SAT Math Section Solutions With Concept Reviews

Explore solving a no-calculator algebra item from College Board test ten, using the formula sheet, back-check with substitution, and choice-elimination strategies.

Derive equation for a television priced at 300 with a 60 down payment and 30 weekly payments, forming 60 + 30w = 300, and apply commutative property to compare forms.

Learn to model shipping charges as a linear function of weight using y = mx + b, derive slope and intercept from two points, and apply to x pounds.

Interpret the graph of height versus base diameter for cylindrical doric columns; show that 5 ft yields 35 ft and 2 ft yields 14 ft, a 21-foot difference.

Simplify the expression square root of nine x squared to 3x when x is positive, and verify by substitution across answer choices to identify the correct option.

Solve question six by factoring x^2-1 as (x+1)(x-1), canceling x-1 (with x not equal to 1), yielding x+1 = -2 and x = -3, then check by substitution.

Read the graph of f(x) to evaluate f(0). The graph shows y = 4 at x = 0, so f(0) = 4; the correct choice is D.

Solve a right-angle geometry problem by using straight line angle sum to set 90 + x + 2x + 2x = 180, then compute 3x and double-check under exam time.

Identify the y-intercept at -4 and the slope from points (0,-4) and (-4,0). Derive the line as x + y = -4 and verify with a second point for accuracy.

Identify the y-intercept by substituting x=0 into the equation y = 2x^2 + 10x + 12, yielding k = 12 for this quadratic graph.

Master the standard circle equation x minus h squared plus y minus k squared equals r squared, identify the center (h,k) and radius r, and watch for negative signs.

Apply similar triangles to equate corresponding angles and use the cosine ratio (adjacent over hypotenuse) to find cos of B, yielding 12/13.

Factor the quadratic x^2 + 5x + 4 to find its x-intercepts at -4 and -1, then compute their distance as 3 on the x-axis.

Plug in the options to test x values and use the square root to verify the positive root that satisfies the equation, showing x = 9, choice B.

Examine two linear equations as lines and determine when the system has no solution by making their slopes equal; derive that a equals negative six.

Solve question 16, a no-choice shipping-cost problem, by setting up and solving T = 5C + 12×3000 to get C = 2200 units shipped to the closer location.

Split the absolute value equation into two cases, obtain A = 2 and B = -3, then compute |A - B| = 5.

Demonstrates how a 10% annual increase compounds over two years, yielding 200 × 1.21 and identifying the constant A as 1.21.

Learn to solve a system of linear equations on the SAT math section using elimination, substitution, or a quick trick: add the equations to get 5x+5y=2500.

Demonstrates solving question 20 by recognizing a difference of squares and factoring to (u+ t)(u− t), then confirms the result by solving for u and t.