Review for College Mathematics A selection of problems intended to maintain students essential algebra skills Print Version

Equations and Modeling A moving company charges $46 to move a certain machine 10 miles and $58 to move the same machine 30 miles. Find an equation that defines this relationship if it is linear. What will it cost to move the machine 25 miles? What is the minimum charge for moving the machine? What is the rate for each mile the machine is moved? Solution: a) b) c) d) MATHEMATICS for COLLEGE READINESS

Equations and Modeling The total cost of producing a certain item consists of paying rent for the building and paying a fixed amount per unit for material. The total cost is $250 it 10 units are produced and $330 if 30 units are produced. a) Find the equation that defines this relationship if it is linear. b) What will it cost to produce 100 units? c) How much is paid in rent? d) What is the cost of the material for each unit? Solution: a) b) c) d) MATHEMATICS for COLLEGE READINESS

Equations and Modeling If x2 + 2x = 3, demonstrate algebraically which of the following is a possible value for x. – 3 –2 –1 3   Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling How many solutions are there to the systems of equations? Solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling The sum of the square of a number and the product of the number and 3 equals 40. Write an equation to model this situation. What are the positive answer(s)?   Solution: a) b) MATHEMATICS for COLLEGE READINESS

Equations and Modeling Two truckers start on a trip at the same time. One heads west at 60 mph while the other heads east at 55 mph. Their CB radios work for a distance up to 500 miles apart. How long will they be able to communicate with each other? Model and solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve the system of equations algebraically. Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve for w: p = 2 ( l + w ) Give your answer in two forms, one answer with a single fraction and the other as a sum or difference of two terms. Solutions: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve for a: Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve for x: Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling The Boosters Club held a spaghetti dinner as a fundraiser. They sold 300 tickets and collected $2200. If an adult’s ticket cost $8.50 and a child’s ticket cost $3.50, how many of each were sold? Model and solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Admission to a school football game was $2 for students and $3 for nonstudents. How many of each group attended if there were 900 people and $1920 collected? Model and solve algebraically. Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve algebraically: x2 – 5 = 3x Solutions: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Bill needs to make 1000 copies before the meeting that starts in 15 minutes. He begins using a machine that makes 30 copies per minute after laminates, a newer machine which copies at 45 pages per minutes become free . Using both machines, will Bill be able to make all the copies before the meeting? Explain algebraically. Solution: MATHEMATICS for COLLEGE READINESS

Equations and Modeling Find the equation of a line with slope of 0 through (6, 10).   Solution: MATHEMATICS for COLLEGE READINESS

Function Theory Which of the following are functions? x3 y = 12 x (x+2) = 5 + y e. y(y + 2) = 4 + x g. x = 4 h. y = 5 Solution: MATHEMATICS for COLLEGE READINESS

Function Theory If f(x) = x2 – 5, find f(b) – f( c) . Solution: MATHEMATICS for COLLEGE READINESS

Function Theory If f(x) = 2x2 – x + 3, find f(x + h) . Solution: MATHEMATICS for COLLEGE READINESS

Function Theory If f(x) = x2 – 4, find f(a + 5) . Solution: MATHEMATICS for COLLEGE READINESS

Function Theory If f(x) = x2 – 3 x + 5, find f(x + h) – f(x) . Solution: MATHEMATICS for COLLEGE READINESS

Function Theory If f(x) = 3x4 – 4x3 -2x2 +x - 5, find f(-x). Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents Simplify: Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents Simplify. Give the answer with positive exponents only: Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents Simplify. Give the answer with positive exponents only: Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents Multiply a. b. c.   d. e. Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents Multiply Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents Multiply Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents If the area of a circle if what is the area of a circle if the radius is 3a? Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents If the volume of a sphere is what is the volume of a sphere with radius 3a? Solution: MATHEMATICS for COLLEGE READINESS

Expressions with Exponents If the volume of a cylinder is find the volume of a cylinder with radius 3x and a height that is twice the radius. Solution: MATHEMATICS for COLLEGE READINESS

Exponential and Logarithmic Functions If , then x = a. 3 + ln t b.   c. d. ln ( t – 3 ) e. ln t – 3 Solution: MATHEMATICS for COLLEGE READINESS

Exponential and Logarithmic Functions If 7x = 3, then x = a. b.   c. d. e. Solution: MATHEMATICS for COLLEGE READINESS

Simplifying Expressions   Simplify a. b. c. d.   Solution: MATHEMATICS for COLLEGE READINESS

Simplifying Expressions   Simplify a. b. c. d.   Solution: MATHEMATICS for COLLEGE READINESS

Simplifying Expressions   Simplify   Solution: MATHEMATICS for COLLEGE READINESS

Simplifying Expressions Evaluate the following expression using x = -3.1 and y = 4.23 4x-2 + y3   Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Factor completely using integer coefficients.   Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Factor completely using integer coefficients.   Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Which of the following is a factor of a. b. c. d. not factorable     Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions   Which of the following is a factor of a. b. c. d.   Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Write in simplest radical form.     Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Write in simplest radical form.     Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Write in simplest radical form.     Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Write in simplest radical form.     Solution: MATHEMATICS for COLLEGE READINESS

Algebraic Expressions Perform the indicated operations and reduce answers to lowest terms. a. b. c. d.     Solution: MATHEMATICS for COLLEGE READINESS

Quadratic Equations Solve algebraically. Solution:   Solution: MATHEMATICS for COLLEGE READINESS

Quadratic Equations Solve algebraically. Solution:   Solution: MATHEMATICS for COLLEGE READINESS

Quadratic Equations Solve algebraically. Solution:   Solution: MATHEMATICS for COLLEGE READINESS

Quadratic Equations Solve algebraically. Solution:   Solution: MATHEMATICS for COLLEGE READINESS

Quadratic Equations Solve algebraically. Solution:   Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions State the restricted values: Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Over the set of real numbers, state where the function is undefined: Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Find the product: Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Calculate and write the answer in scientific notation. a. b. c. d. Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Find the area of a rectangle if the length is and the width is Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Add and simplify Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Simplify Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Simplify Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Simplify: Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Simplify: a. b. c. d. Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Simplify: a. b. c. d. Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions Simplify: a. c. b. d. Solution: MATHEMATICS for COLLEGE READINESS

Rational Expressions What values for x are not allowed? a. c. b. d. Solution: MATHEMATICS for COLLEGE READINESS

Miscellaneous Which of the following sets of numbers could NOT be the measures of the sides of a right triangle? a. c. b. d.   Solution: MATHEMATICS for COLLEGE READINESS

Miscellaneous Find the length of the hypotenuse of the right triangle whose legs are 5 and   Solution: MATHEMATICS for COLLEGE READINESS

Miscellaneous Find the distance between (-3,5) and (-7,8). Solution:   Solution: MATHEMATICS for COLLEGE READINESS

Miscellaneous (-4,6) (-1,-4) (1,6) (-4,-1) Solution: Find the coordinates of the point midway between (-5,2) and (3,-10). (-4,6) (-1,-4) (1,6) (-4,-1) Solution:   MATHEMATICS for COLLEGE READINESS

Miscellaneous 24 18 4 8 Find y in the diagram below. Solution: 9 6 12   Solution: 12 6 9 y MATHEMATICS for COLLEGE READINESS MATHEMATICS for COLLEGE READINESS

Miscellaneous Find y in the diagram below. Solution: 12 8 y 15   Solution: y 8 12 15 MATHEMATICS for COLLEGE READINESS MATHEMATICS for COLLEGE READINESS

Variation Find an equation of variation where y varies inversely as and when Solution: MATHEMATICS for COLLEGE READINESS

Variation Y varies directly as the cube root of x. Y is 30 when x is 1. Find Y when x is 27. 10 90 15 30 Solution:   MATHEMATICS for COLLEGE READINESS

Variation The number of hours (H) it takes to do the job in inversely proportional to the number of people (P) working on it. It takes 4 people 12 hours to do the job. How long would it take 6 people to do the job? 18 hours 10 hours 8.5 hours 8 hours   Solution: MATHEMATICS for COLLEGE READINESS

Content Guide Equations and Modeling Slides 1 – 15 Function Theory Slides 16 – 21 Expressions with Exponents Slides 22 – 30 Exponential and Logarithmic Functions Slides 31 – 32 Simplifying Expressions Slides 33 – 36 Algebraic Expressions Slides 37 – 45 Quadratic Equations Slides 45 – 50 Rational Expressions Slides 51 – 63 Miscellaneous Slides 64 – 69 Variation Slides 70 – 72 MATHEMATICS for COLLEGE READINESS