Algebra 2 Honors Practice Test

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• Factor x^3 - 8.
• What term describes a function's value for extreme values of its independent variable?
• The set {...} shown, containing negative numbers, zero, and positive numbers, is an example of which number system?
• For the cubic P(x) = x^3 - 6x^2 + 11x - 6, what is the product of its zeros?
• Which term is commonly used to refer to the shorter dimension of a two-dimensional figure, opposite of length?
• In a complex number written as a + bi, which part represents the imaginary component?
• Compute the sum of the infinite geometric series with a1 = 8 and r = 1/3.
• What is the end behavior of f(x) = -x^4 + 2x^3 - x?
• For f(x) = x^3 − 9x, identify the critical points and their nature.
• Solve sin x = 1/2 for x in [0, 2π).
• If log_a(b) = c, express log_b(a) in terms of c.
• What is the standard form of a circle with center at (2,-3) and radius 5?
• Expand the circle equation (x - 2)^2 + (y + 3)^2 = 25.
• In a whole number division problem, the final undivided part that is less than the divisor and 'left over' after dividing.
• Which type of function has a graph that is a horizontal line?
• Solve log_2(3x) = 3.
• Which term describes a value that is close to its exact value?
• The number of square units needed to cover a surface.
• Which term refers to a two-dimensional diagram that can be folded into a three-dimensional figure?
• What is the standard form equation of an ellipse centered at the origin with semi-axes a = 4 and b = 3?
• Consider ellipse x^2/16 + y^2/9 = 1. Which statement about a, b, c and foci is true?
• For parabola y = 3x^2 + 6x + 7, what is the x-coordinate of the vertex?
• Real-life math problem used to model everyday situations.
• In the expansion of (x + y)^4, what is the coefficient of x^2 y^2?
• Identify the function defined by y = a*b^x where b > 0 and b ≠ 1.
• Solve x^2 - 3x - 4 ≥ 0.
• Find the vertical asymptotes, holes, and the simplified form of f(x) = (x^2 - 1)/(x^2 - 3x + 2).
• Which term describes a mathematical sentence that uses comparison operators such as <, >, ≤, ≥, or ≠?
• Solve the inequality 2x^2 − 5x + 3 ≤ 0.
• In a geometric sequence with a1 = 4 and r = -3, find a4.
• Which term describes a quantity that varies directly with two variables, in the form z = kxy?
• What is the product of multiplying numbers together?
• Factor x^4 - 5x^2 + 6 completely over the real numbers.
• Which term is a symbol used to indicate a root, read as the nth root of x?
• Solve the 2x2 linear system: 2x - y = 3 and 4x + y = 1. Find the ordered pair (x,y).
• Solve x^2 + 4x + 13 = 0; express the roots in a + bi form.
• Solve sqrt(3x+1) = x+2. Determine the real solutions.
• What symbol, usually a letter, could represent a number?
• What is the unit of measure for angles equal to 1/360 of a complete revolution?
• What is the axis of symmetry of the parabola f(x) = x^2 - 4x + 7?
• Solve log_3(x - 4) - log_3(x + 2) = 1. Determine the solutions and domain.
• What is the name for a number that includes a real and imaginary part?
• A shape with four equal sides.
• Solve the inequality (x - 1)/(x + 4) ≤ 0.
• Which term refers to an operation on a figure by which another image is created?
• What is the vertex and the minimum value of f(x) = x^2 - 4x + 7?
• Compute the dot product of u = <3, -1, 4> and v = <-2, 5, 0>.
• Solve z^2 + 4 = 0 and express the roots in a+bi form.
• The result of adding numbers or expressions together.
• The process of converting a fraction or mixed number to an equivalent fraction or mixed number in which the greatest common factor of the numerator and the denominator of the fraction is one.
• Let f(x) = 2x + 1 and g(x) = x^2. Compute (f∘g)(-2) and (g∘f)(-2).
• The horizontal and vertical number lines used in a coordinate plane.
• In the expression a^n, the exponent n indicates what?
• Which term corresponds to the amount of space occupied in three dimensions, expressed in cubic units?
• Solve the 2x2 linear system x + 2y = 5 and 3x - y = 4; report (x, y).
• For the cubic P(x) = x^3 - 6x^2 + 11x - 6, what is the sum of its zeros?
• Which term describes the two-dimensional plane used for plotting data and locating points?
• Solve sqrt(2x+3) = x+1; list all solutions and identify any extraneous solutions.
• For y = -3(x + 4)^2 + 2, which description is correct?
• In ellipse x^2/25 + y^2/16 = 1, c^2 equals a^2 - b^2. What is c^2?
• What term means having the same value?
• Which term describes the space in three dimensions, often expressed in cubic units?
• What is a two-dimensional diagram that can be folded to form a three-dimensional figure called?
• In the function f(x) = (x^2 - 1)/(x^2 - 3x + 2), which of the following describes its hole and vertical asymptote?
• Which term describes the property of having the same value?
• Which term denotes a polygon with three sides?
• Which term describes the symbol used to indicate a root in an expression?
• Divide x^3 - 2x^2 + x by x - 2; provide the quotient and remainder.
• Given a = 1, b = -4, c = 7, how many real roots does ax^2 + bx + c = 0 have?
• Having the same or constant ratio.
• The result of multiplying numbers together.
• What term describes a mathematical phrase that contains variables, functions, numbers, and/or operations and does not contain an equal or inequality sign?
• For the parabola y = x^2/8, what is the focus?
• Which term refers to a point where lines meet, such as the corners of polygons?
• Which concept describes an invariant property under reflection or rotation?
• What term refers to a number or expression that is multiplied by one or more other numbers or expressions to yield a product?
• Which term describes a straight path with infinite length and no width?
• What is the family of curves that includes circles, ellipses, parabolas, and hyperbolas?
• Which term refers to a collection of numbers where order does not matter and duplicates are not allowed?
• Which term refers to a mathematical process such as addition, subtraction, multiplication, division, raising to a power, or finding the square root?
• Solve log base 3 of (x − 1) = 2.
• In geometry, what is the line segment extending from a vertex to the base and perpendicular to the base called?
• The number that can be written in the form a+bi where i^2 = -1.
• Which word refers to a quantity that can change and is not fixed in an analysis?
• A set is a finite or infinite collection of distinct objects in which order has no significance.
• In the function f(x) = sqrt(x - 1). Determine the domain of the composition f(f(x)).
• Find the projection of a = <4, -2> onto b = <1, 3>, expressed as a vector.
• What is the vertex of the parabola y = -3(x + 4)^2 + 2?
• Which term defines a number that is the result of subtraction?
• Solve the quadratic equation x^2 - 4x - 5 = 0.
• Solve √(3x + 5) = x. What is x?
• In geometry, what is the segment from a vertex perpendicular to the opposite side commonly called?
• What term describes a mathematical sentence stating that the two expressions have the same value?
• Which of the following is not a root of P(x) = x^3 - 6x^2 + 11x - 6?
• What are the solutions of the equation x^2 + 4x + 5 = 0?
• Find the oblique asymptote of R(x) = (2x^2 + x + 1)/(x + 1) and describe the end behavior.
• Which variation describes a quantity that varies jointly with two or more quantities, such as z = kxy?
• The points where a curve intersects the axes are called what?
• Evaluate log base 2 of 8.
• Find the sum of the arithmetic sequence 3, 5, ..., 23.
• For hyperbola x^2/9 - y^2/16 = 1, determine a^2, b^2, c^2 and coordinates of foci.
• Find the sum of the first 5 terms of the geometric series with a1 = 3 and r = -2.
• Which term describes a mathematical phrase that contains variables, numbers, and/or operations and does not contain an equality sign?
• Factor x^4 - 4x^2 + 4 over the reals.
• Evaluate P(0) for P(x) = x^3 - 6x^2 + 11x - 6.
• Which term describes the ratio that characterizes the shape of a conic section?
• Factor (x^2+3)^2 - (2x)^2 using a difference of squares.
• What determinate quantity is adopted as a standard of measurement?
• Determine the end behavior of f(x) = -2x^5 + 3x^3 - x as x approaches infinity and negative infinity.
• Which theorem provides the expansion formula for (a+b)^n with integer n?
• What term describes the behavior of a function as x grows without bound in either direction?
• Rewrite y = 2x^2 - 8x + 3 in vertex form and identify the vertex.
• Find the inverse of f(x) = 2x - 5 and verify by composition.
• Which term denotes the central point where the sides of a polygon meet and where multiple edges of a polyhedron converge?
• What is the set of input values for which a function or relation is defined called?
• What is the formula for the sum of the first n terms of a geometric sequence with first term a1 and common ratio r (r ≠ 1)?
• For the parabola with vertex at origin and focus at (0,2), what is its directrix?
• Divide x^3 - 6x^2 + 11x - 6 by x - 1; provide the quotient and remainder.
• Solve 4^x = 64^{-x}.
• Write the equation of a parabola with vertex at (0,0) and focus at (0,2).
• Which term is the name for the root symbol in mathematics, such as the square root or nth root?
• Which term describes the set of all points at a fixed distance from a given center?
• Solve the system x + y = 7 and x − y = 1; what is (x, y)?
• Decompose the rational function (3x^2 - x - 10)/(x^2 - x - 6) into partial fractions.
• Determine whether the series sum_{n=1}^ ∞ 1/n^2 converges or diverges; if convergent, state the known sum.
• Which term is a statement or conjecture that can be proven to be true based on postulates, definitions, or other proven theorems?
• In graphing a function, which variable is typically treated as the independent variable?
• The sum of the roots of x^2 + 4x + 5 = 0 is which value?
• Compute 16^(3/4).
• Solve the system 3x - 2y = 7 and x + 4y = -5.
• In a mathematical expression, the exponent indicates how many times the base is used as a factor.
• Express log base 12 of 72 in terms of common logarithms.
• What is the shortcut method for dividing a polynomial by a polynomial of the first degree?
• Which statement about the zeros of the polynomial (x - 1)(x + 1)(x - 3)(x + 2) is true?
• Which term describes the progression of numbers in a fixed order, not the total of terms?
• Identify a valid Pythagorean identity valid for all real x.
• Which term describes something tilted at an angle, neither vertical nor horizontal?
• What are the eigenvalues of the matrix [[3, 0], [0, 5]]?
• A polynomial with more than one term is called what?
• Which term is defined as the number of times a number occurs as a factor, as indicated by an exponent?
• From equation (x - 4)^2 + (y + 2)^2 = 25, identify the center and radius.
• Which term refers to the extent of three-dimensional space, typically measured in cubic units?
• Factor x^4 - x^3 - 7x^2 + x + 6.
• An indicated sum of successive terms of a sequence.
• What is the one-dimensional measure that describes the length of a straight segment?
• Expand (x + y)^4.
• Solve x^2 + 2x + 5 = 0; express roots in a + bi form.
• The operation that gives the exponent to which base b must be raised to obtain x is called what?
• Factor x^3 + 3x^2 - 6x - 18 by grouping. What are the roots?
• What is the determinant of the coefficient matrix [[2,-1],[4,1]]?
• An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformation.
• Solve 3x^2 − 12x + 12 ≤ 0.
• What is the name of the U-shaped graph of a quadratic function y = ax^2 + bx + c with a ≠ 0?
• The set {...} containing negative integers, zero, and positive integers is an example of which number system?
• A list of numbers separated by commas.
• What is the standard form of a hyperbola with center at origin, transverse axis along the x-axis, a = 5, b = 4?
• The number that multiplies the variable in an algebraic expression.
• The set of all rational and irrational numbers.
• Find the zeros of f(x) = x^3 - 6x^2 + 11x - 6.
• Which expression represents the nth term a_n for the arithmetic sequence with a1 = 7 and d = -2?
• The process of combining two functions by using the output of one as the input of the other, denoted f(g(x)).
• Evaluate f(0) for f(x) = (3x+5)/(x-2).
• Decompose (x^2 - 3x - 4)/(x^2 - x - 6) into partial fractions.
• Divide x^4 − 1 by x^2 − 1; provide the quotient and remainder.
• What do we call a relation where each value of x is paired with a unique value of y?
• For f(x) = (x^2 - 1)/(x^2 - 4), identify the domain and vertical/horizontal asymptotes.
• If f(x) = x^2 and g(x) = x + 1, what is (g ∘ f)(0)?
• A _______ of a polynomial is a number x such that P(x)=0.
• A specific location in space that has no discernible length or width.
• Which term is the point common to the two rays that form the sides of a polygon?
• Which term refers to the common point where two rays meet in a polygon, and the common point to three or more edges of a polyhedron?
• What name refers to a theorem that gives a formula to expand (a+b)^n without repeated multiplications?
• Find the inverse function of f(x) = (3x+5)/(x-2) and state its domain and range.
• In coordinate geometry, which term refers to the places where a graph intersects the axes, collectively?
• Find a closed form for a_n given the recurrence a_n = 3 a_{n-1} - 2 with a1 = 4.
• Simplify √50.
• In an arithmetic sequence with a1 = 7 and d = -2, find a5.
• What is the unit for measuring angles that is defined so that a full circle contains 360 of these units?
• A population starts at 1000 and doubles every 3 years. Which expression models P(t) for t years?
• In three-dimensional space, which axis is perpendicular to the x-axis?
• The result of adding a finite number of terms is called the sum.
• Sum of the geometric series with a1 = 3, r = 2, n = 4.
• In a geometric sequence with a1 = 4 and r = -3, what is a6?
• Which of the following is a correct factorization of x^4 - x^3 - 7x^2 + x + 6?
• Find the sum of the geometric series with a1 = 5, r = 1/2, and n = 6.
• In a graph, a line that a curve approaches but never reaches, with distance approaching zero.
• A value that does not change.
• Solve 5^{2x} = 25 for x.
• Having the same or constant ratio.
• What is the domain of f(x) = sqrt(x - 1)?
• Compute the determinant of the matrix [[1,2,3],[0,4,5],[7,8,9]].
• Solve 3^(2x) = 81 for x.
• Find the 10th term of the arithmetic sequence with a1 = 7 and common difference d = -2.
• Which term describes a line segment from the center of a circle to the boundary?
• What is the domain of the function f(x) = log_2((x+1)(x-1))?
• Which term describes a set that goes on without end, having no finite size?
• What is the value of (x - 1)(x + 1)(x - 3)(x + 2) when x = 1?
• For y = -3(x - 1)^2 + 4, what is the axis of symmetry?
• Factor x^3 + 3x^2 - 6x - 18 by grouping.
• For a quadratic equation ax^2 + bx + c = 0, what is the name of the expression b^2 - 4ac that determines the number and type of solutions?
• Which type of function has the form y = a*b^x with a base b > 0 and b ≠ 1?
• What term describes a group of two or more equations related to the same situation and sharing variables?
• A rectangle with four congruent sides.
• What term means the number of coordinates used to express a position?
• Factor P(x) = x^3 - 6x^2 + 11x - 6.
• What is the absolute value of -7?
• A polynomial with a single term, such as 5, -2xyz, or xy^4, is called what?
• Solve e^(2x) = 7.
• Which term describes the two-dimensional plane grid used for locating points on a plane?
• In a quadratic equation, the expression b^2 - 4ac is called the ____.
• Which term is used to denote the shorter dimension of a rectangle or similar two-dimensional figure?
• Sum of the arithmetic sequence 3, 5, ..., 15.
• If f(x) = x^2 and g(x) = x+1, compute (f∘g)(x) and (g∘f)(x).
• What term denotes a rule that shows the relationship between two or more quantities; involving numbers and/or variables?
• A general statement written in numbers, symbols, or words, that describes how to determine any term in a pattern or relationship.
• Which term represents the shorter length of a two-dimensional figure?
• The edge of a polygon, the face of a polyhedron, or one of the rays that make up an angle.
• Which concept describes a geometric locus of points equidistant from a fixed center?
• Which term describes the ratio describing the shape of a conic section?
• If f(x) = 3x - 7, what is f^{-1}(x)?
• A parallelogram with four right angles.
• Simplify (8x^3)/(4x^2).
• Which term represents the exponent indicating repeated multiplication of a factor?
• For f(x) = (x − 2)^2 (x − 5), what is the multiplicity of the root x = 2?
• What is the term for a polynomial that is the sum or difference of terms with variables raised to positive integer powers and coefficients that may be real or complex?
• Which term is the set of input values for which a function is defined?
• Solve the nonlinear system where y = x^2 and y = 2x + 3; list all intersection points.
• Solve the system x + y + z = 6; x − y + z = 2; x + y − z = 4. What is (x, y, z)?
• Solve the 2x2 system x - y = 2 and 2x + y = 5; report the solution.
• What are the eigenvalues of the matrix [[2, 1], [1, 2]]?
• A line segment extending from the center of a circle or sphere to a point on the circle or sphere.
• A two-dimensional grid of horizontal and vertical lines used to locate points.
• Determine the oblique asymptote for R(x) = (2x^2 + 3x − 1)/(x − 4) and describe the end behavior.
• In an arithmetic sequence with a1 = 7 and d = -2, what is a3?
• Find f'(x) for f(x) = x^3 − 6x^2 + 9x, and identify the x-values of the critical points along with their nature.
• Which shape has four sides with opposite sides parallel and all angles right angles?
• For ellipse x^2/16 + y^2/9 = 1, what is c, the distance from the center to each focus?
• What is a polygon with three sides?
• What is a closed plane figure with all points at the same distance from the center and satisfying (x-h)^2+(y-k)^2=r^2?