12 prerequisite gaps that commonly contribute to lower SAT Math performance.
These are the prerequisite skills our tutors check first. Run the 2-minute self-test for each one. Anything your student can't do cleanly is a common place for marks to go missing.
- 01
Fraction arithmetic under pressure
2-minute test
Simplify (2/3 + 1/4) ÷ (5/6) in under 40 seconds, working by hand.Drill common-denominator addition and 'divide = multiply by reciprocal' until it's automatic. A calculator is permitted throughout digital SAT Math, but rational-expression questions still depend on this fluency.
- 02
Negative signs and distribution
2-minute test
Expand −3(2x − 5) + (4 − x).Write the minus sign as ×(−1) explicitly while building the habit. Sign errors are a common source of avoidable mistakes.
- 03
Solving for a variable inside a formula
2-minute test
Solve A = P(1 + rt) for r.Practice isolating a variable that isn't x. SAT questions may require rearranging science and finance formulas.
- 04
Slope as a rate of change
2-minute test
A line passes through (2, 7) and (6, 19). What does the slope mean if x is hours?Read slope as 'units of y per one unit of x.' This interpretation is useful across many contextual problems.
- 05
Linear equations from a word problem
2-minute test
Write an equation: a gym charges $25 to join plus $15 a month.Label the variable in writing before writing the equation. Translating the context carefully can prevent avoidable errors.
- 06
Systems of equations — knowing when to substitute vs. eliminate
2-minute test
Solve 3x + 2y = 12 and x − y = 1 twice, once each way.Use substitution when one variable is already isolated and elimination when coefficients line up. Aim to choose the efficient method promptly.
- 07
Percent change vs. percent of
2-minute test
A price rises 20% then falls 20%. Is it back to the original?Use multipliers (×1.2 then ×0.8 = 0.96) rather than combining successive percentage changes directly.
- 08
Ratios, rates, and unit conversion
2-minute test
60 miles per hour is how many feet per second?Set conversions as fractions and cancel units on paper. Unit tracking catches the wrong answer before you bubble it.
- 09
Exponent rules
2-minute test
Simplify (x³y⁻²)² / (x⁴y).Know the five rules securely: product, quotient, power, zero and negative. They appear across algebra and function questions.
- 10
Factoring quadratics on sight
2-minute test
Factor x² − 7x + 12 and 2x² + 5x − 3.Use short, regular factoring practice to build recognition speed alongside a reliable method.
- 11
Reading a function in three forms
2-minute test
For f(x) = (x − 3)² − 4, name the vertex, the roots, and f(5).Practice converting between standard, factored and vertex form so you can interpret a quadratic in any representation.
- 12
Interpreting graphs and tables
2-minute test
From a scatterplot, estimate the line of best fit and predict a value outside the data range.Say what each axis measures before answering. This quick check helps prevent avoidable graph-reading errors.
Not sure which of the twelve applies?
We review the student's course, goals, current challenges and schedule. When appropriate, the Free Math Assessment can help identify specific skill gaps.
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