New SAT Math | A complete course for SAT Math exam prep

Master basic ratio and proportion concepts, learn antecedent and consequent, cross-multiplication, and the means and extremes principle, including mean proportional, duplicate and triplicate ratios, and componendo-dividendo techniques.

Solve a proportion using the product of extremes equals the product of means; set up 3x = 7 × 15, solve for x to get 35.

Learn how to find the third proportional to 16 and 36 by solving 16:36 = 36:x, using the product of extremes equals product of means, yielding a fourth proportional of 81.

Solve the proportion 49/x = x/81 to find the mean proportion between 49 and 81. Conclude that the mean proportion is 63.

Solve a multi-step ratio problem with three cities P, Q, and R to find Q over R as 27/22 by eliminating P from P/Q = 11/12 and P/R = 9/8.

Subtract x from 19 and 31 to make 1 to 4, solve by cross-multiplication, and find x equals 15 with verification.

Substitute p:q = 2:3 and x:y = 4:5 to evaluate the ratio (5px+3qy)/(0.1x+4qy), demonstrating a shortcut and explicit calculation.

Learn how to solve A:B and B:C ratios using cross multiplication and the LCM to derive A:B:C as 9:6:10, including a shortcut method.

Using a/b = 4, deduce b/a = 1/4 and apply cross multiplication. Then compute sqrt(a/b) = 2 and sqrt(b/a) = 1/2, yielding a sum of 5/2.

Use the method of key to solve a SAT math problem: express x, y, z in terms of K, substitute, cancel terms, and show the value equals zero.

Apply the three-variable method by setting a=4k, b=5k, c=9k and compute (a+b+c)/c = 2. Direct substitution a=4, b=5, c=9 also yields 2, confirming option C.

Master percentage concepts through converting between percent and fraction, and apply shortcuts for percent increases and decreases, with examples from profit and loss, price, consumption, expenses, and interest.

Compute 16% of 83 by converting 16% to 16/100 and multiplying, illustrating percent meaning and basic percentage calculations.

Convert 36 percent to a simplified fraction, showing how 36/100 reduces to 9/25, and explain the role of dividing by common factors in SAT math.

Convert percent to decimal by dividing by 100, so 64% becomes 0.64. Understand that the decimal is placed after two digits, yielding 0.64.

Solve a SAT math word problem about a batsman who scores 110 runs with three boundaries and eight sixes, determining the percentage of runs from running between the wickets.

This lecture demonstrates solving a percentage problem using the algebra method by setting 60% of x equal to 420, solving for x to find 700 apples.

The lecture shows how to calculate the percentage error when a number x is multiplied by 5/3 instead of 3/5, yielding a 64% error compared to the true value (5/3)x.

Determine how 20% of x equals y and compute y percent of 20 in terms of x, showing the result as 4% of x.

Compute the percentage of total votes by summing votes, identify the winner with 10,000 of 16,000 votes, yielding 62.5 percent (option b).

solve a percent problem: if 55 percent of the total marks equals 198, then the exam total marks are 360.

Increase the original number by 10% and then decrease by 10% to obtain a value 10 less than the original. Solve for x to find the original number as 1000.

Define average as the sum of elements divided by their count, shown by 3, 5, and 7 giving 5. Use the harmonic mean for average speed with distances, via 2xy/(x+y).

Compute the average of a set of scores by summing the elements and dividing by the number of elements, demonstrated with a seven-element example.

Learn to find five consecutive numbers from their average of 48 by setting them as x, x+1, x+2, x+3, x+4 and solving for x, with x=46 and last term 50.

Factor 47 from 47x + 47y = 5452 to get x + y = 116, then the average of x and y is 58.

Solve a man and his son's age problem by applying the age ratio and total sum; derive each age to satisfy a 66-year combined total.

Apply the sum formula for the first n natural numbers, n(n+1)/2, and divide by n to find the average; the example with 50 numbers gives 1275 and 25.5.

Explore solving an average problem: 24 students with average 35, adding the teacher raises the average by 400 grams to 35.4, solved with conventional and shortcut equations.

Find x from five consecutive numbers x, x+2, x+4, x+6, x+8 with average 45. Compute B and D as 43 and 47, and obtain their product 2021.

Compute the average of numbers between six and thirty four divisible by five. Sum ten, fifteen, twenty, twenty five, and thirty to 100, then divide by five to get twenty.

Determine the missing value x so the arithmetic mean of twelve numbers is 12 by summing to 127 and solving (127 + x)/12 = 12, giving x = 7.

compute the average speed for a round trip between two cities 778 km apart, with equal legs at 56 and 84 km/h; use 2xy/(x+y) to get 67.2 km/h.

Explains a two-number problem with numbers a and b, where one equals m; derive the second as two m minus m and identify option c as the solution.

Compute the average of two of the first 20 natural numbers using sigma notation and the sum formula, and confirm that option C is correct.

Master the rule of alligation for mixing two ingredients to achieve a desired mean price, and learn how price differences set the required quantity ratios.

Apply the rule of allegation to mix sugar priced at Rs 9.30 and Rs 10.80 to obtain a mean price of Rs 10.00; the required ratio is 8:7.

Two rice varieties cost 15 and 20 rupees, and mixing them yields 16.50 rupees; use a 7:3 ratio of cheaper to pricier rice.

Compute the price per gram of the mixed pulses given a 2:3 ratio; type one costs rupees 15. The result shows the mix price at rupees 18 per kilo.

Learn how to solve age problems by framing equations from given conditions, solving for two or three people's ages, and practicing with worked examples and a problem sheet.

Set the present age as x, express after 15 years as x+15 and five years back as x-5, then solve x+15 = 5(x-5) to find x = 10.

Solve a two-person age problem using the ratio 7 to 9. Set up the equation (x-7)/x = 7/9 and solve for x to determine the ages.

Explore two methods to solve an age ratio problem: a quick ratio approach and a formal equation method, concluding the sugar's present age is 15 years.

Solve for the present age x using the equation 1/(x−3) + 1/(x+5) = 1/3; derive and solve a quadratic, concluding the present age is 7.

Solve an age-difference problem using algebra, with a ten-year gap and that 15 years ago the older was twice the younger. Conclude the younger is 25 and older 35 today.

Apply algebra to an age-ratio problem: after six years Minnie's age equals three-sevenths of her father's, leading to the father's present age of 50.

Using a four-by-seven ratio, determine the mother's age as 70, then Ajay's age as 20; with Ramesh at 30, Vijay's age is the mean of 20 and 30, giving 25.

Compute Gulzar's present age by (Gulzar age minus 6) divided by 18 equals his grandson Anup's age, with Anup at 3, yielding Gulzar's age 60.

Explore number-based problems by setting up equations from given conditions to find the numbers or solve the fractions, and learn how problems are analyzed and equations framed.

Translate the difference between a number and its three-fifths equals 50 into an equation, solve for x, and verify the result in this SAT math problem.

Split a number into two parts so the sum of their reciprocals is 1/12, solving a quadratic by factorization to get 20 and 30, then verify.

Solve for two numbers whose sum is 15 and whose squares sum to 113. Set x and 15−x, form x^2+(15−x)^2=113, factor to get 7 and 8, which satisfy the conditions.

Identify a number whose digits sum to ten and, after subtracting 18, yields a number with equal digits, demonstrated by testing options and finding 73 is correct.

Solve the fifth SAT math question where the denominator exceeds numerator by two and adding five to the numerator increases the fraction by one, confirming the fraction 3/5 (option d).

The lecture resolves two equations from the given conditions. It finds x=7 and y=8, so the fraction is 7/8.

Find a fraction whose numerator and denominator increase by two to yield 1/2 and by twelve to yield 3/4, using option checking and a system of equations to get 3/8.

Solve a two-digit number puzzle by modeling it as ten x plus y, applying five times the sum of its digits, and reversing digits after adding nine to verify solution.

Master the laws of indices by understanding base and exponent, adding exponents for like bases, subtracting for division, and applying powers to powers, including negative and zero exponents.

this lecture demonstrates simplifying exponent expressions using power rules, such as turning 243 into 3^5 and applying (a^m)^n = a^{mn}. it also covers negative and fractional exponents.

Rewrite expressions with exponents as x^(a-b), x^(b-c), and x^(c-e) using exponent rules, then multiply to add exponents and cancel terms, yielding x^0 = 1.

Practice solving an exponent problem by applying power rules to deduce x, y, z are equal to one, with the correct option B.

Solve a sat math problem: simplify (x-1)/√x for x = 5+2√6 by showing √(5+2√6) = √2+√3, yielding 2√2+√3 and identifying option b.

Identify cyclic terms and apply exponent rules to rewrite each term. Cancel exponents across the cycle to show the expression simplifies to one.

The lecture uses a constant k to rewrite a, b, c as k-powers, derives 2/y = 1/x + 1/z, and finds y = 2xz/(x+z).

Set x = sqrt(1 + sqrt(1 + sqrt(1 + ...))), derive x^2 - x - 1 = 0, and use the positive root to evaluate the infinite radical.

Simplify the expression 16 x^{-3} y^2 × 8^{-1} x^3 y^{-2} using exponent rules. Cancel x^3 with x^{-3} and y^2 with y^{-2}, and use 8^{-1} to reduce 16 to 2.

Express x as 3^(1/3) + 3^(-1/3) and apply the a+b cubed formula to find x^3 = 10/3 + 3x; hence 3x^3 - 9x = 10, identifying option B.

Learn to factor polynomials by identifying factors and expressing expressions as products of binomials, using grouping and common factors, and applying difference of squares and perfect square trinomial formulas.

Explore how to factor expressions through grouping and common factors. See how taking common terms reveals the factors.

Learn to factor a complex expression by grouping and taking common factors, producing two binomial factors from terms like x squared, y squared, and xy.

Identify how to factor a quadratic expression by spotting common factors and using a bracket to reveal its factors. Conclude with the factors of the given expression.

Apply the square formulas (a+b)^2 and (a-b)^2 to factor expressions like 1+x and x^2, revealing (1+x)^2 and (x-1)^2 and solving for x.

Factor the given expression by extracting a common factor and grouping terms to reveal a product with 2x-3y; the steps divide by four and rearrange terms for complete factorization.

Learn to factor quadratics by splitting the middle term, turning x^2+15x+56 into (x+8)(x+7), and apply the same approach to expressions with coefficient six, producing correct factors.

Factor quadratics with coefficient one by splitting the middle term, as shown in two questions when perfect square forms don’t apply: (x-3)(x-4) and (x+8)(x-7).

Explore rewriting quadratic expressions using the identity a^2 + b^2 = (a+b)^2 − 2ab, applying it to x^2 − 2x + 4 and (3x+5)^2 to simplify.

This lecture demonstrates factoring polynomials using A^2 + B^2 and related identities, applies (A+B)^2 and (A−B)^2 tricks, and works through two examples to obtain final factors.

Learn to factor polynomials using common factors and identities like a^2 + 2ab + b^2, applying these formulas to simplify expressions in SAT Math practice.

This lecture uses the a^2 − b^2 identity to rewrite expressions as (a−b)(a+b) and simplify the given problem to the final result, 16 r^2.

The lecture shows how to rewrite a polynomial in standard form using A, B, C as X, -2Y, and Z, apply the squared-sum formula, and obtain a factorization X^2+4Y^2+Z^2+2XY-2YZ-ZX.

Explore a cyclic expression in x, y, z and apply the identity a+b+c=0 implies a^3+b^3+c^3=3abc to rewrite it as 3xyz, with the factorization (x-y)(y-z)(z-x).

The lecture defines A, B, C as x+y-2z, y+z-2x, z+x-2; shows A+B+C=0; and proves that A^3+B^3+C^3-3ABC=0.

learn how to factor the cubic x^3 + 3x^2 - 4 by testing x = 1 with the remainder theorem and factoring it into (x - 1)(x + 2)^2.

Apply the remainder theorem to factor the cubic x^3+4x^2-11x-30 by testing factors of 30, identify x+2 as a factor, perform division, and factor into (x+2)(x-3)(x+5).

Use the remainder theorem to test divisibility by x+3, substituting x = -3 into the expression and solving for a, concluding the value is -5.

Define polynomials as a_n x^n + ... with a_n ≠ 0 and n non-negative; classify linear, quadratic, and cubic forms; evaluate values, find zeros, and relate zeros to coefficients.

Find the zeros of the polynomial 2x^2+5x-12, which are -4 and 3. Verify the sum and product relations: sum equals minus b over a, product equals c over a.

Explore solving a polynomial zero problem by linking zeros to coefficients and using the constant term and leading coefficient. Derive the value of e and conclude e equals 3.

Derive the quadratic polynomial from the given sum and product of zeros: the sum is minus five and the product is six, yielding the polynomial x^2 + 5x + 6.

the lecture analyzes the quadratic x^2 + 7x + B = 0 with roots 2/3 and -3, using alpha and beta to link the sum and product to coefficients and deduce a = 3 and b = -6.

Apply the factor theorem to the polynomial 2x^2+7x+10, given that x+a is a factor, by evaluating f(-a) = 0 to determine a.

Solve cubic by factoring and division to find zeros; reveal a factor x - 2/3 and a square x^2 + 6x + 9, giving zeros 2/3 and -3, double root.

Derive the zeros of a polynomial with roots alpha and beta using the given sum -12 and product -3 to form and solve the quadratic.

Divide 2x^2 - x + 3 by 2 - x to find quotient -2x - 3 and remainder 9, and verify that dividend equals divisor times quotient plus remainder.

Divide polynomials using the division algorithm, arranging terms in decreasing powers, find the quotient and remainder, and verify the result step by step.

Subtract five from the polynomial 3x^3 + 10x^2 - 14x + 9 so that it is divisible by 3x - 2. Use long division to obtain zero remainder.

Divide the polynomial x^4+2x^3+8x^2+12x+8 by x^2+5, obtain a remainder of P x+Q, and solve to find P=2 and Q=-7.

determine the divisor g(x) in a polynomial division using the division algorithm, given the dividend, quotient x-2, and remainder -2x+4, yielding g(x) = x^2 - x + 1.

Verify the cubic’s zeros alpha, beta, gamma (3, -1, -1/3) and apply the zeros-coefficients relations to confirm A, B, C match the polynomial.

Derive a cubic equation from zeros alpha, beta, gamma using their sum, pairwise sums, and product given as zero, -7, and -40, yielding x^3 - 7x + 40.

Apply Viète’s relations to zeros alpha, beta, gamma to get their sum and pairwise products. Then form p(x) = x^3 − (sum) x^2 + (pairwise sum) x − product and compare coefficients.