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Questions and Answers
Calculate the sum of the fractions $\frac{3}{5} + \frac{4}{21}$. What is the result?
Calculate the sum of the fractions $\frac{3}{5} + \frac{4}{21}$. What is the result?
In the formula $D = \sqrt{2rh + h^2}$ for the maximum distance visible from a height $h$, what value should be used for $h$ if the observation deck of the CN Tower is 1,135 ft high and needs to be converted to miles?
In the formula $D = \sqrt{2rh + h^2}$ for the maximum distance visible from a height $h$, what value should be used for $h$ if the observation deck of the CN Tower is 1,135 ft high and needs to be converted to miles?
To find the maximum profit when producing microwaves according to the formula $P = \frac{1}{10}x(200 - x)$, what is the profit when producing 30 microwaves?
To find the maximum profit when producing microwaves according to the formula $P = \frac{1}{10}x(200 - x)$, what is the profit when producing 30 microwaves?
What is the monthly salary of an executive if her total yearly earnings are $97,200, including an $8,400 Christmas bonus?
What is the monthly salary of an executive if her total yearly earnings are $97,200, including an $8,400 Christmas bonus?
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How high does a 14-foot ladder reach if it is placed 2 feet away from the base of a building?
How high does a 14-foot ladder reach if it is placed 2 feet away from the base of a building?
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If a jeweler has rings that are 20% silver, how much silver must be added to reduce the gold content of the alloy to 60%?
If a jeweler has rings that are 20% silver, how much silver must be added to reduce the gold content of the alloy to 60%?
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For the division of the polynomials $\frac{9y^2 - 25}{3y^2 + 16y - 35}$ and $\frac{y^2 + 6y - 7}{3y^2 + 2y - 5}$, what is the simplified result?
For the division of the polynomials $\frac{9y^2 - 25}{3y^2 + 16y - 35}$ and $\frac{y^2 + 6y - 7}{3y^2 + 2y - 5}$, what is the simplified result?
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What is the maximum visible distance (D) someone can see from a height of 1,135 ft above the ground using the formula D = $\sqrt{2rh + h^2}$?
What is the maximum visible distance (D) someone can see from a height of 1,135 ft above the ground using the formula D = $\sqrt{2rh + h^2}$?
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What is the value of f(-4)?
What is the value of f(-4)?
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What is the range of the function f(x) given?
What is the range of the function f(x) given?
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Which expression correctly represents the volume V of the box from the cardboard?
Which expression correctly represents the volume V of the box from the cardboard?
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What is the domain for the volume V(x) of the box?
What is the domain for the volume V(x) of the box?
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If f(8) = 1 in a one-to-one function, what is f⁻¹(1)?
If f(8) = 1 in a one-to-one function, what is f⁻¹(1)?
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What is the amount of salt in the barrel after 10 minutes?
What is the amount of salt in the barrel after 10 minutes?
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How much will an investment of $1,000 grow to at the end of 4 years with an interest rate of 10% compounded monthly?
How much will an investment of $1,000 grow to at the end of 4 years with an interest rate of 10% compounded monthly?
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What is the exponential form of the equation log 4 16 = 2?
What is the exponential form of the equation log 4 16 = 2?
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What is the value of log 7 343?
What is the value of log 7 343?
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How would you express ln(x + 1) = 4 in exponential form?
How would you express ln(x + 1) = 4 in exponential form?
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What is the logarithmic form of the equation 3^4 = 81?
What is the logarithmic form of the equation 3^4 = 81?
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What is the result of log_5 5^625?
What is the result of log_5 5^625?
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Using the Laws of Logarithms, how can log_9 (x/8) be rewritten?
Using the Laws of Logarithms, how can log_9 (x/8) be rewritten?
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What is the total amount of an investment of $3,000 at 6% interest compounded quarterly after 3 years?
What is the total amount of an investment of $3,000 at 6% interest compounded quarterly after 3 years?
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If the interest rate is increased to 7%, what will the value of the investment be at the end of 3 years?
If the interest rate is increased to 7%, what will the value of the investment be at the end of 3 years?
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Calculating for 8% interest compounded quarterly, what is the amount at the end of 3 years?
Calculating for 8% interest compounded quarterly, what is the amount at the end of 3 years?
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Determine the formula for the amount of an investment, A(t), compounded quarterly over t years at an interest rate r.
Determine the formula for the amount of an investment, A(t), compounded quarterly over t years at an interest rate r.
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What is the domain of the function f(x) = log_8(x + 3)?
What is the domain of the function f(x) = log_8(x + 3)?
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Using the Laws of Logarithms, how would you simplify log_3(AB^5)?
Using the Laws of Logarithms, how would you simplify log_3(AB^5)?
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What conditions must be met for the expression log_a(2x / yz) to be valid?
What conditions must be met for the expression log_a(2x / yz) to be valid?
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When simplifying the expression log_5(7) + log_2(5), what is the potential result?
When simplifying the expression log_5(7) + log_2(5), what is the potential result?
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What is the shape of the suspension cables in a suspension bridge?
What is the shape of the suspension cables in a suspension bridge?
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In the equation $9x^2 + 16y^2 = 144$, what are the lengths of the major and minor axes of the ellipse?
In the equation $9x^2 + 16y^2 = 144$, what are the lengths of the major and minor axes of the ellipse?
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For the hyperbola represented by the equation $\frac{y^2}{36} - \frac{x^2}{49} = 1$, what are the lengths of the transverse and conjugate axes?
For the hyperbola represented by the equation $\frac{y^2}{36} - \frac{x^2}{49} = 1$, what are the lengths of the transverse and conjugate axes?
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What allows you to identify that the graph of the equation $\frac{(x+1)^2}{16} - \frac{(y-1)^2}{9} = 1$ is a hyperbola?
What allows you to identify that the graph of the equation $\frac{(x+1)^2}{16} - \frac{(y-1)^2}{9} = 1$ is a hyperbola?
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What is the correct form of the vertex for the parabola defined by the equation $(x - 4)^2 = 4(y + 1)$?
What is the correct form of the vertex for the parabola defined by the equation $(x - 4)^2 = 4(y + 1)$?
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In the equation $9x^2 + 16y^2 - 36x + 160y + 292 = 0$, what type of conic section does it represent after completing the square?
In the equation $9x^2 + 16y^2 - 36x + 160y + 292 = 0$, what type of conic section does it represent after completing the square?
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How do you find the foci of an ellipse from its standard form equation $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$?
How do you find the foci of an ellipse from its standard form equation $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$?
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What characterizes the asymptotes of the hyperbola defined by the equation $\frac{(x + 1)^2}{16} - \frac{(y - 1)^2}{9} = 1$?
What characterizes the asymptotes of the hyperbola defined by the equation $\frac{(x + 1)^2}{16} - \frac{(y - 1)^2}{9} = 1$?
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What is the factored form of the expression $x^3 + 8y^3$?
What is the factored form of the expression $x^3 + 8y^3$?
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Which expression is the result of factoring $216s^3 - 125t^6$?
Which expression is the result of factoring $216s^3 - 125t^6$?
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What is the completely factored form of the expression $4x^2 - 81$?
What is the completely factored form of the expression $4x^2 - 81$?
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What is the domain of the expression $\frac{7t^2 - 8}{2t + 6}$?
What is the domain of the expression $\frac{7t^2 - 8}{2t + 6}$?
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What is the simplified result of multiplying $(x^2 + 2xy + y^2)$ and $(x^2 - y^2)$?
What is the simplified result of multiplying $(x^2 + 2xy + y^2)$ and $(x^2 - y^2)$?
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For the quadratic equation $x^2 - 17x + 4 = 0$, what are the real solutions?
For the quadratic equation $x^2 - 17x + 4 = 0$, what are the real solutions?
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What is the solution to the equation $|3x| = 7$?
What is the solution to the equation $|3x| = 7$?
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Which of the following correctly represents the heights of the ball thrown straight upward with initial speed $72 ft/s$ over time according to the formula $h = -16t^2 + v_0t$?
Which of the following correctly represents the heights of the ball thrown straight upward with initial speed $72 ft/s$ over time according to the formula $h = -16t^2 + v_0t$?
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Study Notes
Pre-Calculus Semester 1 Exam Review
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Multiple Choice Questions: The review includes multiple-choice questions, focusing on performing indicated operations. Examples are provided for adding fractions and performing other arithmetic operations.
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Numeric Response Questions: Exercises involve problems related to the curvature of the Earth. Formula for maximum distance visible from a tall building, radius of the earth (r = 3960 mi), and distance of the CN Tower (1,135 ft) are given. The questions also cover simplifying rational expressions and algebra.
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Multiple-Choice, Word Problems, and Other Operations: The question set contains multiple choice, word problems, and other calculations including various algebra questions. Example of a word problem is finding the number of ovens a company must manufacture for a profit of $750. Another one calculates a monthly salary from an annual salary amount.
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Expressions and Equations: The review includes evaluating expressions involving imaginary numbers, complex numbers, and radicals. Also covered are simplifying expressions, including exponential and logarithmic expressions.
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Graphs, Polynomials, Identities and Transformations: The review covers topics like determining if a function is a monomial, binomial, etc, and evaluating expressions involving logarithms. Other questions involve sketching graphs of functions and piecewise functions, identifying graphs and determining the domain.
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Polynomial Functions: Problems involve factoring expressions, identifying types of polynomials, determining graphs of functions and asymptotes, real zeros, etc.
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Exponential and Logarithmic Functions: The review covers exponential equations, logarithmic equations, finding solutions and converting to and from exponential form, using properties of logs, evaluating logs and exponential functions.
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Equations and Inequalities: Problems include solving exponential equations and inequalities, performing operations on expressions, and transforming expressions. Also included are questions on sets, intervals, performing operations and expressing solutions in interval notation.
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Radicals and Exponents: The study guide covers questions working with radicals, radicals with exponents, rational expressions and simplifying exponential expressions with variables.
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Other Topics: Problems cover a broad range of other precalculus concepts, including numeric responses involving multiple concepts and finding the maximum distance from a height using formulas.
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Description
Prepare for your Pre-Calculus Semester 1 exam with this comprehensive review. It includes multiple-choice questions, numeric response problems, and word problems that cover key concepts such as operations with fractions, curvature of the Earth, and algebraic expressions. This is an essential tool for mastering the material and excelling in your course.
