SHSAT cheat sheet

The ELA half of the SHSAT consists of Revising/Editing items and Reading Comprehension items; there is no penalty for a wrong answer, so no question should be left blank.

Main idea: the central claim of a passage is stated or implied in the opening and closing lines, and every correct answer choice must be supported by the whole passage rather than one stray sentence.

Inference rule: an acceptable inference is one the text forces you to make; an answer that is merely plausible or true in real life but not supported by the passage is wrong.

Transition logic: 'however' and 'nevertheless' signal contrast; 'therefore' and 'thus' signal cause and effect; 'for example' signals illustration; 'in addition' signals continuation.

Comma splice: two independent clauses joined by only a comma are incorrect; fix with a period, a semicolon, or a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so).

Subject-verb agreement: cross out prepositional phrases between the subject and verb, since the verb agrees with the head noun, not with a noun inside the phrase.

Modifier placement: an introductory descriptive phrase modifies the noun that comes immediately after the comma, so a mismatch produces a dangling modifier.

Pronoun rule: a pronoun must agree with its antecedent in number and gender and must point to exactly one clear noun in the sentence.

Vocabulary in context: substitute each answer choice into the original sentence and keep only the choice that preserves the sentence's logic and tone.

Percent change = (new value − original value) ÷ original value × 100; percent increase and percent decrease use the same original amount as the denominator.

Slope = (y₂ − y₁) ÷ (x₂ − x₁); parallel lines have equal slopes, and perpendicular slopes are negative reciprocals that multiply to −1.

Right triangles: a² + b² = c²; 45-45-90 sides are in ratio 1 : 1 : √2; 30-60-90 sides are in ratio 1 : √3 : 2.

Areas: triangle = ½bh; circle = πr²; trapezoid = ½(b₁ + b₂)h; cylinder volume = πr²h.

Statistics: mean = sum ÷ count; median = middle value of the ordered list (average the two middle values if the count is even); range = maximum − minimum.

Probability = number of favorable outcomes ÷ total number of equally likely outcomes, always a value from 0 to 1 inclusive.

Distance = rate × time; rearrange as rate = distance ÷ time or time = distance ÷ rate.

Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1 for any nonzero x.

Angle sums: triangle = 180°, quadrilateral = 360°, and any polygon with n sides has interior angles totaling (n − 2) × 180°.