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Questions and Answers
If sin θ = 0.7 and θ is in quadrant II, what are the exact values of cos θ?
If sin θ = 0.7 and θ is in quadrant II, what are the exact values of cos θ?
- -0.7
- 0.743
- -0.743 (correct)
- 0.7
What is the value of tan θ when sin θ = 0.7 and θ is in quadrant II?
What is the value of tan θ when sin θ = 0.7 and θ is in quadrant II?
- 0.943
- -1.206
- 1.206
- -0.943 (correct)
When graphing the function y = 2x² - 8x + 5, what is the axis of symmetry?
When graphing the function y = 2x² - 8x + 5, what is the axis of symmetry?
- x = 2
- x = 3 (correct)
- x = 1
- x = 4
What is the maximum value of the function y = 2x² - 8x + 5?
What is the maximum value of the function y = 2x² - 8x + 5?
Which form represents the equation of a quadratic function in vertex form?
Which form represents the equation of a quadratic function in vertex form?
Which gear among the three with radii 4 cm, 2 cm, and 1 cm creates the largest angle between their centers?
Which gear among the three with radii 4 cm, 2 cm, and 1 cm creates the largest angle between their centers?
If the quadratic function h = -10t² + 300t + 9750 is rewritten in vertex form, what is the significance of the vertex?
If the quadratic function h = -10t² + 300t + 9750 is rewritten in vertex form, what is the significance of the vertex?
When determining the coordinates of the vertex for the function y = 2x² - 8x + 5, what are the coordinates?
When determining the coordinates of the vertex for the function y = 2x² - 8x + 5, what are the coordinates?
What is the general term $t_n$ for the arithmetic sequence 6, 9.5, 13, 16.5?
What is the general term $t_n$ for the arithmetic sequence 6, 9.5, 13, 16.5?
Given the arithmetic sequence where $t_6 = 86$ and $t_9 = 50$, what is $t_{15}$?
Given the arithmetic sequence where $t_6 = 86$ and $t_9 = 50$, what is $t_{15}$?
In the arithmetic sequence -16, 5, 26, 47, what is the position of the term with a value of 866?
In the arithmetic sequence -16, 5, 26, 47, what is the position of the term with a value of 866?
What is the sum of the arithmetic series 7 + 18 + 29 + ... + 381?
What is the sum of the arithmetic series 7 + 18 + 29 + ... + 381?
How many seats are in a theater with 20 rows, where the first row has 60 seats and each row increases by 8 seats?
How many seats are in a theater with 20 rows, where the first row has 60 seats and each row increases by 8 seats?
Given the geometric sequence with $t_2=20$ and $t_4=500$, find the general term.
Given the geometric sequence with $t_2=20$ and $t_4=500$, find the general term.
What is the sum $S_6$ of the geometric series 4 - 8 + 16 - 32 + ...?
What is the sum $S_6$ of the geometric series 4 - 8 + 16 - 32 + ...?
If the third term of a geometric sequence is 3 and the sixth term is $1/9$, what is the first term?
If the third term of a geometric sequence is 3 and the sixth term is $1/9$, what is the first term?
What is the quadratic formula used to find the roots of a quadratic equation?
What is the quadratic formula used to find the roots of a quadratic equation?
When solving the equation $0.5x^2 - 3x = 4$ by graphing, what kind of graph would be used?
When solving the equation $0.5x^2 - 3x = 4$ by graphing, what kind of graph would be used?
What is the first step to solve $2x^2 = 5x + 3$ using technology?
What is the first step to solve $2x^2 = 5x + 3$ using technology?
What is the completely factored form of the expression $2(4x - 1) + 9(4x - 1) + 10$?
What is the completely factored form of the expression $2(4x - 1) + 9(4x - 1) + 10$?
What is required for the quadratic equation $3x^2 - 6x + 1 = 0$ when using the quadratic formula?
What is required for the quadratic equation $3x^2 - 6x + 1 = 0$ when using the quadratic formula?
Which of the following is the perimeter of a shape involving radicals $2 \sqrt{3} + 8$ when simplified?
Which of the following is the perimeter of a shape involving radicals $2 \sqrt{3} + 8$ when simplified?
In simplifying $18\sqrt{27} - 25\sqrt{75}$, what would be the correct simplified result?
In simplifying $18\sqrt{27} - 25\sqrt{75}$, what would be the correct simplified result?
How can the expression $200$ be converted to simplest mixed radical form?
How can the expression $200$ be converted to simplest mixed radical form?
What is the vertex form of the quadratic equation $y = x^2 - x - 6$?
What is the vertex form of the quadratic equation $y = x^2 - x - 6$?
Which equation represents the height of the rocket after $x$ seconds?
Which equation represents the height of the rocket after $x$ seconds?
What does the point of intersection between the rocket's path and the boy's line of sight represent?
What does the point of intersection between the rocket's path and the boy's line of sight represent?
What is the solution to the equation system $3x - y = -5$ and $4x^2 - y + 8x = -2$?
What is the solution to the equation system $3x - y = -5$ and $4x^2 - y + 8x = -2$?
If the square of the first number subtracting the second number equals 5, and the first number is equal to the second number subtracting 7, what is the first number?
If the square of the first number subtracting the second number equals 5, and the first number is equal to the second number subtracting 7, what is the first number?
Graphically solving the inequality $-2x^2 + 3x > -7$ involves determining which of the following?
Graphically solving the inequality $-2x^2 + 3x > -7$ involves determining which of the following?
What does the system $y < -3x^2 - 3x + 1$ represent in graphical terms?
What does the system $y < -3x^2 - 3x + 1$ represent in graphical terms?
In Amber's savings scenario, which combination of hours worked achieves her savings goal?
In Amber's savings scenario, which combination of hours worked achieves her savings goal?
What is the non-permissible value of 'c' for the expression $\frac{c^2 + 10c + 16}{c^2 - c - 72}$?
What is the non-permissible value of 'c' for the expression $\frac{c^2 + 10c + 16}{c^2 - c - 72}$?
Which step must be taken first to solve the equation $2x - 3 = 5$?
Which step must be taken first to solve the equation $2x - 3 = 5$?
What is the simplification of the expression $\frac{6x(x - 4)(x - 5)}{4x^2 - 36}$?
What is the simplification of the expression $\frac{6x(x - 4)(x - 5)}{4x^2 - 36}$?
What is the reciprocal of 4 plus 1?
What is the reciprocal of 4 plus 1?
To solve the equation $\frac{1}{x + 2} = \frac{1}{5x}$, what should be done first?
To solve the equation $\frac{1}{x + 2} = \frac{1}{5x}$, what should be done first?
For the expression $\frac{2a^2 - 9a - 5}{a^2 + a - 12}$, what is the first step to simplify it?
For the expression $\frac{2a^2 - 9a - 5}{a^2 + a - 12}$, what is the first step to simplify it?
Which of the following values would make the denominator of the expression $\frac{6c^2 + c - 2}{3c^2 - c - 4}$ equal to zero?
Which of the following values would make the denominator of the expression $\frac{6c^2 + c - 2}{3c^2 - c - 4}$ equal to zero?
To solve the quadratic equation $2x^2 - 7 = 3 - x$, which term should be moved to one side before applying the quadratic formula?
To solve the quadratic equation $2x^2 - 7 = 3 - x$, which term should be moved to one side before applying the quadratic formula?
What is the result of solving the equation $4x - 7 = 6x + 3$?
What is the result of solving the equation $4x - 7 = 6x + 3$?
Which of the following represents the correct piecewise function form for $y = -x + 2$ and $y = x^2 - x - 6$?
Which of the following represents the correct piecewise function form for $y = -x + 2$ and $y = x^2 - x - 6$?
What is the vertical asymptote of the function $y = \frac{1}{f(x)}$ when $f(x) = x + 3$?
What is the vertical asymptote of the function $y = \frac{1}{f(x)}$ when $f(x) = x + 3$?
When graphing the function $f(x) = x^2 - 2$, which of the following is true about the y-intercept?
When graphing the function $f(x) = x^2 - 2$, which of the following is true about the y-intercept?
Which of the following equations represent the graphical solution of the system of equations $y = -x + 2$ and $y = x^2 - x - 6$?
Which of the following equations represent the graphical solution of the system of equations $y = -x + 2$ and $y = x^2 - x - 6$?
What type of function is represented by the equation $y = \frac{1}{f(x)}$?
What type of function is represented by the equation $y = \frac{1}{f(x)}$?
How many invariant points are present in the function $f(x) = x + 3$ and its reciprocal?
How many invariant points are present in the function $f(x) = x + 3$ and its reciprocal?
Which expression correctly identifies the roots of the quadratic equation $x^2 - 10x - 24 = 0$?
Which expression correctly identifies the roots of the quadratic equation $x^2 - 10x - 24 = 0$?
Flashcards
General term of an arithmetic sequence (tn)
General term of an arithmetic sequence (tn)
The n-th term of an arithmetic sequence is found by adding the first term (a1) to the product of the common difference (d) and (n-1).
Sum of an arithmetic series (Sn)
Sum of an arithmetic series (Sn)
The sum of an arithmetic series with n terms is equal to the average of the first and last term, multiplied by the number of terms.
General term of a geometric sequence (tn)
General term of a geometric sequence (tn)
The n-th term of a geometric sequence is calculated by multiplying the first term (a1) by the common ratio (r) raised to the power of (n-1).
Sum of a finite geometric series (Sn)
Sum of a finite geometric series (Sn)
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Sum of an infinite geometric series (S∞)
Sum of an infinite geometric series (S∞)
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Reference Angle
Reference Angle
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Trigonometric ratios (sin θ, cos θ, tan θ)
Trigonometric ratios (sin θ, cos θ, tan θ)
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Solving trigonometric equations
Solving trigonometric equations
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Vertex Form of a Quadratic Function
Vertex Form of a Quadratic Function
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Standard Form of a Quadratic Function
Standard Form of a Quadratic Function
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Completing the Square
Completing the Square
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Vertex of a Parabola
Vertex of a Parabola
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Axis of Symmetry
Axis of Symmetry
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x-intercepts of a Parabola
x-intercepts of a Parabola
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y-intercept of a Parabola
y-intercept of a Parabola
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Direction of Opening of a Parabola
Direction of Opening of a Parabola
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Non-Permissible Value
Non-Permissible Value
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Simplifying Rational Expressions
Simplifying Rational Expressions
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Reciprocal
Reciprocal
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Rational Equations
Rational Equations
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Solving Radical Equations
Solving Radical Equations
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Simplifying a Rational Expression
Simplifying a Rational Expression
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Finding Non-Permissible Values
Finding Non-Permissible Values
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Solving Rational Equations
Solving Rational Equations
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Quadratic Formula
Quadratic Formula
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Factoring Quadratic Equations
Factoring Quadratic Equations
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Solving Quadratic Equations by Graphing
Solving Quadratic Equations by Graphing
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Radical Expressions
Radical Expressions
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Radical Equations
Radical Equations
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Simplifying Radicals
Simplifying Radicals
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Mixed Radical Form
Mixed Radical Form
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Combining Like Radicals
Combining Like Radicals
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Linear-Quadratic System
Linear-Quadratic System
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Quadratic-Quadratic System
Quadratic-Quadratic System
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Point of Intersection
Point of Intersection
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Substitution Method
Substitution Method
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Elimination Method
Elimination Method
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Graphing an Inequality
Graphing an Inequality
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Solving a Quadratic Inequality Algebraically
Solving a Quadratic Inequality Algebraically
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Solving a Quadratic Inequality Graphically
Solving a Quadratic Inequality Graphically
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Reflecting y = f(x) across the x-axis
Reflecting y = f(x) across the x-axis
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Stretching y = f(x) vertically
Stretching y = f(x) vertically
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Shifting y = f(x) upwards
Shifting y = f(x) upwards
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Shifting y = f(x) to the right
Shifting y = f(x) to the right
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Shifting y = f(x) to the left
Shifting y = f(x) to the left
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Compressing y = f(x) horizontally
Compressing y = f(x) horizontally
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Stretching y = f(x) horizontally
Stretching y = f(x) horizontally
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Reflecting y = f(x) across the y-axis
Reflecting y = f(x) across the y-axis
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Study Notes
Mathematics 20-1 Course Review Assignment
- The document is a review assignment for Mathematics 20-1, covering topics like sequences and series, trigonometry, quadratic functions, radical expressions, rational expressions and equations, and systems of equations.
Sequences and Series
- Arithmetic sequences: The assignment includes problems involving finding the general term, a specific term, the number of terms, and the sum of arithmetic sequences.
- Geometric sequences: Problems about finding the general term and the sum of geometric series are also presented.
- Series patterns: The assignment includes problem types requiring analysis of arithmetic and geometric sequences and series. Example issues are finding missing terms, determining the nth term, and total sums, in various types of series.
- Real-world applications: The review assignment includes questions about scenarios where these sequence and series concepts appear in real-world situations, involving seating arrangements in a theatre, for example.
Trigonometry
- Angles in standard position: Determining the quadrant and reference angle of given angles.
- Trigonometric ratios: Calculating sine, cosine and tangent for angles.
- Applications: Solving problems that utilize trigonometric concepts, involving horizontal distance, angle determination, and triangle side/angle calculations.
Quadratic Functions
- Vertex form: Graphing quadratic functions, determining the vertex, axis of symmetry, direction of opening, intercepts and maximum/minimum values
- Standard form: Problems in this section involve completing the square to convert between standard and vertex forms and finding the characteristics of parabolas (vertex, intercepts etc).
- Applications: Applying quadratic functions to real-world problems.
- Equation solving: Includes both graphical and algebraic methods for solving quadratic equations, including use of the quadratic formula and factoring.
Radical Expressions and Equations
- Simplifying radicals: Converting entire radicals to mixed radicals in the simplest form.
- Combining like terms: Simplifying radical expressions and combining like terms within expressions that contain radicals.
- Products and Quotients: Simplifying radical expressions, including products and quotients within mixed radical form.
- Solving radical equations: Using algebraic methods to solve equations containing radicals.
Rational Expressions and Equations
- Non-permissible values: Identifying values that make a rational expression undefined.
- Simplifying rational expressions: Reducing rational expressions to simplest form.
- Operations with rational expressions: Simplifying rational expressions containing operations (adding, subtracting, multiplication and division.).
- Solving equations with rational expressions: Using algebraic methods to solve equations containing rational expressions.
Systems of Equations
- Graphical solutions: Solving systems of equations using graphical methods.
- Algebraic solutions: Solving systems using algebraic techniques including substitution to solve quadratic and linear systems, and the understanding of intersection points
Absolute Value and Reciprocal Functions
- Graphing absolute value functions: Sketching the graph of an absolute value function.
- Graphing reciprocal functions: Sketching the graph of the reciprocal of a function.
- Finding vertical asymptotes: Determining the vertical asymptotes of a reciprocal function.
- Finding invariant points: Determining invariant points in the related graphic functions (points where the original and reciprocal functions intersect).
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