18 Questions
Match the following theorems with their descriptions:
Exterior Angle Theorem (EAT) = The interior angles of any triangle have a sum of 180 degrees Angle Sum of a Triangle Theorem = Any exterior angle of a triangle is equal to the sum of the opposite interior angles Opposite Angle Theorem (OAT) = When two straight lines cross, opposite angles are equal. Exponent Property = None of the above
Match the following algebraic processes with their descriptions:
Cross Multiplication = Simplification of polynomial-based fractions by dividing like factors Partial Fraction Decomposition = Evaluating an algebraic expression by breaking down a rational expression into simpler forms Inverse of Multiplication = Dividing from top and bottom of a fraction Combining Like Fractions = Simplifying fractions by adding or subtracting like terms
Match the following logarithmic properties with their descriptions:
Log Property of Multiplication = log a(xy) = log a(x) + log a(y) Log Property of Division = log a(x/y) = log a(x) - log a(y) Change of Base Formula = log a(b) = log c(b) / log c(a) Log Property of Exponentiation = log a(x^n) = n log a(x)
Match the following pre-algebra properties with their descriptions:
Commutative Property of Addition = a + b = b + a Associative Property of Multiplication = a × (b × c) = (a × b) × c Distributive Property = a × (b + c) = a × b + a × c Identity Property of Addition = a + 0 = a
Match the following trigonometric identities with their descriptions:
Pythagorean Identity = sin^2(x) + cos^2(x) = 1 Reciprocal Identity = sin(x) = 1 / csc(x) Quotient Identity = tan(x) = sin(x) / cos(x) Cofunction Identity = sin(x) = cos(π/2 - x)
Match the following algebraic techniques with their descriptions:
Factoring = Expressing an expression as a product of simpler expressions Complete the Square = Solving quadratic equations by adjusting the form of the equation Inverse of Addition = Subtracting the same value from both sides of an equation Inverse of Multiplication = Dividing both sides of an equation by a value
Match the following geometric shapes with their respective formulas for the area:
Circle = A = πr² Trapezoid = A = (a + b)h/2 Right Triangle = A = (b × h)/2 Parallelogram = A = bh
Match the following algebraic identities with their respective expansions:
(x + y)² = x² + 2xy + y² (x - y)² = x² - 2xy + y² (x + y)³ = x³ + 3x²y + 3xy² + y³ (x - y)³ = x³ - 3x²y + 3xy² - y³
Match the following trigonometric functions with their respective definitions:
sin(θ) = opposite side / hypotenuse cos(θ) = adjacent side / hypotenuse tan(θ) = opposite side / adjacent side csc(θ) = hypotenuse / opposite side
Match the following calculus concepts with their respective formulas:
Volume of a Right Circular Cone = V = (1/3)πr²h Surface Area of a Sphere = SA = 4πr² Volume of a Cylinder = V = πr²h Lateral Surface Area of a Cone = LSA = πr√(r² + h²)
Match the following algebraic expressions with their respective factorizations:
acx³ + adx² + bcx + bd = (ax² + b)(cx + d) a(b + c) = ab + ac a² + 2ab + b² = (a + b)² a³ - b³ = (a - b)(a² + ab + b²)
Match the following geometric formulas with their respective shapes:
c² = a² + b² - 2abcos(θ) = Triangle (Law of Cosines) h = arcsin( opposite side / hypotenuse) = Right Triangle A = (a + b)h/2 = Trapezoid V = (1/3)πr²h = Right Circular Cone
Match the algebraic identity with its expansion:
(x + y)^2 = x^2 + 2xy + y^2 (x - y)^2 = x^2 - 2xy + y^2 (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3 (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3
Match the type of fraction with its description:
Improper fraction = The degree of the numerator is higher than the degree of the denominator Proper fraction = The degree of the numerator is smaller than the degree of the denominator Mixed fraction = A combination of a whole number and a proper fraction Rational expression = A fraction where the numerator and denominator are polynomials
Match the theorem with its statement:
Fundamental Theorem of Algebra = An nth degree polynomial has n (not necessarily distinct) zeros Quadratic Formula = If p(x) = ax^2 + bx + c, and 0 ≤ b^2 - 4ac, then the real zeros of p are x = (-b ± √(b^2 - 4ac))/2a Binomial Theorem = (x + y)^n = x^n + nx^(n-1)y + ... + y^n Remainder Theorem = If p(x) = a_nx^n + ... + a_1x + a_0, then p(a) = a_n(a)^n + ... + a_1a + a_0
Match the factorization with its expression:
x^2 - a^2 = (x - a)(x + a) x^3 + a^3 = (x + a)(x^2 - ax + a^2) x^4 - a^4 = (x^2 - a^2)(x^2 + a^2) x^3 - a^3 = (x - a)(x^2 + ax + a^2)
Match the polynomial characteristic with its description:
Zero of a polynomial = A value of x that makes the polynomial equal to zero Factor of a polynomial = An expression that divides the polynomial evenly Root of a polynomial equation = A value of x that satisfies the equation p(x) = 0 Solution of a polynomial equation = A value of x that satisfies the equation p(x) = 0
Match the procedure with its application:
Partial fraction decomposition = Solving improper fractions that can't be separated into a proper fraction and an improper fraction Long division = Simplifying an improper fraction by dividing the numerator by the denominator Cross multiplication = Simplifying a fraction by canceling out common factors Synthetic division = Evaluating a polynomial at a specific value of x
Test your knowledge of geometry formulas and theorems, including the Exterior Angle Theorem, Angle Sum of a Triangle Theorem, and Opposite Angle Theorem. Review and learn key concepts and formulas to improve your geometry skills.
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