Math 233A Intermediate Algebra Fall 202 Study Guide for Exam 2 Exam 2 is scheduled for Wednesday, October 3 rd. You may use a 3" 5" note card (both sides) and a scientific calculator. You are expected to know (or have written on your note card) any formulas you may need. Think about any formulas you needed for homework. For example: solving rules, interest formula, perimeter of a rectangle, etc... For Exam 2, you will need to be able to:. Simplify expressions by using the distributive property and combining like terms. 2. * expressions don t come with equal signs (you simplify expressions) * equations come with equal signs (you solve equations) 2. Solve linear equations using the addition property and multiplication property of equality. 2. Solve equations: * clearing fractions or decimals by multiplying by the LCD (for fractions) or a power of ten (for decimals) * distributing across parentheses * collecting like terms (add/subtract coefficients of like terms) * adding/subtracting terms to get all variables one side (addition property of equality) * multiplying by the reciprocal to get the variable alone (multiplication property of equality) Check all solutions by plugging it in to the original equation. 3. Solve a geometric problem by plugging in what you know and solving for what you don t know. 2.2 22 Ex: C 2 r, C 44,, r? 7 4. Use formulas to solve for a specific variable. 2.2 Ex: use the formula A h( b b 2 ), to solve for b. 2 5. Use linear equations to solve application problems, such as, solving mixture problems, motion problems, problems involving money, and so on. 2.3, 2.4 Solve an application problem by: * defining a variable. x is usually the second thing mentioned and the first thing mentioned is in terms of x. * writing an equation that represents the relationship in the problem * solving the equation * answering the question asked. Plug x into the then statement. No formulas will be provided on the exam so be sure to write them on your index card. 6. Solve inequalities and graph the solution sets on a number line. 2.5 * For x a use (-------- or open dot * For x a use [-------- or closed dot * For x a use --------) or open dot * For x a use --------] or closed dot **Flip the symbol when multiplying or dividing by a negative!** 7. Solve compound inequalities that have solutions as ranges depending on the word and or or. 2.5 * For a x b use (---------) or open dots * For a x b use [------] or closed dots * For a x b use (---------] open and closed dots * For a x b use [------) open and closed dots * For x a or x b use -) (-- or open dots * For x a or x b use -] [-- or closed dots * For x a and x b use (----(-- or open dots * For x a and x b use [---[-- or closed dots * For x a and x b use --)----) or open dots * For x a and x b use -]---] or closed dots 8. Solve inequalities and equations involving absolute value. 2.6 Practice Problems for Exam 2 After reading your notes and looking over your homework, attempt these problems. Try to do them without looking at your notes or book. After you ve attempted the problems, check your answers. The solutions to all Chapter Test problems, even and odd, are available in the back of the book. Lastly, based on how you did on these problems revise the info you will write on your index card.
Chapter 2 Exam Review Intermediate Algebra Name. Simplify. 4 2( x 2y) x 5y 2. Simplify. 2 3 x x 5 3 7 3. Simplify. 5x 9y (2x 3) 2x 7y 4 4. Simplify. 0.( x 80) 0.2x 4 5. Solve for x. 2x 7( x 3) 5( x 4) 6. Solve for x. 5x 4(3 2x) 3( x) 7. Solve for x. 8. Solve for x. 2x 4 2( x 8) 0.4x 0. 0.7 0.3(6 2x) 9. Solve for x. 3 2 x x 4 2 3 0. Solve for x. (3x 4) 5 (2 3 x 8)
. Solve for x. 2(2x 4) 3x 6 3 5 4 2 2. Solve for y. ( y 3) 6 ( 3 2( y 27) y 2) y 2 3. Solve y 3 ( x 4) for y, in y mx b 3 form. 4. Solve 4x 6y 32 for y, in y mx b form. 5. Solve P 2l 2w for w. 6. Solve A h( b B) for b. 2 7. Given the perimeter formula for a rectangle, find P, whenl 2. 5and w 3. 7 P 2l 2w 8. Given the perimeter formula for a rectangle, find l, when P 30 and w 6. P 2l 2w 9. Find the volume of the sphere by using the formula. Use 3.4 as an approximation for. 4 V r 3 ; r 6 3 20. Given the area formula for a trapezoid, find h, when A 6. 5, b 4, and b 7 A h( b b 2 ) 2 2
2. A circular table has a circumference of 62.5 ft. What is the diameter? What is the radius? Remember: C 2 r, and use 3. 4 22. If you took out a loan for $3500 at a 5% simple interest rate, how quickly would you have to pay back the loan to only have to pay $437.50 in interest? Remember: i prt 23. The area of a triangular road sign is 70 feet squared. If the base of the sign measures 4 feet, what is the height of the sign? The area of a triangle is A bh. 2 24. The distance from Louisville to Dallas is 89 miles. If you drove 63 mph, how long will it take? Remember: d r t 25. In 965, women made up.2% of the U.S. military. With an increase at the rate of 0.4% per year, in which year will women make up 7.2% of the military? 26. You are choosing between two long-distance telephone plans. One plan has a monthly fee of $5 with a charge of $0.05 per minute. The other plan has a monthly fee of $5 with a charge of $0.07 per minute. For how many minutes of long-distance calls will the costs for the two plans be the same?
27. After a 20% price reduction, a cordless phone sold for $48. What was the phone s price before the reduction? 28. A salesperson earns $300 per week plus 5% commission of sales. How much must be sold to earn $800 in a week? 29. In a new development, 50 one- and two-bedroom condominiums were sold. Each one-bedroom condominium sold for $20 thousand and each two-bedroom condominium sold for $50 thousand. If sales totaled $7050 thousand, how many of each type of unit was sold? 30. A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 00 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used? 3. At a college production of Evita, 400 tickets were sold. The ticket prices were $8, $0, and $2, and the total income from ticket sales was $3700. How many tickets of each type were sold if the combined number of $8 and $0 tickets sold was 7 times the number of $2 tickets sold?
32. Company A charges $750 plus $20 for each widget. Company B charges $900 plus $2.50 for each widget. How many widgets would it take for both companies to cost the same? 33. How many ounces of 20% and 90% alcohol should you mix together to obtain 4 ounces of 40% alcohol? 34. If French roast coffee sells for $7.50 per pound and vanilla hazelnut coffee sells for $.50 per pound, how many pounds of vanilla hazelnut should you mix with 2 pounds of French roast to get a blend that is sold for $0 per pound? 35. Say you were famous and the paparazzi were chasing you. You re running 2 miles an hour, and they re running 0 miles an hour. You get to your house, and they are mile behind. How long did it take to get home? Rate Time Distance You Paparazzi
36. Two cars are 225 miles apart. They start traveling towards each other at the same time, but one car is going 5 miles an hour faster than the other. If it took 3 hours for the cars to pass each other, what was each car s rate? Rate Time Distance 37. Solve, express your answer in interval notation, and graph the solution 8( x 5) (2 7x) 4 38. Solve, express your answer in interval notation, and graph the solution. 2(4x ) 3x 3( x 2) 39. Solve, express your answer in interval notation, and graph the solution. 3(2 x) 3x 0 6x 40. Solve, express your answer in interval notation, and graph the solution 5 3 ( x 5) (6 2x) 8 6 4 4. Solve the inequality, express your answer in interval notation, and graph the solution. 5x 8 7 or 3x 8 0
42. Solve the inequality, express your answer in interval notation, and graph the solution. 2x 3 and 3x 2 43. Solve the inequality, express your answer in interval notation, and graph the solution. 4 3x 5 20 44. Solve and express your answer in interval notation. a) x + 2 + 9 6 b) x 2 + 4 5 c) 2x 2 4 2 d) 3x 3 9 45. Solve the following. a) 2y 6 = 0 2y b) 4y + 3 = 4y + 5 c) x 3 < -2 d) x + 4 > -2