2025-2026 Algebra and Trigonometry
Algebra - correct answer Branch of mathematics dealing with symbols and rules.
Trigonometry - correct answer Study of relationships between angles and sides.
Complex Numbers - correct answer Numbers in the form a + bi, where i is imaginary.
Real Numbers - correct answer All numbers on the number line, including rationals.
Linear Equations - correct answer Equations of the first degree, form ax + b = 0.
Quadratic Equations - correct answer Second-degree polynomial equations, form ax² + bx + c =
0.
Discriminant - correct answer Part of quadratic formula, b² - 4ac, determines roots.
Functions - correct answer Relations that assign exactly one output for each input.
One-to-One Functions - correct answer Each output is mapped from exactly one input.
Many-to-One Functions - correct answer Multiple inputs can map to the same output.
Inverse Functions - correct answer Functions that reverse the effect of the original function.
Polynomials - correct answer Expressions consisting of variables raised to whole number
powers.
Graphing - correct answer Visual representation of equations on a coordinate plane.
Exponential Functions - correct answer Functions of the form y = a^x, where a > 0.
Logarithmic Functions - correct answer Inverse of exponential functions, y = log_a(x).
Transformations of Graphs - correct answer Changes to the graph's position, size, or
orientation.
Rational Root Theorem - correct answer Provides possible rational roots of polynomial
equations.
Factor Theorem - correct answer States a polynomial has a factor if it equals zero.
Quadratic Inequalities - correct answer Inequalities involving quadratic expressions, e.g., ax² +
bx + c > 0.
Coordinate Geometry - correct answer Study of geometric figures using a coordinate system.
Exercises - correct answer Practice problems to reinforce concepts learned.
Preliminaries - correct answer Basic concepts and definitions needed for further study.
,Section Numbers - correct answer Indicate specific topics within the mathematics curriculum.
Graphing y = f(x + c) - correct answer Horizontal shift of the graph by c units.
Graphing y = f(x) + C - correct answer Vertical shift of the graph by C units.
Graphing y = f(ax) - correct answer Horizontal compression or expansion by factor a.
Graphing y = Af(x) - correct answer Vertical stretch or compression by factor A.
Pythagorean Theorem - correct answer a² + b² = c² for right triangles.
Slope Form - correct answer y = mx + b, where m is slope.
Point-Point Form - correct answer Equation using two points to find slope.
Slope-Point Form - correct answer y - y₁ = m(x - x₁) format.
Mutual Positions of Lines - correct answer Describes relationships between intersecting lines.
Circles - correct answer Set of points equidistant from center.
Solving Geometry Problems - correct answer Application of coordinate geometry in problem-
solving.
Rational Equations - correct answer Equations involving ratios of polynomials.
Exponential Equations - correct answer Equations where variables appear as exponents.
Logarithmic Equations - correct answer Equations involving logarithms of variables.
Radical Equations - correct answer Equations containing square roots or higher roots.
Sine Function - correct answer Ratio of opposite side to hypotenuse.
Tangent Function - correct answer Ratio of opposite side to adjacent side.
Cosine Function - correct answer Ratio of adjacent side to hypotenuse.
Cotangent Function - correct answer Ratio of adjacent side to opposite side.
Inverse Trigonometric Functions - correct answer Functions that reverse trigonometric ratios.
Trigonometric Identities - correct answer Equations involving trigonometric functions that hold
true.
Law of Sines - correct answer a/sin(A) = b/sin(B) = c/sin(C).
Law of Cosines - correct answer c² = a² + b² - 2ab*cos(C).
Radians - correct answer Angle measurement based on circle radius.
ℝ - correct answer Symbol representing the set of real numbers.
, Addition - correct answer Operation combining two numbers to produce a sum.
Multiplication - correct answer Operation combining two numbers to produce a product.
Closed Under Addition - correct answer Sum of two real numbers is a real number.
Closed Under Multiplication - correct answer Product of two real numbers is a real number.
Additive Identity - correct answer Zero; x + 0 = x for any real number x.
Multiplicative Identity - correct answer One; x ⋅ 1 = x for any real number x.
Additive Inverse - correct answer Number −x such that x + (−x) = 0.
Multiplicative Inverse - correct answer Number x⁻¹ such that x ⋅ x⁻¹ = 1.
Associative Law of Addition - correct answer (x + y) + z = x + (y + z).
Commutative Law of Addition - correct answer x + y = y + x for all real numbers.
Associative Law of Multiplication - correct answer (x ⋅ y) ⋅ z = x ⋅ (y ⋅ z).
Commutative Law of Multiplication - correct answer x ⋅ y = y ⋅ x for all real numbers.
Distributive Law - correct answer x ⋅ (y + z) = x ⋅ y + x ⋅ z.
Zero Factor Property - correct answer x ⋅ y = 0 if x = 0 or y = 0.
Subtraction Definition - correct answer x − y = x + (−y) for real numbers.
Division Definition - correct answer x ÷ y = x ⋅ y⁻¹ for y ≠ 0.
Integers - correct answer Whole numbers including positive, negative, and zero.
ℤ - correct answer Symbol representing the set of integers.
Rational Numbers - correct answer Numbers expressible as a ratio of integers.
ℚ - correct answer Symbol representing the set of rational numbers.
Irrational Numbers - correct answer Numbers that cannot be expressed as a fraction.
Example of Irrational Number - correct answer √2, which cannot be expressed as a ratio.
Rational Number - correct answer A number that can be expressed as m/n.
Irrational Number - correct answer A number that cannot be expressed as m/n.
Linear Equation - correct answer An equation of the form ax + b = 0.
Equivalent Equations - correct answer Equations with the same solution set.
Reduced Fraction - correct answer A fraction where numerator and denominator are coprime.
Algebra - correct answer Branch of mathematics dealing with symbols and rules.
Trigonometry - correct answer Study of relationships between angles and sides.
Complex Numbers - correct answer Numbers in the form a + bi, where i is imaginary.
Real Numbers - correct answer All numbers on the number line, including rationals.
Linear Equations - correct answer Equations of the first degree, form ax + b = 0.
Quadratic Equations - correct answer Second-degree polynomial equations, form ax² + bx + c =
0.
Discriminant - correct answer Part of quadratic formula, b² - 4ac, determines roots.
Functions - correct answer Relations that assign exactly one output for each input.
One-to-One Functions - correct answer Each output is mapped from exactly one input.
Many-to-One Functions - correct answer Multiple inputs can map to the same output.
Inverse Functions - correct answer Functions that reverse the effect of the original function.
Polynomials - correct answer Expressions consisting of variables raised to whole number
powers.
Graphing - correct answer Visual representation of equations on a coordinate plane.
Exponential Functions - correct answer Functions of the form y = a^x, where a > 0.
Logarithmic Functions - correct answer Inverse of exponential functions, y = log_a(x).
Transformations of Graphs - correct answer Changes to the graph's position, size, or
orientation.
Rational Root Theorem - correct answer Provides possible rational roots of polynomial
equations.
Factor Theorem - correct answer States a polynomial has a factor if it equals zero.
Quadratic Inequalities - correct answer Inequalities involving quadratic expressions, e.g., ax² +
bx + c > 0.
Coordinate Geometry - correct answer Study of geometric figures using a coordinate system.
Exercises - correct answer Practice problems to reinforce concepts learned.
Preliminaries - correct answer Basic concepts and definitions needed for further study.
,Section Numbers - correct answer Indicate specific topics within the mathematics curriculum.
Graphing y = f(x + c) - correct answer Horizontal shift of the graph by c units.
Graphing y = f(x) + C - correct answer Vertical shift of the graph by C units.
Graphing y = f(ax) - correct answer Horizontal compression or expansion by factor a.
Graphing y = Af(x) - correct answer Vertical stretch or compression by factor A.
Pythagorean Theorem - correct answer a² + b² = c² for right triangles.
Slope Form - correct answer y = mx + b, where m is slope.
Point-Point Form - correct answer Equation using two points to find slope.
Slope-Point Form - correct answer y - y₁ = m(x - x₁) format.
Mutual Positions of Lines - correct answer Describes relationships between intersecting lines.
Circles - correct answer Set of points equidistant from center.
Solving Geometry Problems - correct answer Application of coordinate geometry in problem-
solving.
Rational Equations - correct answer Equations involving ratios of polynomials.
Exponential Equations - correct answer Equations where variables appear as exponents.
Logarithmic Equations - correct answer Equations involving logarithms of variables.
Radical Equations - correct answer Equations containing square roots or higher roots.
Sine Function - correct answer Ratio of opposite side to hypotenuse.
Tangent Function - correct answer Ratio of opposite side to adjacent side.
Cosine Function - correct answer Ratio of adjacent side to hypotenuse.
Cotangent Function - correct answer Ratio of adjacent side to opposite side.
Inverse Trigonometric Functions - correct answer Functions that reverse trigonometric ratios.
Trigonometric Identities - correct answer Equations involving trigonometric functions that hold
true.
Law of Sines - correct answer a/sin(A) = b/sin(B) = c/sin(C).
Law of Cosines - correct answer c² = a² + b² - 2ab*cos(C).
Radians - correct answer Angle measurement based on circle radius.
ℝ - correct answer Symbol representing the set of real numbers.
, Addition - correct answer Operation combining two numbers to produce a sum.
Multiplication - correct answer Operation combining two numbers to produce a product.
Closed Under Addition - correct answer Sum of two real numbers is a real number.
Closed Under Multiplication - correct answer Product of two real numbers is a real number.
Additive Identity - correct answer Zero; x + 0 = x for any real number x.
Multiplicative Identity - correct answer One; x ⋅ 1 = x for any real number x.
Additive Inverse - correct answer Number −x such that x + (−x) = 0.
Multiplicative Inverse - correct answer Number x⁻¹ such that x ⋅ x⁻¹ = 1.
Associative Law of Addition - correct answer (x + y) + z = x + (y + z).
Commutative Law of Addition - correct answer x + y = y + x for all real numbers.
Associative Law of Multiplication - correct answer (x ⋅ y) ⋅ z = x ⋅ (y ⋅ z).
Commutative Law of Multiplication - correct answer x ⋅ y = y ⋅ x for all real numbers.
Distributive Law - correct answer x ⋅ (y + z) = x ⋅ y + x ⋅ z.
Zero Factor Property - correct answer x ⋅ y = 0 if x = 0 or y = 0.
Subtraction Definition - correct answer x − y = x + (−y) for real numbers.
Division Definition - correct answer x ÷ y = x ⋅ y⁻¹ for y ≠ 0.
Integers - correct answer Whole numbers including positive, negative, and zero.
ℤ - correct answer Symbol representing the set of integers.
Rational Numbers - correct answer Numbers expressible as a ratio of integers.
ℚ - correct answer Symbol representing the set of rational numbers.
Irrational Numbers - correct answer Numbers that cannot be expressed as a fraction.
Example of Irrational Number - correct answer √2, which cannot be expressed as a ratio.
Rational Number - correct answer A number that can be expressed as m/n.
Irrational Number - correct answer A number that cannot be expressed as m/n.
Linear Equation - correct answer An equation of the form ax + b = 0.
Equivalent Equations - correct answer Equations with the same solution set.
Reduced Fraction - correct answer A fraction where numerator and denominator are coprime.
