Honors Mathematics 3 Practice Exam

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• What is det(M) for M = [ [2, 1], [5, 3] ]?
• Which operation is used to eliminate a radical in an equation?
• Which criterion states that two triangles are similar if two angles of one are congruent to two angles of the other?
• Using the binomial theorem, expand (x + 3)^4 and identify the coefficient of x^2.
• In a right triangle, the sine of an angle is defined as the ratio of which two sides?
• Which description best defines Exponential Decay?
• Domain of a function is which of the following?
• Which term describes two triangles that are related by proportional corresponding sides and equal corresponding angles?
• Which criterion uses two angles and the included side?
• If m∠ABC = 25° and m∠CBD = 35°, what is m∠ABD?
• What is an extraneous solution?
• Find the vertical and horizontal asymptotes of R(x)=(3x^2-2x+4)/(x^2+1).
• Which criterion uses two angles and the non-included side?
• Which quantity measures the area of a sector of a circle?
• Solve sin θ = 1/2 for θ in [0, π].
• Holes in rational functions occur when
• If the height of a pyramid is doubled while base area remains the same, by what factor does the volume increase?
• For two parallel lines cut by a transversal, the alternate exterior angles are congruent.
• What is the standard form of the equation of a circle with center (h,k) and radius r?
• For θ = π/3, evaluate sin^2 θ + cos^2 θ.
• If corresponding sides of two similar triangles are scaled by a factor k, what is the ratio of their perimeters?
• Which statement best describes Exponential Growth?
• SSS Congruence: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
• Does the geometric series ∑_{n=0}^∞ (1/3)^n converge, and if so, what is its sum?
• Triangles with corresponding angles equal in measure and corresponding sides in proportion are called
• In the logarithm notation log_b(a), what does the symbol b represent?
• Which term describes any number that cannot be expressed as a fraction?
• Two angles whose measures add up to 90 degrees are called what?
• In a circle, which term represents the length along the circumference corresponding to a central angle?
• In ASA congruence, which parts are congruent?
• Which statement expresses the Linear Pair Postulate?
• What is one statement that describes standard deviation?
• For the parametric curve x = t^2, y = t, which of the following is dy/dx in terms of t (t ≠ 0)?
• Which angles are formed in a Z pattern when two lines are cut by a transversal?
• HL congruence applies to which type of triangles?
• For the hyperbola x^2/25 - y^2/9 = 1, the foci lie at (±c, 0). Which of the following gives c?
• When multiplying two powers with the same base, what do you do to the exponents?
• Factor x^4 - 5x^2 + 6 into irreducible factors over the real numbers.
• Which criterion states that if the three pairs of corresponding sides are proportional, the triangles are similar?
• In an isosceles triangle, which angles are congruent?
• Any number that can be expressed as a fraction describes which concept?
• An observational study is best described as which of the following?
• Which value equals sin^2 θ + cos^2 θ for any angle θ?
• Let u = (3, -2, 5) and v = (1, 0, -4). What is the magnitude |v|?
• Which statement reflects the Angle Addition Postulate?
• Compute the scalar projection of u onto v where u = (4, 2, 0) and v = (-1, 2, 1).
• For ellipse x^2/16 + y^2/9 = 1, the foci are at (±√7, 0).
• For x = t^2, y = t, compute the speed ds/dt at t = 2.
• Which property can be used to deduce a = b, b = c, therefore a = c?
• Which term describes a ray that divides an angle into two equal angles?
• Solve tan x = √3 for x in [0, 2π).
• Which statement reflects the Segment Addition Postulate?
• For f(x) = ax^2 + bx + c with a ≠ 0 on a restricted domain making f invertible, which expression gives f^{-1}(y) on the left-hand monotonic branch (x ≤ -b/(2a))?
• Which expression best represents the standard form for a transformed sine graph?
• Compute P(2) for P(x) = 2x^3 - 3x^2 + x - 5.
• Compute the dot product u·v for u=(3,-2,5) and v=(1,0,-4).
• Solve x(x-2)(x+4)=0. List the solutions.
• If f is a bijection, which statement correctly describes the graphs of f and f^{-1} and their compositions?
• A line that intersects two lines in the same plane at different points is called a what?
• In an Exponential (Geometric) Sequence, how is each term generated?
• Two angles whose measures sum to 180 degrees are called what?
• In a right triangle, which of the following represents the cosine of angle θ as a ratio?
• Determine f∘g(x) and its domain given f(x)=√(x+4) and g(x)=x^2.
• Compute |w| for w = (−2, 5, −1).
• Which statement describes the Multiplication Property?
• When you raise a power to another power, how do you combine the exponents?
• If two triangles are similar, what is true about their corresponding sides?
• A quantity is congruent (equal) to itself. Which property states that?
• Which term describes any number that can be expressed as a fraction?
• If x = y, what is 2x when compared with 2y?
• For ellipse x^2/16 + y^2/9 = 1, identify the major axis length, minor axis length, and the coordinates of the vertices and co-vertices.
• Compute the limit of a_n = (3n^2 + 2n + 1)/(n^2 - 4) as n → ∞.
• Which statement expresses the Congruent Complements Theorem?
• Which transformation affects the x-values, producing horizontal stretch or compression?
• Find the distance between two points in polar coordinates (r1, θ1) and (r2, θ2) using the law of cosines.
• What is the coefficient of x^3 in the expansion of (x + 3)^4?
• Which expression describes inverse variation between two quantities?
• Solve (x - 1)(x + 2)(x - 3) = 0. Which set contains all roots?
• Multiply (3+2i)(1-i) and express in a+bi form; then convert to polar form r(cos φ + i sin φ).
• In AAS congruence, which parts are congruent?
• The surface area of a pyramid is the sum of which components?
• Triangles in which all corresponding parts are equal in measure are called
• In the form y = a sin(bx - c) + d, which parameter controls horizontal shift?
• Any number that cannot be expressed as a fraction describes which concept?
• Which statement expresses the Vertical Angles Theorem?
• Perform polynomial division of P(x)=2x^3-3x^2+x-5 by D(x)=x-2. What are the quotient Q(x) and remainder R?
• Which expression represents a^ (m/n) as a radical?
• Consider the telescoping series ∑_{n=1}^{∞} (1/n − 1/(n+1)). Does it converge, and if so, to what value?
• If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
• Which criterion states that if an angle of one triangle is congruent to the corresponding angle of another triangle and the including sides are proportional, the triangles are similar?
• Compute the product AB where A = [ [1, 2], [3, 4] ] and B = [ [0, -1], [2, 3] ].
• Which theorem states that alternate exterior angles are congruent when two lines are parallel?
• The ellipse x^2/16 + y^2/9 = 1 has area equal to
• Convert 4(cos 60° + i sin 60°) to a+bi.
• Compute the area enclosed by one loop of r = 1 + cos θ.
• If ∠A ≅ ∠B, then which statement about supplements is true?
• Which postulate guarantees congruence of two right triangles when the hypotenuse and a corresponding leg are congruent?
• Which division method is used for dividing polynomials by a polynomial, not limited to linear divisors?
• Which equation is in slope-intercept form?
• Which equation represents a direct variation between y and x?
• Having corresponding sides proportional and corresponding angles equal describes which concept?
• A statement that can be proven is called a what?
• Which expression gives the surface area of a cone in terms of radius r and slant height s?
• Compute f∘g(2) given f(x)=√(x+4) and g(x)=x^2.
• For the geometric sequence a1 = 3, r = 1/2, what is S6, the sum of the first six terms?
• The mid-segment of a triangle is the segment joining the midpoints of two sides. This segment is parallel to the third side and has what length relation to that side?
• Which property states that if equal quantities are added to equal quantities, the sums are equal?
• For R(x) = (x^2 - 4)/(x^2 - 1), identify the domain and any holes or vertical asymptotes.
• Which term describes the behavior of the graph of a function as x approaches positive infinity or negative infinity?
• In the form y = a sin(bx - c) + d, which parameter controls vertical shift?
• Which theorem states that three sides of one triangle congruent to three sides of another triangle implies the triangles are congruent?
• Which term describes two angles that occupy corresponding positions at each intersection of a transversal with two lines?
• Find the 5th term of the arithmetic sequence with a1 = 7 and d = -2.
• If a = b, then b = a is an example of which property?
• In SAS congruence, which parts must be congruent?
• The lateral surface area of a right circular cylinder is given by which expression?
• Which statement expresses the Congruent Supplements Theorem?
• Which statement describes a vertical asymptote?
• If a function has a vertical asymptote at x = 3, what does the graph do as x approaches 3?
• What is det(AB) for A = [ [1, 2], [3, 4] ] and B = [ [0, -1], [2, 3] ]?
• Which term is defined as two angles that form a straight line?
• Which statement best defines a sector of a circle?
• Which of the following is an example of a segment bisector?
• Compute the area A = (1/2) ∫_{-π/2}^{π/2} (2 cos θ)^2 dθ for the area enclosed by r = 2 cos θ over that interval.
• A ray, line or segment that divides a segment into two parts of equal measure is called
• If log_b(a) = c, which equation is equivalent?
• Interior angles on the same side of the transversal are supplementary.
• Compute det of N = [ [4, -2, 1], [0, 3, -1], [2, 5, 0] ].
• If an angle measures π radians, what is its measure in degrees?
• What is the horizontal asymptote of R(x)=(3x^2-2x+4)/(x^2+1)?
• Which statement describes the method to convert degrees to radians?
• Which statement best defines Inverse Variation?
• Pairs of angles formed by two lines and a transversal that make an F pattern are called what?
• Let u = (3, -2, 5) and v = (1, 0, -4). What is the magnitude |u|?
• Two angles formed by intersecting lines and facing in the opposite direction are called what?
• Which statement correctly justifies that u×v is perpendicular to both u and v?
• If the radius of a sphere is doubled, by what factor does its volume increase?
• In the form y = a sin(bx - c) + d, which parameter controls horizontal compression or expansion?
• Let u = (3, -2, 5) and v = (1, 0, -4). What is the dot product u · v?
• Which term describes a line or ray that divides a segment into two equal parts?
• Which description best defines Exponential Growth?
• In the same hyperbola, what is c if the foci are at (±c, 0)?
• Which of the following is the standard form of the equation of a circle centered at (h,k) with radius r?
• Which expression gives the surface area of a cylinder with radius r and height h?
• Evaluate the sum of the first 8 terms of a geometric series with initial term a0 = 7 and common ratio r = -1/3.
• In the vertex form y = a(x - h)^2 + k, the vertex is at what point?
• For the geometric sequence with a1 = 3 and r = 1/2, what is a6?
• Which statement defines a survey?
• The volume of a pyramid is given by which expression?
• Which congruence criterion applies when two sides and the included angle are congruent?
• Convert rectangular coordinates (-3, 4) to polar coordinates (r, θ) with r ≥ 0 and θ ∈ [0, 2π).
• In a geometric sequence, the constant ratio between consecutive terms is called:
• Which of the following describes Exponential Decay?
• Which rule helps identify possible rational zeros of a polynomial?
• A rational exponent can be rewritten as which form?
• Convert z = -4 + 3i to polar coordinates (r, θ) with r ≥ 0 and θ ∈ [0, 2π).
• Which expression gives the volume of a right circular cone with radius r and height h?
• If A and B are independent with P(A)=0.5 and P(B)=0.4, what is P(A∩B)?
• In a right triangle, which ratio defines sine?
• Compute (x^3)^4.
• Which expression exhibits a sine function with both a phase shift and a vertical shift?
• What best defines an experiment?
• Which pattern describes same-side interior angles formed by two lines and a transversal?
• What is the mean of a data set?
• If a = b and b = c, then a = c illustrates which property?
• What are holes in a rational equation?
• An equation involving a radical expression in which the variable sits under a radical is called what?
• Find the length of the curve x = t^2, y = t from t = 0 to t = 1.
• Which expression gives the surface area of a sphere of radius r?
• Given f(x) = x^2 - 1 with domain [0, ∞), what is f^{-1}(y)?
• Determine the end behavior of P(x) = -4x^5 + 3x^4 - x + 7 as x → ∞ and as x → -∞.
• The lateral area of a solid is the area of all the lateral faces. Which statement is true about lateral area?
• For the ellipse with a = 6 and b = 4, what are the coordinates of the minor vertices?
• Which statement describes the method to convert radians to degrees?
• When solving equations, what is a good practice to avoid extraneous solutions?
• A fair coin is flipped 6 times. What is the probability of exactly 3 heads?
• Solve the linear system 2x + y = 7 and x − y = 1; find (x, y).
• Two parallel lines are cut by a transversal. Which statement about a pair of corresponding angles is true?
• If an angle measures π/3 radians, what is its measure in degrees?
• For the parametric curve x = t^2, y = t, what is dy/dx when t = 3?
• A ray that begins at the vertex of an angle and divides the angle into two equal angles is called
• Which statement describes the Division Property?
• Which statement describes a horizontal asymptote?
• What does a horizontal asymptote describe?
• Which statement describes the Substitution Property?
• Which expression correctly gives the sum S_n of a geometric series with first term a0 and ratio r?
• Compute the cross product u×v for u=(3,-2,5) and v=(1,0,-4). Which vector is correct?
• In a right triangle, which ratio defines tangent?
• If AB = 4 and BC = 7, and A, B, C are collinear with B between A and C, what is AC?
• Which expression exhibits a standard cosine graph with horizontal shift and vertical shift?
• Which approach involves substituting potential zeros until one yields zero, and then applying synthetic division to factor further?
• In an exponential (geometric) sequence, the fixed factor used to obtain the next term is called:
• What is the remainder when P(x) = 2x^3 - 3x^2 + x - 5 is divided by x+1?
• In the ellipse x^2/36 + y^2/16 = 1 with a ≥ b, if a = 6 and b = 4, which are the coordinates of the major vertices?
• CPCTC stands for which statement?
• In y = a(x - h)^2 + k, if |a| > 1, the parabola is
• Which equation represents a cube root function?
• The square root function y = sqrt(x) is the inverse of which function (with appropriate domain restriction)?
• Which statement reflects the Division Property applied to a = b and c = d ≠ 0?
• Compute ds/dt for the curve x = t^2, y = t at t = 0.5.
• Range of a function is which of the following?
• Solve 2^{x+1} = 3^{2x-1}. Give x in closed form.
• Find the modulus and argument of z = -3 + 3i; express in polar form.
• What is the standard equation of a horizontal hyperbola with center at origin and a = 5, b = 3?
• Which of the following is a correct algebraic manipulation showing 1 + tan^2 θ equals sec^2 θ using sin and cos?
• Which statement about the cube root function y = ∛x is true?
• Let f(x) = √x and g(x) = x^2. Which statement about the domains of f∘g and g∘f is true?
• Find the inverse M^{-1} of M = [ [2, 1], [5, 3] ].
• If the radius of a sphere is doubled, by what factor does its surface area increase?
• If r1 = 3, r2 = 4, and Δθ = π, what is the distance d between the two points in polar coordinates?
• Which expression gives the volume of a sphere with radius r?
• Which formula is used to solve any quadratic equation?
• Which pattern describes alternate interior angles formed by two lines and a transversal?
• Which expression represents a^ (p/q) as a radical?
• In direct variation, which statement is true about y and x?
• Which method is most efficient for dividing a polynomial by a binomial of the form x - c?
• Let f(x) = x^3 + x and y = f(x). Express (f^{-1})'(y) in terms of x.
• When dividing two powers with the same base, what operation is performed on the exponents?
• The sum of the interior angles of a triangle equals 180 degrees.
• If A and B are independent events with P(A)=0.5 and P(B)=0.4, what is P(A|B)?
• Two triangles have side lengths 6, 8, 10 and 9, 12, 15. Are they similar?
• Which transformation affects the y-values of a function, producing vertical stretch or compression?
• Solve the quadratic equation 2x^2 − 3x + 5 = 0. Find the roots.
• Which statement correctly describes the Subtraction Property?
• In a right triangle, which of the following represents the tangent of angle θ as a ratio?