Complete Digital SAT (Reading, Writing & Math) & ACT Prep Study Guide: Formulas, Grammar Rules & Flashcards

Comprehensive Active-Recall Curriculum: Comprehensive Digital SAT and ACT exam preparation covering high-frequency vocabulary in context, Standard English Conventions grammar and punctuation, rhetoric and transitions, Heart of Algebra, Advanced Math quadratics and functions, geometry, trigonometry, and ACT Science data interpretation. Practice 6 progressive flashcard decks (192 cards total) spanning foundational principles (basic), intermediate problem-solving (intermediate), and advanced exam mastery (advanced).

👉 Explore All Digital SAT (Reading, Writing & Math) & ACT Prep Flashcard Decks on Flashcards.World →

---

Why Active Recall & Spaced Repetition Work for This Exam

Mastering Digital SAT (Reading, Writing & Math) & ACT Prep requires retrieving precise definitions, formulas, diagnostic rules, and edge-case distinctions under timed pressure. Passive re-reading creates an illusion of competence; active recall (testing yourself before viewing the answer) and spaced repetition strengthen long-term synaptic retrieval pathways.

Study Phase	Decks Covered	Target Mastery Level	Daily Active-Recall Protocol
Phase 1: Foundations (Weeks 1–2)	Decks 1 & 2 (Basic)	90%+ Instant Recall	32 new cards/day + full review of missed concepts
Phase 2: Application (Weeks 3–5)	Decks 3 & 4 (Intermediate)	Multi-step synthesis	32 new cards/day + interleaved Phase 1 review
Phase 3: Exam Mastery (Weeks 6–8)	Decks 5 & 6 (Advanced)	Timed exam readiness	Full 192-card spaced-repetition rotation + weak-spot drills

---

Deck 1: High-Frequency Digital SAT & ACT Vocabulary in Context & Rhetorical Transitions (32 Cards — Basic)

What this deck covers: High-yield Digital SAT Reading & Writing vocabulary in context, rhetorical logical transitions, tone markers, and text structure patterns.

High-Yield Prompt / Question	Core Concept & Mechanism	Exam Application & Details
In Digital SAT Words in Context questions, what does 'equivocal' mean and what is its opposite?	Open to more than one interpretation	ambiguous or deliberately evasive. Its direct opposite in SAT passages is 'unequivocal' (leaving no doubt; unambiguous).
What does 'ephemeral' mean in an SAT reading passage about ecological or artistic phenomena?	Lasting for a very short time	fleeting or transitory (e.g., ephemeral desert blooms or short-lived cultural trends). Contrast with 'enduring' or 'perennial'.
How is the verb 'corroborate' tested in SAT scientific and historical passages?	To confirm, support, or give validity to a hypothesis, claim, or finding with new independent evidence.	Antonyms: refute, contradict, undermine.
What is the precise meaning of 'ubiquitous' in SAT Reading and Writing?	Present, appearing, or found everywhere simultaneously	omnipresent (e.g., smartphones have become ubiquitous in modern classrooms).
What does 'mitigate' mean when discussing environmental policy or medical outcomes on the SAT?	To make less severe, serious, or painful	to alleviate or moderate the negative impact of a problem (not to eliminate it completely, which is 'eradicate').
How is 'ameliorate' used in SAT social science passages?	To make something bad or unsatisfactory better	to improve conditions (e.g., reforms designed to ameliorate urban poverty). Contrast with 'exacerbate' (to make worse).
What does 'exacerbate' mean and how does it contrast with 'alleviate'?	To make a problem, bad situation, or negative feeling worse or more intense (synonyms: aggravate, compound).	It is the direct antonym of 'alleviate' or 'mitigate'.
In SAT rhetorical analysis, what does it mean to 'repudiate' a hypothesis or doctrine?	To refuse to accept, reject outright, or disown the validity or authority of a claim (stronger than merely questioning or qualifying it).	To refuse to accept, reject outright, or disown the validity or authority of a claim (stronger than merely questioning or qualifying it).
What does 'pragmatic' mean when describing a policymaker or scientist on the SAT?	Dealing with things sensibly and realistically in a way that is based on practical rather than theoretical or idealistic considerations.	Dealing with things sensibly and realistically in a way that is based on practical rather than theoretical or idealistic considerations.
What is the meaning of 'fastidious' in SAT character or author descriptions?	Very attentive to and concerned about accuracy, precision, and minute detail	meticulously careful or hard to please.
What does 'ostensible' (or 'ostensibly') signal in an SAT passage?	Stated or appearing to be true, but not necessarily so	outward or superficial appearance masking an underlying reality (e.g., 'his ostensible generosity hid a desire for publicity').
What does 'precarious' mean in SAT passages about economics or wildlife?	Not securely held or in position	dangerously likely to fall, collapse, or fail; dependent on chance or uncertain conditions.

👉 Practice Deck 1: High-Frequency Digital SAT & ACT Vocabulary in Context & Rhetorical Transitions (32 Flashcards) →
🔍 Browse All Basic Digital SAT (Reading, Writing & Math) & ACT Prep Sets →

---

Deck 2: Standard English Conventions: Punctuation, Clauses, Modifiers & Agreement Rules (32 Cards — Basic)

What this deck covers: Complete grammar and punctuation mastery for Digital SAT Standard English Conventions and ACT English: semicolons, colons, dashes, modifiers, verb tense, and pronoun-antecedent agreement.

High-Yield Prompt / Question	Core Concept & Mechanism	Exam Application & Details
What is the Golden Rule for using a semicolon (;) on the Digital SAT and ACT?	A semicolon must join two complete, standalone Independent Clauses (IC	IC), making it grammatically equivalent to a period. The only exception is a 'super-comma' separating complex list items that already contain internal commas.
If two answer choices on the SAT are identical except one uses a period (.) and the other uses a semicolon (;) in the exact same spot, what can you conclude?	Both answer choices are automatically WRONG (unless the semicolon is functioning as a super-comma in a complex list), because a period and a	Both answer choices are automatically WRONG (unless the semicolon is functioning as a super-comma in a complex list), because a period and a semicolon between two clauses are grammatically interchangeable.
What is the strict grammatical requirement for the clause BEFORE a colon (:) on the SAT and ACT?	The clause preceding a colon MUST be a complete, standalone Independent Clause (it cannot end in a verb or preposition like 'such as:', 'including:', or 'are:').	What follows the colon can be a list, a single word/phrase, or an explanatory independent clause.
How do em-dashes (—) function on the Digital SAT and ACT?	1.	A single dash functions like a colon (after an Independent Clause to introduce an explanation or dramatic twist: IC — explanation). 2. A pair of dashes (— ... —) sets off a non-essential interrupting phrase in the middle of a sentence. You can never mix a comma and a dash arou...
What defines a Comma Splice error, and what are the four ways to fix it?	Joining two Independent Clauses with ONLY a comma (IC, IC) is always ungrammatical on the SAT/ACT. Fix it with: 1. Period (IC. IC) 2. Semicolon (IC	IC) 3. Comma + FANBOYS coordinating conjunction (IC, and IC) 4. Subordinating one clause (Although DC, IC).
What are the 7 FANBOYS coordinating conjunctions, and when do they take a comma?	For, And, Nor, But, Or, Yet, So.	Use a comma BEFORE a FANBOYS conjunction ONLY when it joins two complete Independent Clauses (Subject + Verb on both sides). Do NOT put a comma before 'and' or 'but' when it merely joins two verbs sharing the same subject (compound predicate).
Why is 'however,' 'therefore,' 'moreover,' or 'consequently' between two independent clauses with only commas (IC, however, IC) ALWAYS wrong?	Words like 'however,' 'therefore,' and 'moreover' are conjunctive adverbs, NOT FANBOYS coordinating conjunctions. Joining two independent clauses with ', however,' creates a comma splice. It must be punctuated as 'IC	however, IC' or 'IC. However, IC'.
How do you identify and fix a Dangling or Misplaced Modifier at the start of a sentence?	When a sentence begins with an introductory modifying phrase (especially a participial phrase starting with an -ing or -ed verb, like 'Walki	When a sentence begins with an introductory modifying phrase (especially a participial phrase starting with an -ing or -ed verb, like 'Walking through the museum, ...'), the very first noun immediately following the comma MUST be the person or thing performing that action.
How do prepositional phrases affect Subject-Verb Agreement on the SAT and ACT?	They NEVER affect the verb! The grammatical subject is never inside a prepositional phrase (e.g., 'of the students,' 'along with the mayor,' 'in addition to the findings').	Cross out all prepositional phrases between the subject and verb: 'The collection [of rare ancient coins] IS priceless.'
What is the rule for Subject-Verb Agreement with inverted sentence structures (e.g., 'There is/are' or prepositional phrase first)?	When a sentence begins with 'There is/are,' 'Here is/are,' or a prepositional phrase ('Behind the mountains lies/lie two valleys'), the true grammatical subject comes AFTER the verb.	Find the noun after the verb to check singular vs. plural.
Are indefinite pronouns like 'everyone,' 'each,' 'everybody,' 'anyone,' 'neither,' and 'either' singular or plural?	They are strictly SINGULAR and take singular verbs ('Each of the researchers HAS submitted a report'	'Neither of the hypotheses WAS confirmed').
How do you punctuate Essential (Restrictive) vs. Non-Essential (Non-Restrictive) relative clauses?	• Essential clauses narrow down the noun's identity and take NO commas (clauses starting with 'that' are always essential and never take commas). • Non-essential clauses add extra info that can be deleted without brea...	they must be bookended by two commas, two dashes, or two parentheses ('which' clauses are typically non-essential).

👉 Practice Deck 2: Standard English Conventions: Punctuation, Clauses, Modifiers & Agreement Rules (32 Flashcards) →
🔍 Browse All Basic Digital SAT (Reading, Writing & Math) & ACT Prep Sets →

---

Deck 3: Heart of Algebra: Linear Equations, Inequalities, Systems & Desmos Strategies (32 Cards — Intermediate)

What this deck covers: Core SAT & ACT linear algebra: slope-intercept, point-slope, standard form, parallel and perpendicular lines, linear systems with no/infinite solutions, absolute value inequalities, and built-in Desmos calculator shortcuts.

High-Yield Prompt / Question	Core Concept & Mechanism	Exam Application & Details
What are the three forms of a linear equation and what does each form immediately reveal?	1.	Slope-Intercept Form: y = mx + b (reveals slope m and y-intercept ). 2. Point-Slope Form: y - y1 = m(x - x1) (reveals slope m and a point (x1, y1) on the line). 3. Standard Form: Ax + By = C (slope m = -A/B, y-intercept = C/B, x-intercept = C/A).
How do you calculate the slope m between two points (x1, y1) and (x2, y2), and what are the slopes of horizontal and vertical lines?	m = (y2 - y1) / (x2 - x1) = Rise / Run.	• Horizontal line (y = k): slope m = 0. • Vertical line (x = h): slope m is UNDEFINED (division by zero).
In a real-world linear word problem y = mx + b, what do the slope m and y-intercept b represent?	• Slope (m): The constant rate of change (change in y per 1-unit increase in x, signaled by words like 'per,' 'each,' 'every,' 'rate').	• y-intercept (b): The initial value, starting fee, or baseline amount when x = 0.
What is the relationship between the slopes of parallel lines vs. perpendicular lines?	• Parallel lines: Have the EXACT SAME slope (m1 = m2) and different y-intercepts.	• Perpendicular lines: Their slopes are negative reciprocals of each other (m1 * m2 = -1, so m2 = -1/m1). Example: if m1 = 2/3, the perpendicular slope is -3/2.
When does a system of two linear equations in Standard Form (a1x + b1y = c1 and a2x + b2y = c2) have NO solution?	When the lines are parallel and distinct: the ratio of x-coefficients equals the ratio of y-coefficients, but does NOT equal the ratio of co	When the lines are parallel and distinct: the ratio of x-coefficients equals the ratio of y-coefficients, but does NOT equal the ratio of constants: a1 / a2 = b1 / b2 != c1 / c2.
When does a system of two linear equations (a1x + b1y = c1 and a2x + b2y = c2) have INFINITELY MANY solutions?	When the two equations represent the exact same line (coincident lines): all three ratios are equal: a1 / a2 = b1 / b2 = c1 / c2.	When the two equations represent the exact same line (coincident lines): all three ratios are equal: a1 / a2 = b1 / b2 = c1 / c2.
When does a system of two linear equations (a1x + b1y = c1 and a2x + b2y = c2) have EXACTLY ONE solution?	When the two lines have different slopes and therefore intersect at a single point: a1 / a2 != b1 / b2.	When the two lines have different slopes and therefore intersect at a single point: a1 / a2 != b1 / b2.
How do you quickly solve an SAT linear system question asking for a combination like '3x + 3y' or 'x - y' instead of individual x and y?	Always check if simply adding or subtracting the two given equations directly yields the target expression! Example: If 5x + 2y = 14 and 2x	Always check if simply adding or subtracting the two given equations directly yields the target expression! Example: If 5x + 2y = 14 and 2x + 5y = 21, adding them gives 7x + 7y = 35, so x + y = 5 and 3x + 3y = 15 in 5 seconds.
What rule must you remember when multiplying or dividing both sides of an inequality by a negative number?	You MUST flip (reverse) the direction of the inequality sign! Example: -3x > 12 becomes x < -4.	Multiplying or dividing by a positive number, or adding/subtracting any number, does NOT flip the sign.
How do you solve an absolute value equation |ax + b| = c?	• If c < 0: There is NO real solution (since absolute value is never negative).	• If c = 0: Set ax + b = 0 (1 solution). • If c > 0: Split into two equations: ax + b = c OR ax + b = -c (2 solutions).
What is the quick formula for the sum and product of the two solutions to |x - a| = b (where b > 0)?	The two solutions are x = a + b and x = a - b, which are symmetric around the center point x = a.	• Sum of solutions = (a + b) + (a - b) = 2a. • Midpoint of solutions = a.
How do you write an absolute value equation or inequality for a variable x that is within distance d of a target value T?	|x - Target| <= Distance, i.e., |x - T| <= d, which simplifies to T - d <= x <= T + d.	Example: A machine fills bottles to 500 mL with a tolerance of ±4 mL => |x - 500| <= 4.

👉 Practice Deck 3: Heart of Algebra: Linear Equations, Inequalities, Systems & Desmos Strategies (32 Flashcards) →
🔍 Browse All Intermediate Digital SAT (Reading, Writing & Math) & ACT Prep Sets →

---

Deck 4: Problem Solving & Data Analysis: Ratios, Percentages, Probability & Statistics (32 Cards — Intermediate)

What this deck covers: High-yield SAT & ACT quantitative reasoning: percent change, successive percent multipliers, unit conversions, mean/median/standard deviation, margin of error, study design, and conditional probability.

High-Yield Prompt / Question	Core Concept & Mechanism	Exam Application & Details
What is the exact formula for Percent Change (Percent Increase or Decrease)?	Percent Change = ((New Value - Original Value) / Original Value) * 100%.	Crucial trap: Always divide by the ORIGINAL starting value (the value after 'than' or 'from'), never the new value!
How do you express a p% increase and a p% decrease as single decimal multipliers?	• A p% increase multiplies the original value by (1 + p/100).	Example: +18% => multiply by 1.18. • A p% decrease multiplies the original value by (1 - p/100). Example: -18% => multiply by 0.82.
Why does increasing a price by 20% and then decreasing the new price by 20% NOT return to the original price?	Because the second percentage applies to the larger intermediate value! Multiply the factors: 1.20 * 0.80 = 0.96, which represents a net 4%	Because the second percentage applies to the larger intermediate value! Multiply the factors: 1.20 * 0.80 = 0.96, which represents a net 4% DECREASE from the original price.
If a discounted item costs $85 after a 15% discount and an 8% sales tax is applied to the discounted price, how do you find the original price P?	Always apply multipliers to the original price P: Discounted price = 0.85 * P = 85 => P = $100.	Trap: Never add 15% onto $85 ($85 * 1.15 = $97.75 is wrong!).
How do you convert squared or cubed units (e.g., square feet to square yards, or cubic meters to cubic centimeters)?	Square or cube the linear conversion factor! Since 1 yard = 3 feet: • 1 square yard = (3 feet)^2 = 9 square feet.	• 1 cubic yard = (3 feet)^3 = 27 cubic feet.
What is the Dimensional Analysis (Factor-Label) method for multi-step rate conversions on the SAT?	Write the starting rate as a fraction with units, then multiply by conversion fractions arranged so unwanted units cancel diagonally (numera	Write the starting rate as a fraction with units, then multiply by conversion fractions arranged so unwanted units cancel diagonally (numerator with denominator) until only the target units remain.
How do you calculate the Combined Work Rate of two machines or people working together?	Add their individual rates: 1/T_total = 1/T_A + 1/T_B, which simplifies to T_total = (T_A * T_B) / (T_A + T_B).	Example: If A takes 3 hours and B takes 6 hours, together they take (3*6)/(3+6) = 18/9 = 2 hours.
What is the formula for Average Speed over a multi-part trip, and why is it NOT the average of the speeds?	Average Speed = Total Distance / Total Time.	If you drive 60 mph going there and 40 mph returning over the same distance d, Average Speed = 2d / (d/60 + d/40) = 48 mph (the harmonic mean, NOT 50 mph!).
How do you quickly use the Sum Formula for the Arithmetic Mean (Average) on the SAT and ACT?	Total Sum = (Mean) * (Number of items).	Whenever a question gives the average of n numbers, immediately multiply to get their Sum. If a new number is added, New Mean = (Old Sum + New Number) / (n + 1).
How do you find the Median of a dataset with an odd vs. even number of values (including from a frequency table or histogram)?	Order all N values from least to greatest.	The median is at position (N + 1) / 2: • If N is odd (e.g., N = 25), the median is the single middle value at position (25+1)/2 = 13th value. • If N is even (e.g., N = 24), the median is the average of the 12th and 13th values.
How does adding or removing an extreme Outlier affect the Mean vs. the Median?	• The Mean is sensitive (non-resistant) to outliers and gets pulled strongly in the direction of the outlier.	• The Median is resistant to outliers and changes very little or not at all.
In a skewed distribution (right-skewed vs. left-skewed), how do the Mean and Median compare?	• Positively / Right-skewed (long tail to the right): Mean > Median.	• Negatively / Left-skewed (long tail to the left): Mean < Median. • Symmetric distribution: Mean = Median.

👉 Practice Deck 4: Problem Solving & Data Analysis: Ratios, Percentages, Probability & Statistics (32 Flashcards) →
🔍 Browse All Intermediate Digital SAT (Reading, Writing & Math) & ACT Prep Sets →

---

Deck 5: Passport to Advanced Math: Quadratics, Discriminant, Exponentials & Polynomials (32 Cards — Advanced)

What this deck covers: Advanced SAT & ACT algebra: quadratic forms, vertex formulas, discriminant root analysis, Vieta's formulas, exponential growth/decay with fractional time intervals, rational equations, and polynomial remainder theorem.

High-Yield Prompt / Question	Core Concept & Mechanism	Exam Application & Details
What are the three algebraic forms of a Quadratic Function, and what geometric feature does each display as constants in the equation?	1.	Standard Form: f(x) = ax^2 + bx + c -> displays the y-intercept (0, c). 2. Factored (Intercept) Form: f(x) = a(x - r1)(x - r2) -> displays the x-intercepts/roots (r1, 0) and (r2, 0). 3. Vertex Form: f(x) = a(x - h)^2 + k -> displays the vertex (minimum or maximum) at (h, k).
How do you find the Vertex (h, k) and Axis of Symmetry of a parabola in Standard Form y = ax^2 + bx + c?	• Axis of symmetry (and x-coordinate of vertex): h = -b / (2a).	• y-coordinate of vertex (minimum if a > 0, maximum if a < 0): k = f(-b / ) = c - b^2 / (4a). • If given the x-intercepts r1 and r2, the vertex x-coordinate is their midpoint: h = (r1 + r2) / 2.
What is the Quadratic Formula and what is the Discriminant D?	x = [-b ± sqrt(b^2 - 4ac)] / (2a).	The Discriminant is the expression inside the radical: D = b^2 - 4ac.
How does the sign of the Discriminant D = b^2 - 4ac determine the number of real solutions (x-intercepts) of a quadratic?	• D > 0: Exactly TWO distinct real solutions (graph crosses the x-axis twice). • D = 0: Exactly ONE real solution (a double root	vertex is tangent to the x-axis). • D < 0: ZERO real solutions (two complex conjugate roots; parabola never touches the x-axis).
What are Vieta's Formulas for the Sum and Product of the solutions to ax^2 + bx + c = 0?	• Sum of solutions (r1 + r2) = -b / a.	• Product of solutions (r1 * r2) = c / a. High-yield SAT shortcut: Never use the full quadratic formula when a question asks for the sum or product of solutions—just calculate -b/a or c/a!
How do you determine the number of intersection points between a line y = mx + d and a parabola y = ax^2 + bx + c?	Set the two equations equal (ax^2 + bx + c = mx + d), move all terms to one side to form a single quadratic ax^2 + (b - m)x + (c - d) = 0, a	Set the two equations equal (ax^2 + bx + c = mx + d), move all terms to one side to form a single quadratic ax^2 + (b - m)x + (c - d) = 0, and evaluate its Discriminant D = B^2 - 4AC: • D > 0 => 2 intersections • D = 0 => 1 intersection (tangent) • D < 0 => 0 intersections.
How do you Complete the Square to convert x^2 + bx + c = 0 into Vertex Form or Circle Form?	Take half of the linear coefficient b, square it ((b/2)^2), and add it to both sides: x^2 + bx + (b/2)^2 = (x + b/2)^2.	Take half of the linear coefficient b, square it ((b/2)^2), and add it to both sides: x^2 + bx + (b/2)^2 = (x + b/2)^2.
What are the three Special Factoring Identities tested constantly on the SAT and ACT?	1.	Difference of Squares: a^2 - b^2 = (a - b)(a + b) 2. Square of a Binomial Sum: (a + b)^2 = a^2 + 2ab + b^2 3. Square of a Binomial Difference: (a - b)^2 = a^2 - 2ab + b^2.
In the Exponential Growth/Decay model f(t) = a * b^(t / k), what do a, b, and k represent?	• a = initial value when t = 0. • b = growth/decay factor per interval (b = 1 + r for growth	b = 1 - r for decay; b = 2 for doubling; b = 0.5 for half-life). • k = length of time required for ONE full growth/decay period!
If a bacterial colony doubles every 15 minutes and time t is measured in HOURS, vs. if t is measured in MINUTES, what is the exponent?	• If t is in minutes (and 1 period = 15 minutes): f(t) = a * 2^(t / 15).	• If t is in hours (so 4 periods occur per 1 hour): f(t) = a * 2^(4t). Test plug-in: after 15 minutes (t = 0.25 hours), the exponent must equal 1!
How do you rewrite an annual exponential growth equation P(t) = 1000(1.12)^t (where t is in years) to show the monthly growth rate?	Since 1 year = 12 months, replace t with (12t) and take the 12th root of the base so the value at t = 1 stays identical: P(t) = 1000 * (1.12	Since 1 year = 12 months, replace t with (12t) and take the 12th root of the base so the value at t = 1 stays identical: P(t) = 1000 * (1.12^)^(12t) ≈ 1000 * (1.00949)^(12t).
What are the six core Laws of Exponents and Radicals?	1.	x^a * x^b = x^(a + b) 2. x^a / x^b = x^(a - b) 3. (x^a)^b = x^(a * b) 4. (xy)^a = x^a * y^a 5. x^(-a) = 1 / x^a 6. x^(m / n) = n-th root of (x^m) = (n-th root of x)^m.

👉 Practice Deck 5: Passport to Advanced Math: Quadratics, Discriminant, Exponentials & Polynomials (32 Flashcards) →
🔍 Browse All Advanced Digital SAT (Reading, Writing & Math) & ACT Prep Sets →

---

Deck 6: Geometry, Trigonometry, Complex Numbers & ACT Science Data Interpretation (32 Cards — Advanced)

What this deck covers: High-yield SAT & ACT geometry, circle equations, radian arc length/sector area, right-triangle and unit-circle trigonometry, matrices, complex numbers, and ACT Science experimental data reasoning.

High-Yield Prompt / Question	Core Concept & Mechanism	Exam Application & Details
What is the Standard Form Equation of a Circle in the xy-plane, and how do you convert x^2 + y^2 + Dx + Ey + F = 0 into it?	(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius (note: the signs inside parentheses are opposite, and the right side is r SQUARED!).	Convert general form by completing the square for both x and y: h = -D/2, k = -E/2, and r^2 = F_moved + h^2 + k^2.
What are the side-length ratios of the two Special Right Triangles (45°-45°-90° and 30°-60°-90°)?	• 45°-45°-90° (Isosceles Right Triangle): x : x : x*sqrt(2).	• 30°-60°-90° (Half of an Equilateral Triangle): x (opposite 30°) : x*sqrt(3) (opposite 60°) : 2x (hypotenuse).
What are the four most common Pythagorean Triples tested on the SAT and ACT?	• 3 - 4 - 5 (and multiples: 6-8-10, 9-12-15, 15-20-25) • 5 - 12 - 13 (and 10-24-26) • 8 - 15 - 17 • 7 - 24 - 25 Recognizing these saves sign	• 3 - 4 - 5 (and multiples: 6-8-10, 9-12-15, 15-20-25) • 5 - 12 - 13 (and 10-24-26) • 8 - 15 - 17 • 7 - 24 - 25 Recognizing these saves significant calculation time on right-triangle problems.
What is the Complementary Angle Identity for Sine and Cosine tested on nearly every Digital SAT?	In any right triangle with acute angles A and B (where A + B = 90° or π/2 radians): sin(A) = cos(B) = cos(90° - A), and cos(A) = sin(B) = sin(90° - A).	Why? Because the side Opposite angle A is the exact same side Adjacent to angle B!
How are sin(θ), cos(θ), and tan(θ) defined in a right triangle (SOH-CAH-TOA) and on the Unit Circle?	• sin(θ) = Opposite / Hypotenuse = y-coordinate on the unit circle.	• cos(θ) = Adjacent / Hypotenuse = x-coordinate on the unit circle. • tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ) = y / x.
How do you convert between Degrees and Radians, and how many radians are in a full circle?	A full 360° circle is 2π radians, so 180° = π radians.	• Degrees to Radians: multiply by (π / 180°). • Radians to Degrees: multiply by (180° / π).
What are the formulas for Arc Length s and Sector Area A of a circle in Degrees vs. Radians?	Both equal the fraction of the full circle (θ / 360° or θ / 2π) times the circumference or area: • In Degrees: Arc Length = (θ / 360°) * 2πr	Sector Area = (θ / 360°) * πr^2. • In Radians: Arc Length s = r * θ; Sector Area A = (1/2) * r^2 * θ.
What is the Inscribed Angle Theorem vs. Central Angle in a circle?	A central angle (vertex at the center) equals the measure of its intercepted arc.	An inscribed angle (vertex on the circumference) equals HALF the measure of its intercepted arc (θ_inscribed = (1/2) * θ_central). Corollary: Any angle inscribed in a semicircle (intercepting a 180° diameter) is a 90° right angle!
What is the relationship between a Radius and a Tangent Line at the point of tangency on a circle?	A tangent line to a circle is ALWAYS perpendicular (forms a 90° right angle) to the radius drawn to the point of tangency.	Thus, their slopes are negative reciprocals (m_tangent = -1 / m_radius).
When two parallel lines are cut by a transversal, which angle pairs are congruent and which are supplementary?	• Congruent (equal): Alternate Interior, Alternate Exterior, Corresponding, and Vertical angles.	• Supplementary (sum to 180°): Consecutive Interior (Same-Side Interior) angles and Linear Pairs.
What are the Triangle Inequality Theorem and the Exterior Angle Theorem?	• Triangle Inequality: The third side c of any triangle must lie strictly between the difference and the sum of the other two sides: |a - b| < c < a + b.	• Exterior Angle Theorem: An exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles.
In Similar Triangles (proven by AA similarity), how do the ratios of corresponding lengths, perimeters, areas, and volumes scale?	If the linear scale factor of corresponding sides is k = a / b: • Ratio of Perimeters, Altitudes, or Medians = k • Ratio of Areas (or Surfac	If the linear scale factor of corresponding sides is k = a / b: • Ratio of Perimeters, Altitudes, or Medians = k • Ratio of Areas (or Surface Areas) = k^2 • Ratio of Volumes (for similar 3D solids) = k^3.

👉 Practice Deck 6: Geometry, Trigonometry, Complex Numbers & ACT Science Data Interpretation (32 Flashcards) →
🔍 Browse All Advanced Digital SAT (Reading, Writing & Math) & ACT Prep Sets →

---

Complete 6-Deck Quick-Access Directory

Deck #	Deck Title	Level	Cards	Direct Practice Link
Deck 1	High-Frequency Digital SAT & ACT Vocabulary in Context & Rhetorical Transitions	basic	32	Open Deck 1 →
Deck 2	Standard English Conventions: Punctuation, Clauses, Modifiers & Agreement Rules	basic	32	Open Deck 2 →
Deck 3	Heart of Algebra: Linear Equations, Inequalities, Systems & Desmos Strategies	intermediate	32	Open Deck 3 →
Deck 4	Problem Solving & Data Analysis: Ratios, Percentages, Probability & Statistics	intermediate	32	Open Deck 4 →
Deck 5	Passport to Advanced Math: Quadratics, Discriminant, Exponentials & Polynomials	advanced	32	Open Deck 5 →
Deck 6	Geometry, Trigonometry, Complex Numbers & ACT Science Data Interpretation	advanced	32	Open Deck 6 →

👉 Launch Full Digital SAT (Reading, Writing & Math) & ACT Prep Spaced-Repetition Track →