Nova's SAT Math Prep Course

Substitute an odd integer, like 1, into the answer choices to identify the option that yields an even result, showing how substitution guides the correct answer.

Use substitution to test choices: plug values into C and D, rule out A and B as even, keep C or D, then try another value to confirm C.

Use substitution with x/y greater than 1, test options (x=3, y=2; then x=6, y=2), and eliminate until the correct choice is d.

Solve a substitution problem by testing odd numbers and evaluating whether results are even or odd to eliminate options, concluding that option c is the answer.

Identify a substitution with x as a perfect square and y as 9, then compare options, noting a, b, and c yield perfect squares while d yields 13, the non-square.

Explore a substitution problem where x is odd and y is even, showing why only one answer could be even and why the other choices cannot be even.

In this substitution problem, set k as one fourth of the number between 0 and 1, eliminate options by comparison, and verify with (1/4)^2 < 1/4, confirming D.

Demonstrate substitution to solve quickly by setting h = 1 and testing each answer choice for equality with 2. A yields 3, B -1, C 3, D 2; thus D.

Use substitution with an even integer m to test the answer choices. Show that m=2 yields 22 and m=0 yields 6, confirming choice c as the solution.

Analyze substitution problem 7 by taking the square root of x squared to identify even numbers, apply elimination of false statements, and conclude that statement b is the correct choice.

Evaluate a substitution problem where X is divisible by eight but not by three; substitute into answer choices to identify the option that is not an integer, concluding C.

Solve a substitution problem with integers p and q using pq equals 2 and pq plus 2 equals 4, deducing that one integer lies between 2 and 4, option D.

Identify that X and Y are prime numbers, test pairs (3,2), (5,3), and (17,3) to compute X−Y, eliminate options a, b, and d, and conclude that c is correct.

Apply substitution by testing answer choices for a digit sum of 18, eliminate incorrect options, and use the tens-versus-hundreds digit check to confirm B, in Nova's SAT math prep course.

Explore solving a two-digit substitution problem where the tens digit is twice the units digit, use elimination on options by testing reversed digits, and conclude with choice d.

Practice substitution by plugging in answer choices to test the expression for a value of one. Eliminate options like C, and confirm D as the correct solution.

Apply substitution: a digit-sum of 12 rules out b, and the 10th digit being one third of the units digit eliminates a and 48, confirming answer D.

Apply substitution (plugging in) techniques to substitution problem 4, a halving bus scenario across stops, then verify the answer by solving forwards and backwards.

Use substitution by plugging in answer choices to verify values quickly, eliminating option A and confirming option B as the correct result.

Practice substitution by plugging in answer choices to test which yields negative one. Eliminate zero, then plug in one, which gives negative one, so the answer is B.

Apply substitutions in a defined functions example by replacing x with two and y with three in the formula, yielding three that you enter into the box.

Explore defined functions in the SAT math prep course with example 2, where leading terms are squared and anything divided by itself is one, so the answer is B.

Plug in k = 1 to test the parity of the two-part expression, then multiply the inner expression by 4 per the definition, yielding 8k − 4 (choice c).

Follow substitutions in defined functions example 4, replacing X with -π and then with 2π to derive the final result.

Apply the two-part definition of odd and even to show u is odd and v is even, compute 5 and 10, and obtain a difference of 5, answer a.

In defined functions example 6, explore base and exponent roles, evaluate 2^2^3 versus (2^2)^3, and analyze negative bases and exponents to assess true statements and the commutative property.

Substituting into the definition clarifies the base and exponent, and the power raised to a power multiplies exponents, so (x^y)^z does not equal x^(y^z).

Apply algebraic steps to solve for y in the equation xy = -x, using squaring, factoring y^2, and the zero product property, concluding y = 0 (answer a).

Apply the area of a square formula, x squared, to compare 9 squared over 3 squared and 3 squared, both yielding 9, in defined functions example 9; answer is b.

Substitute P with 3 in the given formula, simplify to 8 over 1, and conclude the answer is D.

Apply defined functions problem-solving with mcq strategies, using ascending or descending answer order and value substitution to identify the correct choice.

Substitute values into a defined function formula, compute the square of 25, and confirm that the answer is option B.

Examine the circle area by substituting the radius as d/2 into pi r^2 to get pi(d/2)^2. This yields 36 pi and identifies option D as the correct answer.

Identify variable substitutions by position: assign zero to x, one to y, and a to z, then equate the two expressions to deduce a equals zero, confirming option c.

Simplify defined functions problem 6 by combining like terms: 4 minus x^2 equals x^2, then 4 = 2x^2, x^2 = 2, and x equals square root of 2.

Defined functions problem 7 explores a star operation and algebraic reasoning, including a difference of squares, to determine which statement is false and identify the correct choice.

Apply the defined function x star y equals x divided by y to substitute into the expression, simplify to x over y z, and identify the correct choice d.

substitute into the equation and simplify to x sqrt(y) minus 2x. factor out x and identify the x value that yields zero for all y, the answer a.

Master defined functions by solving problem 10 through stepwise substitution from the innermost parentheses, using squares, divisions, and square roots to reach the final value a.

Evaluate a function by composing f with itself: from the graph, f(-1) = 3 and f(3) = 1, so f(f(-1)) equals 1.

Explore horizontal parabolas from a y-squared function opening left, with an x-intercept at 2; compare the two top graphs with negative slopes to identify the one with slope about -1.

Analyze how the graph of f(x) intersects the horizontal line y = 1, revealing that f(x) equals 1 at three distinct x-values.

Learn how a function models a real-life sales graph, tracing rapid growth from 0 to 5, slower growth from 5 to 10, a dramatic drop, and a peak near 10.

Convert the expression to radical notation, specifically the fourth root of 2x-3. Ensure the radicand is nonnegative (2x-3 ≥ 0) and solve to obtain x ≥ 3/2.

Test function values by plugging table entries with x = 0 and x = 1, eliminate choices A and C, and identify D as the correct function.

Identify x-values where f(x) equals 2; the caption shows that for x between 2 and 3, f(x) = 2, with 2.5 as a potential answer choice.

Solve for v via the square root steps in the equation, then evaluate h(v) to obtain 4, confirming the correct choice D.

Use symmetry about x axis on the function x = y^2, yield x = -y^2, then shift left by one to obtain x = -y^2 - 1 for problem 5.

Solve the equation v(x) = 110 to find x. Derive sqrt(x) = 3 and |x| = 9, yielding x = 9 after discarding -9.

Learn to rewrite a quadratic as y = a(x - h)^2 + k to locate vertex height of a projectile, identify (h, k) as (q, p), and evaluate at t=4.

determine the parabola parameter by using a square of area 16 and symmetry about the y-axis; solve for a from the intersection at point B and find a equals eight.

Apply the Pythagorean theorem to a right triangle to find height 4, then compute the area as one-half times base 3 and height 4, yielding the final answer a.

Solve a triangle angle problem by forming 100 + 50 + C = 180, simplifying to C = 30.

Explain that (a x)^2 equals a^2 x^2 and compare multiples of x^2, showing 4x^2 is twice 2x^2, and concluding with answer B.

Apply cross-multiplication to compare fractions, determine the larger product on the same side, and conclude that 15/16 is greater than 7/9, making option a the answer.

Find a common denominator by multiplying top and bottom, apply inversion and multiplication, then add to get three, confirming the answer is a.

Solve a proportional problem: set the ratio of 1/5 to 1/4 equal to the ratio of 1/4 to x, use reciprocals and cross-multiplication to find x, yielding x = 5/16.

Explore how squaring a proper fraction lowers its value and a square root raises it, while C and D exceed 1 because 8/7 > 1; the answer is a.

Show that A is irrelevant and b governs the right side; applying the fourth power to negative y yields the result, i.e. negative y to the fourth, choosing C.

Compute a fraction from the given coordinates (0, 4) and (9, 6), simplify 100/96 to 25/24, and conclude that the answer is a.

this lecture walks through solving a sat math note problem by comparing fractional x in (0,1) using square roots and powers, setting x to 1/4 to prove choice a.

Analyze how squaring and square roots affect fractions between 0 and 1, compare 5/6 to its square root, and conclude that statement 3 is false, guiding the correct answer.

Explore inequalities in an SAT problem using a counterexample with x=2 and y=1 to compare left and right expressions, and show how x>y>0 leads to a weaker-than-one result.

Explore a number theory example by equating expressions from dividing n by 2 and by 5, using quotient and remainder to solve n and identify choice B.

Apply divisibility in number theory by parity to determine when a fraction is an integer. With p=2 and q=3, the result is an integer; the answer is D.

Evaluate statements about consecutive integers a, b, c, including divisibility by 3 and 4 and even-odd sums, concluding that statement 2 is true and statement 3 is false, answer B.

Apply number theory concepts with primes, using process of elimination on expressions like three minus two, five minus two, and eleven minus two to determine the option, answer is D.

Solve a number theory puzzle by simplifying nested expressions with absolute value and negation. Find x by solving the resulting equation to confirm x equals 3, the answer is C.

Express integers in standard forms like 2k+1 and 4v+3 to identify odd and even structures. Use factorization and parity checks to determine the correct choice, which is C.

primes greater than two are odd, so x and y are odd; odd times odd stays odd, and no odd is divisible by 2, so the answer is a.

Show how x and y express as multiples of 2 and 5, deriving 5x = 10p and 5y = 10q, and conclude 10 is the largest number listed, answer d.

Solve a number theory problem with consecutive even integers A, B, and C, derive that A < -3 from their average inequality, and identify the negative solution.

Assess how prime and even properties interact in a number theory problem by testing x and y values, and conclude that none of the statements are true.

Identify cube numbers 8, 27, 64, and 125 between two and two hundred that are perfect squares. Since 64 equals 8 squared, the answer is C.

Solve number theory problems by plugging in answer choices, using digit sum and digit difference constraints to quickly eliminate options and identify the correct choice.

Review the division algorithm with remainder 1, expressing P as 9Q+1, test cases show P=10 and P=19, and confirm statement 3 (3z+1) is true, so the answer is C.

Explore how P and Q being odd (P=2x+1, Q=6y+1) makes PQ odd, then explain why PQ/2 is not an integer and why PQ is not necessarily a multiple of 12.

Determine the smallest prime greater than 53 by testing candidates: 54, 34, 55, 57, and reveal that 59 is prime, so the answer is D.

Use the straight angle rule A+B=180 and the ratio A/B=7/2 to solve for A and B, yielding B=40 and C as the answer.

Apply vertical angle relationships and a straight angle to form a system of two equations in two unknowns; solving yields y = 84, so the answer is b.

Solve angles in a right triangle using angle sum and vertical angles; find x = 30, z = 60, y = 60, and w = 30, in geometry triangles example.

Apply the exterior angle theorem to set x+60 equal to the remote interior sum x+90, solve for x by removing x and 60 from both sides, yielding x=30.

In a geometry quadrilaterals example, identify right triangles and a rectangle, then compute the perimeter by summing the sides 4, 5, 4, 4, and 3 to reach 20.

Solve for the cube edge by setting volume E^3 equal to surface area 6E^2, factor to E^2(E-6)=0, discard zero, and conclude the edge length is six.

Compute arc length from a 60-degree intercepted arc by applying the fraction 60/360, which is 1/6 of the circumference; here 4 pi, yielding 2/3 pi.

Subtract the circle area from the rectangle area to get the shaded regions; with the rectangle area 15 and circle area pi, r = 1, the answer is B.

Subtract the small circle area from the large circle using radii three and one; the shaded area is 8 pi, ratio to the small circle is 8, yielding answer C.

Explain the relationship between a square's diagonal and a circle's radius, using a radius of 2 to show SP also has length 2, and identify the correct answer as D.

Solve a right triangle using the Pythagorean theorem to find y, resulting in y = sqrt(27) and identifying option B.

Apply the area formula pi r^2 to circle p, radius 1, and circle q, radius 1/2. The shaded region equals pi minus pi/4, i.e., 3 pi over 4.

Four arcs form a circle with radius three inside a six by six square. The shaded region equals 36 minus 9 pi.

Apply the circle area formula pi r^2 to find r = sqrt(2) from area 2 pi, then four radii form a square side 4 sqrt(2) for an area of 32.

Use the triangle angle sum to solve for y, given t = 51 degrees and s + t + y = 180, yielding y = 78 degrees and answer D.

solve geometry problems in sat math prep by identifying parallel lines cut by a transversal, applying alternate interior angles and supplementary relationships to determine angles A and B.

Apply parallel-line and corresponding angles concepts to set 5x + x = 360 around a point. Solve for x as 60 and identify the correct option C.

Determine the isosceles triangle angles with base angles 59 degrees. Apply the 180-degree angle sum to get 62 degrees and prove PQ is the largest side.

Compute the shaded region by subtracting the smaller circle area (pi x^2/4) from the larger circle area (pi x^2), yielding 3 pi x^2/4; option a is correct.

Compare the square and circle with diameter six, compute areas 36 and 9 pi, subtract to get 36 − 9 pi, halve the four shaded regions, yielding C.

Apply the Pythagorean theorem to a right triangle to find PS as 6 and QS as sqrt(61), solving side lengths in two triangles.

Use the angle sum y plus x plus 20 equals 70 to derive y equals 50 minus x. With x greater than 15, y is less than 35 via manipulation.

Explore solving a geometry problem with parallel lines L and K, where corresponding angles are equal, leading to y = 75.

Calculate the shaded region by subtracting the area of the smaller triangle from the larger triangle, using a 45-degree hypotenuse and equal base and height to relate measurements.

Choose radii with the larger circle twice the smaller, compute areas with pi r^2, find shaded region 3pi, and obtain the ratio 3:1.

Apply the Pythagorean theorem to the isosceles right triangle PST to find x equals sqrt(2). Subtract the smaller triangle area from the larger to obtain a shaded area of 1/2.

Calculate the area of triangle PQS as 15 from base five times height, then compute the large triangle PRQ as 40 minus 15 to get 25, with the answer D.

Determine the value a by summing the areas of two right triangles (base 2, height 4, each area 4) and subtracting this unshaded region from the square's area of 16.

Compute the circle radius from area 9 pi, then find the circumference and arc length for a 30-degree sector to deduce the perimeter as 6 + pi/2.

Solve for r from A = pi r^2 to get r = sqrt(A/pi), then substitute into C = 2 pi r to obtain C = 2 pi sqrt(A/pi).

Use eyeballing to identify that angle y is less than 90 degrees, likely between 65 and 85, with D as the correct answer.

Identify how the larger triangle's area equals base times height, estimate the shaded region as about half, and use answer choices order by size to pick the closest option.