent radii and right triangles to locate the origin and y-intercept, then deduce x-coordinates.

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.

Identify the circle point (6,8) on x^2+y^2=100, compute the slope 8/6 = 4/3, then find the tangent slope as the negative reciprocal, -3/4.