Targeted cheat sheets, College Board distractor traps, and interactive practice problems for every recurring question type on the Digital SAT and ACT.
When solving rational equations by multiplying through by a common denominator, you may introduce extraneous solutions—solutions that make a denominator equal to zero in the original equation.
The Conflicting Viewpoints passage in ACT Science features 2-4 scientists or students presenting competing theories. There are few or no graphs; questions test comparing hypotheses, identifying shared assumptions, and testing new evidence.
Logarithms are the inverse of exponentiation: log_b(x) = y means b^y = x. Key laws include log(ab) = log a + log b, log(a/b) = log a - log b, and log(a^k) = k log a.
The ACT tests matrix addition/subtraction, scalar multiplication, and 2x2 determinants. The determinant of [[a, b], [c, d]] is calculated as ad - bc.
Cross-Text questions feature Text 1 and Text 2 discussing the same topic with different angles or conclusions. The question asks how Text 2's author would respond to a specific finding or perspective in Text 1.
Words in Context questions test common academic words used in specific rhetorical ways (e.g., 'table' meaning to postpone, 'plastic' meaning malleable, 'champion' meaning to advocate). Always predict a simple synonym before looking at choices.
Standard deviation measures how spread out values are from the mean. A dataset where values are clustered tightly around the center has a smaller standard deviation than one with values scattered across the extremes.
Margin of error accounts for random sampling variability. To decrease margin of error, you must INCREASE sample size (n). The margin of error applies ONLY to the population from which the random sample was drawn, not to subgroups or different populations.
The Digital SAT frequently tests the standard form of a circle (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius. When given in expanded polynomial form x² + y² + Ax + By + C = 0, you must complete the square for both x and y to find the center or radius.
Parabolas appear in standard form y = ax² + bx + c, vertex form y = a(x - h)² + k, and factored form y = a(x - p)(x - q). The vertex (h, k) represents the maximum when a < 0 and minimum when a > 0. The x-coordinate of the vertex is given by x = -b / (2a).
Two linear equations have: NO SOLUTION if lines are parallel (same slopes, different y-intercepts); INFINITELY MANY SOLUTIONS if equations represent the exact same line (same slope, same y-intercept); EXACTLY ONE SOLUTION if slopes are different.
Exponential models follow the general formula y = a(1 + r)^t for growth and y = a(1 - r)^t for decay, where a is the initial value, r is the rate of change per unit t, and (1 ± r) is the growth/decay factor.
The built-in Desmos calculator allows you to find equations through points using regression: enter table values into x1 and y1, then type y1 ~ mx1 + b for linear or y1 ~ ax1² + bx1 + c for quadratic. Desmos calculates m and b instantly.
A recurring SAT favorite is the complementary angle identity: sin(x°) = cos(90° - x°). In a right triangle, the acute angles sum to 90°. If sin(A) = cos(B), then A + B = 90°.
When a polynomial P(x) is divided by (x - c), the remainder is simply P(c). If (x - c) is a factor of P(x), then the remainder is zero, meaning P(c) = 0.
Semicolons (;) link two independent clauses without a conjunction. Colons (:) and single dashes (-) MUST follow a complete independent clause to introduce an explanation, list, or dramatic elaboration.
Transitions indicate relationships between sentences: Contrast (however, nevertheless, conversely), Addition/Elaboration (furthermore, moreover, in addition), Causation/Result (consequently, therefore, thus), or Exemplification (for instance, specifically).
When a sentence begins with an introductory descriptive phrase (like 'Walking through the ancient ruins, ...'), the noun immediately following the comma MUST be the actual subject performing the action.
In Digital SAT Rhetorical Synthesis, students are provided 4-6 bulleted research notes and an explicit goal (e.g. 'The student wants to emphasize a difference between...', 'The student wants to introduce X to an unfamiliar audience').
Quantitative evidence questions present an academic passage arguing a claim alongside a bar chart, scatter plot, or table. The correct choice must be both factually accurate according to the graphic AND logically support the hypothesis in the text.
