A SELECTION OF PROBLEMS INTENDED TO MAINTAIN STUDENTS ESSENTIAL ALGEBRA SKILLS INSTRUCTOR COPY Review for College Mathematics.

Slides:

Advertisements

Similar presentations

Jeopardy Exponents Operations on Real Numbers Geometry Polynomials Properties of Real Numbers Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300.

Advertisements

MATH Part 2. Linear Functions - Graph is a line Equation of a Line Standard form: Ax + By = C Slope Intercept Form: y = mx + b m = slope b = y – intercept.

Chapter 7 The Basic Concepts of Algebra © 2008 Pearson Addison-Wesley. All rights reserved.

Released Items Aligned to McDougal Littell “Algebra 1” Copyright 2007

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. 1. 3x +(– 6x) Warm-Up.

Warm Up Write down objective and homework in agenda Lay out homework (Literal Equations) Homework (Kuta Multi-Step Inequalities, any 18)

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.

Algebra Review. Polynomial Manipulation Combine like terms, multiply, FOIL, factor, etc.

1 1.0 Students solve equations and inequalities involving absolute value. Algebra 2 Standards.

Other Types of Equations

Math Standards Grades 9-12 Wesley Kroupa. -Use procedures to transform algebraic expressions A.1.1. Example: Simplify 3(x + 5) − 2(7 − 2x) Example:

Exam Review 1 st Semester Algebra I. Topics Covered Chapter 2 – Equations and Functions Chapter 2 Chapter 3 – Graphing Linear Equations Chapter 3 Chapter.

Chapter 8 Review Quadratic Functions.

Mathematical Processes GLE  I can identify the operations needed to solve a real-world problem.  I can write an equation to solve a real-world.

1 Preliminaries Precalculus Review I Precalculus Review II

Write a fraction that is equivalent to 0.777….

Algebra 2 Bellwork – 3/4/15.

1 Roots & Radicals Intermediate Algebra. 2 Roots and Radicals Radicals Rational Exponents Operations with Radicals Quotients, Powers, etc. Solving Equations.

Basic Concepts of Algebra

Write the standard number 38,440 in scientific notation. A × 10 6 B × 10 3 C × 10 4 D ×

OBJECTIVES: STUDENTS WILL BE ABLE TO… EVALUATE NTH ROOTS OF REAL NUMBERS USING RADICAL NOTATION AND RATIONAL EXPONENT NOTATION. 7.1: N TH ROOTS AND RATIONAL.

Algebra 2/Trig Midterm review. Solve and graph equations and inequalities Radical equations:

?v=cqj5Qvxd5MO Linear and Quadratic Functions and Modeling.

EXAMPLE 2 Rationalize denominators of fractions Simplify

A quadratic equation is written in the Standard Form, where a, b, and c are real numbers and. 5.8 – Solving Equations by Factoring Zero Factor Property:

Solving Quadratic Equations

Warm Up Simplify the following x + 2x x + 2 – 3x Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 1.

7.8 Applications of Quadratic Equations 8.1 Basic Properties and Reducing to Lowest Terms.

MATHEMATICAL PROCESSES SPI  I can generate ratios to solve problems involving velocity, density, pressure, and population density.

Unit: 2 The Powers That Be. Unit Essential Question: How can rational and irrational numbers be expressed by exponents, square roots and scientific notation?

College Algebra Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

1. A quadratic equation is an equation equivalent to one of the form Where a, b, and c are real numbers and a  0 To solve a quadratic equation we get.

Regents Review #1 Expressions & Equations (x – 4)(2x + 5) 3x 3 – 4x 2 + 2x – 1 (4a – 9) – (7a 2 + 5a + 9) 4x 2 + 8x + 1 = 0 (x – 5) 2 = 25 10x 3 5x 5 x.

Algebra II Semester 2 Review Click on the red squares to find the work and answers for the given question.

Review Know all of the formulas of variations.

Objective I will use square roots to evaluate radical expressions and equations. Algebra.

AHSGE MATHEMATICS PRACTICE SESSION. STANDARD I: The student will be able to perform basic operations on algebraic expressions. OBJECTIVE 1. Apply order.

Grade 8 Pre-Algebra Introduction to Algebra.

Warm Up! Write down the objective and homework in your agenda Lay out homework (Writing & Simplifying expressions wkst) Homework (Kuta Rational Exponents.

Multiplication Properties of Exponents

EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

What We Need to Know to Help Students’ Scores Improve What skills the test measures How the test relates to my curriculum What skills my students already.

5.4 Elimination Using Multiplication Algebra 1 Objective: Each student will understand if addition and subtraction does not eliminate a variable – how.

PSSA – Assessment Coach Mathematics- Grade 11. Chapter 1 Lesson 1 Orders of Operations and Number Properties.

Y-Intercept Form Forms of a Line Point Slope Form Standard Form Ax+By+C Rise Run Y- intercept Perpendicular- Slopes Negative Reciprocals Parallel–Slopes.

1.2 Quadratic Equations. Quadratic Equation A quadratic equation is an equation equivalent to one of the form ax² + bx + c = 0 where a, b, and c are real.

Warm Up Write down objective and homework in agenda Lay out homework (none) Homework (Distance & PT worksheet)

Math 1314 College Algebra Final Review Solutions.

Operations on Real Numbers

Right Triangle The sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse.

College Entrance Test Review

04 Evaluate nth Roots and Use Rational Exponents

EXAMPLE 2 Rationalize denominators of fractions Simplify

Five-Minute Check (over Lesson 1-5) Mathematical Practices Then/Now

High School – Pre-Algebra - Unit 4

Objective: SSBAT multiply polynomial expressions.

Review for College Mathematics

Warm Up Write down objective and homework in agenda

12. Modelling non-linear relationships

CHAPTER R: Basic Concepts of Algebra

9-2 Pythagorean Theorem.

Learning Resource Services

07/12/2018 Starter L.O. To be able to Solve a quadratic by factorising

KS4 Mathematics A6 Quadratic equations.

Algebra 1 Chapters 7-10.

Exponents and Radicals review: Chapter 1

Presentation transcript:

A SELECTION OF PROBLEMS INTENDED TO MAINTAIN STUDENTS ESSENTIAL ALGEBRA SKILLS INSTRUCTOR COPY Review for College Mathematics

Equations and Modeling A moving company charges $46 to move a certain machine 10 miles and $58 to move the same machine 30 miles. a) Find an equation that defines this relationship if it is linear. b) What will it cost to move the machine 25 miles? c) What is the minimum charge for moving the machine? d) What is the rate for each mile the machine is moved? Solution: a) b) c) d) 1 MATHEMATICS for COLLEGE READINESS C = 0.6 m + 14 $55 $40 $0.60 per mile

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) 2 MATHEMATICS for COLLEGE READINESS C = 4x + 210, where x = number of units produced. $610 $210 $4 per unit

Equations and Modeling If x 2 + 2x = 3, demonstrate algebraically which of the following is a possible value for x. a) – 3 b) –2 c) –1 d) 0 e) 3 Solution: a) – 3 3 MATHEMATICS for COLLEGE READINESS

Equations and Modeling How many solutions are there to the systems of equations? Solve algebraically. Solution: Infinite: the lines coincide so the solution is 4 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. a) Write an equation to model this situation. b) What are the positive answer(s)? Solution: a) b) 5 MATHEMATICS for COLLEGE READINESS n =5

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: 4 hr 20 min. 6 MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve the system of equations algebraically. Solution: empty set: The lines are parallel. 7 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: 8 MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve for a: Solution: 9 MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve for x: Solution: 10 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? Solution: 230 adult tickets 70 children’s tickets 11 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: 120 nonstudents. 780 students. 12 MATHEMATICS for COLLEGE READINESS

Equations and Modeling Solve algebraically: x 2 – 5 = 3x Solutions: 13 MATHEMATICS for COLLEGE READINESS

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. 14 MATHEMATICS for COLLEGE READINESS Equations and Modeling Solution: No, it will take almost 17 min to make the copies.

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

Function Theory MATHEMATICS for COLLEGE READINESS 16 Which of the following are functions? a.x 3 y = 12 b.x 2 + y 2 = 20 c.x 3 + y = 15 d.x (x+2) = 5 + y e. f.y(y + 2) = 4 + x g. x = 4 h. y = 5 Solution: c, d, e, h

Function Theory MATHEMATICS for COLLEGE READINESS 17 If f(x) = x 2 – 5, find f(b) – f( c). Solution:b 2 – c 2

Function Theory MATHEMATICS for COLLEGE READINESS 18 If f(x) = 2x 2 – x + 3, find f(x + h). Solution:

Function Theory MATHEMATICS for COLLEGE READINESS 19 If f(x) = x 2 – 4, find f(a + 5). Solution:a 2 +10a+21

Function Theory MATHEMATICS for COLLEGE READINESS 20 If f(x) = x 2 – 3 x + 5, find f(x + h) – f(x). Solution: 2xh + h 2 – 3h

Function Theory MATHEMATICS for COLLEGE READINESS 21 If f(x) = 3x 4 – 4x 3 -2x 2 +x - 5, find f(-x). Solution: 2xh + h 2 – 3h

Expressions with Exponents MATHEMATICS for COLLEGE READINESS 22 Simplify: Solution:

Simplify. Give the answer with positive exponents only: 23 MATHEMATICS for COLLEGE READINESS Expressions with Exponents Solution:

Simplify. Give the answer with positive exponents only: 24 MATHEMATICS for COLLEGE READINESS Expressions with Exponents Solution :

Multiply a. b. c. 25 MATHEMATICS for COLLEGE READINESS d. e. Solution: Expressions with Exponents

26 MATHEMATICS for COLLEGE READINESS Solution: Expressions with Exponents Multiply

27 MATHEMATICS for COLLEGE READINESS Solution: Expressions with Exponents Multiply

If the area of a circle if what is the area of a circle if the radius is 3a? 28 MATHEMATICS for COLLEGE READINESS Expressions with Exponents Solution:

If the volume of a sphere is what is the volume of a sphere with radius 3a? 29 MATHEMATICS for COLLEGE READINESS Expressions with Exponents Solution:

If the volume of a cylinder is find the volume of a cylinder with radius 3x and a height that is twice the radius. 30 MATHEMATICS for COLLEGE READINESS Expressions with Exponents Solution:

If, then x = a. 3 + ln t b. 31 MATHEMATICS for COLLEGE READINESS Exponential and Logarithmic Functions c. d. ln ( t – 3 ) e. ln t – 3 Solution:e. ln t – 3

If 7 x = 3, then x = a. b. 32 MATHEMATICS for COLLEGE READINESS c. d. e. Solution: Exponential and Logarithmic Functions

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

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

35 MATHEMATICS for COLLEGE READINESS Simplifying Expressions Simplify Solution: 5k k -16

36 MATHEMATICS for COLLEGE READINESS Simplifying Expressions Evaluate the following expression using x = -3.1 and y = x -2 + y 3 Solution:

Factor completely using integer coefficients. 37 MATHEMATICS for COLLEGE READINESS Algebraic Expressions Solution: 12 m 2 n 3 (m 2 + 4)

Factor completely using integer coefficients. 38 MATHEMATICS for COLLEGE READINESS Algebraic Expressions Solution: (4m – 3) (3m + 2)

39 MATHEMATICS for COLLEGE READINESS Algebraic Expressions Which of the following is a factor of a. b. c. d. not factorable Solution: c. (4x + 3)

40 MATHEMATICS for COLLEGE READINESS Algebraic Expressions Which of the following is a factor of a. b. c. d. Solution:b. (x + 2)

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

42 MATHEMATICS for COLLEGE READINESS Algebraic Expressions Write in simplest radical form. Solution: 7x 2 y

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

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

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

Solve algebraically. 46 MATHEMATICS for COLLEGE READINESS Quadratic Equations Solution:

Solve algebraically. 47 MATHEMATICS for COLLEGE READINESS Quadratic Equations Solution:

Solve algebraically. 48 MATHEMATICS for COLLEGE READINESS Quadratic Equations Solution:

Solve algebraically. 49 MATHEMATICS for COLLEGE READINESS Quadratic Equations Solution:

Solve algebraically. 50 MATHEMATICS for COLLEGE READINESS Quadratic Equations Solution:

Rational Expressions MATHEMATICS for COLLEGE READINESS 51 State the restricted values: Solution: x ≠ –3, 2

Over the set of real numbers, state where the function is undefined: 52 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution: The expression is undefined over the set of real numbers where -2<x<2 or x = -3 or 3.

Find the product: 53 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution :

Calculate and write the answer in scientific notation. a. b. c. d. 54 MATHEMATICS for COLLEGE READINESS Rational Expressions aSolution:

Find the area of a rectangle if the length is and the width is 55 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution:

Add and simplify 56 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution:

Simplify 57 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution:

Simplify 58 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution:

Simplify: 59 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution:

Simplify: a. b. c. d. 60 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution: b

Simplify: a. b. c. d. 61 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution : a

Simplify: a.c. b. d. 62 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution: d

What values for x are not allowed? a.c. b.d. 63 MATHEMATICS for COLLEGE READINESS Rational Expressions Solution:b

64 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: a

65 MATHEMATICS for COLLEGE READINESS Miscellaneous Find the length of the hypotenuse of the right triangle whose legs are 5 and Solution:6

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

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

68 MATHEMATICS for COLLEGE READINESS Miscellaneous MATHEMATICS for COLLEGE READINESS Find y in the diagram below. a. 24 b. 18 c. 4 d. 8 Solution: y a

69 MATHEMATICS for COLLEGE READINESS Miscellaneous MATHEMATICS for COLLEGE READINESS Find y in the diagram below. Solution: y

c. d. 70 MATHEMATICS for COLLEGE READINESS Variation Find an equation of variation where y varies inversely as and when a. b. Solution:d

71 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. a. 10 b. 90 c. 15 d. 30 Solution: b. 90

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? a. 18 hours b. 10 hours c. 8.5 hours d. 8 hours 72 MATHEMATICS for COLLEGE READINESS Variation Solution: d

Equations and Modeling Slides 1 – 15 Function TheorySlides 16 – 21 Expressions with ExponentsSlides 22 – 30 Exponential and Logarithmic FunctionsSlides 31 – 32 Simplifying ExpressionsSlides 33 – 36 Algebraic ExpressionsSlides 37 – 45 Quadratic EquationsSlides 45 – 50 Rational ExpressionsSlides 51 – 63 MiscellaneousSlides 64 – 69 VariationSlides 70 – 72 MATHEMATICS for COLLEGE READINESS Content Guide