SHSAT Algebra prep
The largest single math content area on the SHSAT, accounting for ~35–40% of math questions. Here are the specific topics tested and the techniques worth mastering.
- What algebra is on the SHSAT?
- Linear equations and inequalities, systems of equations, polynomials and factoring, quadratics, exponents, word problems requiring algebraic translation. Roughly 35–40% of math questions.
- What level of algebra is tested?
- Approximately through Algebra 1, with some early Algebra 2 topics (factoring quadratics, basic exponent rules). No calculus, no trigonometry, no advanced algebra.
- What's the most-tested algebra topic?
- Linear equations and basic word problems. These appear in nearly every administration and account for many of the easier math questions.
The algebra topics that matter
Linear equations
Single-variable linear equations (3x + 5 = 14) appear early in every section. Multi-step linear equations with variables on both sides, parentheses, and fractions are also common. Mastery means solving these quickly and reliably without making arithmetic errors.
Key techniques:
- Distribute first if there are parentheses
- Collect variable terms on one side, constant terms on the other
- Clear fractions by multiplying both sides by the denominator
- Check your work by substituting back into the original equation
Systems of equations
Two-variable systems solved by substitution or elimination. The SHSAT typically tests systems where both equations are linear; both solution methods work, but most students find one easier than the other and should default to it.
Example: 2x + 3y = 18 and x − y = 1. Solve for x in the second equation (x = y + 1), substitute into the first (2(y+1) + 3y = 18), simplify (5y + 2 = 18), solve (y = 3.2, x = 4.2).
Linear inequalities
Solved like equations with one key difference: when you multiply or divide both sides by a negative number, flip the inequality direction. Example: −2x > 6 becomes x < −3.
Polynomials and factoring
Multiplying polynomials using the distributive property (and the special-case FOIL for binomial × binomial). Factoring:
- Common factor: 6x² + 9x = 3x(2x + 3)
- Difference of squares: x² − 25 = (x + 5)(x − 5)
- Trinomial factoring: x² + 5x + 6 = (x + 2)(x + 3) — find two numbers that multiply to 6 and add to 5
Quadratics
The SHSAT tests basic quadratics: solving x² = 49 (x = ±7), factoring quadratic expressions, and recognizing the structure of (x + a)² = x² + 2ax + a² (the completing-the-square pattern). The quadratic formula is rarely required — most SHSAT quadratics factor cleanly.
Exponents
Basic exponent rules:
- x^a · x^b = x^(a+b)
- x^a ÷ x^b = x^(a−b)
- (x^a)^b = x^(ab)
- x^0 = 1 (for x ≠ 0)
- x^(−a) = 1/x^a
The SHSAT tests these rules in straightforward applications. No complex exponential equations or logarithms.
Word problems requiring algebraic translation
The category that separates strong test-takers from medium ones. The skill is translating English into math:
- "Three more than twice a number" → 2x + 3
- "The sum of three consecutive even integers is 54" → n + (n+2) + (n+4) = 54
- "A jacket on sale for 25% off" → 0.75 × original price
- "Two trains, one leaving 2 hours later" → distance = rate × time, with separate equations for each train
How to study algebra for the SHSAT
- Start with foundations. If single-variable linear equations aren't automatic, that's the place to start. Don't move on until you can solve linear equations reliably and quickly.
- Master one topic at a time. Do 15–25 problems on a single topic until accuracy is consistent before moving to the next.
- Practice word problems separately. Word problems test translation skill that pure algebra practice doesn't develop. Spend dedicated time on word problems even if you're strong on the underlying algebra.
- Practice without a calculator. The SHSAT doesn't allow calculators. Build arithmetic fluency by practicing mental math regularly.
Common questions
Do I need to know the quadratic formula?
Helpful but rarely necessary. Most SHSAT quadratics can be solved by factoring or by recognizing patterns like (x + a)² = x² + 2ax + a². Knowing the quadratic formula provides a fallback, but you shouldn't depend on it.
Is calculus on the SHSAT?
No. The SHSAT does not test calculus. The most advanced math tested is basic Algebra 2 topics like factoring quadratics and exponent rules. The vast majority of math is pre-algebra through Algebra 1 level.
How many word problems are on the SHSAT?
Word problems are roughly 15–20% of math questions, but the line between "word problem" and "regular problem" is blurry — many algebra and geometry questions are framed in word-problem form. Plan to do well on translation-based problems regardless of how they're categorized.
Should I memorize algebra formulas?
Memorize the basic ones (exponent rules, special factoring patterns, area/volume formulas if you consider those algebra). Don't memorize obscure formulas — the SHSAT tests application of basic concepts, not recall of advanced ones.