SAT Math Foundations Course

SAT algebra questions test linear equations, expressions, and functions. Start by isolating the variable using inverse operations: addition and subtraction undo each other, and multiplication and division undo each other.

The slope-intercept form y = mx + b describes a line where m is the slope and b is the y-intercept. A positive slope rises from left to right, and a negative slope falls.

Common SAT traps include applying an operation to only one side of an equation, confusing slope with y-intercept, and treating an expression as if it were an equation. Build accuracy by solving a short set of algebra questions daily, then review each mistake and name the exact rule you missed before moving on.

Linear function drill: when a word problem gives a starting value and a rate, write y = mx + b with b as the starting value and m as the rate. Then identify the unknown: x, y, m, or b.

• Solve two-step equations by undoing addition or subtraction before multiplication or division.
• For a system, graph, substitute, or eliminate; choose the method that requires the fewest steps.
• Check inequalities with a test point and remember to reverse the sign when multiplying or dividing by a negative.

On test day, keep your written work neat: one step per line. A clear setup lets you find sign and copy errors quickly and makes checking faster.

Percent problems can be solved by converting the percent to a decimal and multiplying. Ratios compare quantities, and proportions show that two ratios are equal.

Translate word problems carefully: words like of usually mean multiplication, and is often represents equals.

Percent toolkit: to increase a value by p%, multiply by 1 + p/100; to decrease it, multiply by 1 − p/100. Successive changes must be applied one after another, not added.

• Ratio: keep the order of the ratio; 2 : 3 is not the same as 3 : 2.
• Proportion: cross-multiply to solve, then check that the units line up.
• Word problems: underline the unknown, translate the sentence into symbols, and read the final question once more.

After solving, substitute your answer back into the original sentence. If it does not fit the story, the error is usually in the setup rather than the arithmetic.

SAT geometry covers angles, triangles, circles, area, perimeter, and volume. Know the key formulas: area of a rectangle is length times width, area of a triangle is one half base times height, and circumference is 2πr.

The sum of interior angles of a triangle is 180 degrees, and for a polygon with n sides it is (n - 2) × 180 degrees.

Angle relationships: vertical angles are equal, angles on a straight line add to 180°, and a transversal crossing parallel lines creates equal corresponding angles and supplementary interior angles.

• Circle: a radius drawn to a tangent point forms a 90° angle with the tangent.
• Triangles: the largest angle faces the longest side; the Pythagorean theorem applies only to right triangles.
• Volume: for a prism, volume = base area × height; for a cylinder, V = πr²h.

When a figure is missing, draw it and label everything. If the figure is drawn to scale, use it to eliminate impossible choices before calculating.

Data analysis questions use mean, median, mode, range, and probability. The mean is the sum divided by the count, the median is the middle value, and the range is the largest value minus the smallest.

Probability is favorable outcomes divided by total outcomes. Read tables and graphs carefully and identify the units before calculating.

Table reading drill: identify the row and column labels before doing any arithmetic. Ask what the table counts: people, dollars, percentages, or time.

• Mean: sum ÷ count; if one value is extreme, the mean shifts but the median may stay stable.
• Median: with an even count, average the two middle values after sorting.
• Probability: write favorable/total and simplify; for two independent events, multiply the probabilities.

For graph questions, check whether the axis starts at zero. A graph that does not start at zero can make small differences look large.

Manage time by answering easier questions first and marking harder ones for review. Eliminate clearly wrong answer choices, substitute values when possible, and check your work after solving.

On calculator-allowed questions, still estimate before calculating to catch mistakes. On no-calculator questions, simplify expressions and use exact values.

Pacing plan: divide the section into thirds. In the first third, answer questions you know immediately and skip long problems. In the second third, finish medium questions. In the last third, return to skipped questions and eliminate choices.

• Read the last line of the question first so you know what to find before reading the data.
• For algebra, substitute a convenient number when variables are in the answer choices.
• For word problems, define the variable with a word, not just a letter.

When you finish early, use the extra minutes to recheck signs, units, and the final question. A correct method with a copied sign error is still a wrong answer.