Math 65: 2019 Spring Term
Note: I try to give good steps to work the problems, but sometimes you may want to look for some more help. Our department put the following web page together. The steps are different, but may help.
https://spot.pcc.edu/slc/mathresources/output/html/
Week 1:
Review equation solving and graphing. Look at graphing notes for more help.
Learn methods to solve a system of linear equations.
Problems:
5.1: Work at least nine problems from 23 – 42. At least three need to have one solution, at least three have to have no solution and at least three have to have an infinite number of solutions.
Week 2:
5.1 Learn how to find number of solutions for a system without graphing. Learn how to see if a given ordered pair is a solution to a system.
5.2 Learn how to solve a system of equations by substitution.
5.3 Learn how to solve a system of equations by addition/elimination.
5.2, 5.3 Learn how to solve application problems with two variables and a system of equations.
Problems:
5.1
- Work at least three problems from 17-22. One problem should result in an ordered pair that is a solution and the at least one problem should result in an ordered pair that is not a solution.
- Work at least three problems from 43- 50. One problem should result in one solution, one problem in no solution and one problem in an infinite number of solutions.
5.2
- Work at least six problems from 11-60.
5.3
- Work at least six problems from 7-38.
Note: On both 5.2 and 5.3 At least two need to have one solution, at least two have to have no solution and at least two have to have an infinite number of solutions.
Week 3:
5.2 – 5.4 Learn how to solve application problems.
Setup at least 16 application problems by setting up the two variables, a chart (if needed), and two equations. The 16 problems need to be from 5.2 – 5.4 and include:
- 4 mixture problems
- 4 investment problems
- 4 ticket or point value problems
- 2 compare two companies
- 2 rectangle problems.
Half of these 16 problems need to be solved completely and write answers with complete sentences.
Week 4:
Study for test on Thursday of week 4 by making a practice test of one of each of the following:
- Determine if a point is a solution (see 5.1).
- Find number of solutions (5.1).
- Solve by graphing (5.4).
- Solve by substitution (5.4).
- Solve by elimination (5.4).
- Solve a worded problem using a mixture (5.4).
- Solve a worded problem using an investment or buying two types of tickets (5.4)
- Solve a worded problem using geometry (5.4).
On this practice test write some vocab problems from Ch 5 and Ch 6. Examples would include, names of methods to solve systems of equations, how to determine the number of solutions looking at the slopes and y-intercepts, how do the graphs look for one solution, no solution, and infinite number of solutions, terminology from chapter 6 on polynomials, degree, coefficients, etc.
On this practice test work write problems on multiplying monomials from 6.1, 7, 8, 13, and14.
A lighter load this week. Please read 6.1 and 6.2.
Please write the following notes in your notebook at this link. You will receive extra credit if they are written in your notebook. You do not need to write the comments in the examples. Please know how to simply multiplication of monomials and division of monomials.
Please work the following problems for HW #4.
- 6.1: 7, 8, 13, 14, 35 – 40, 49 – 52.
- 6.4: 1 – 4.
- 6.7: 3, 4, 13, 14.
Week 5:
Chapter six on exponent rules and scientific notation.
Problems:
- 6.1: 10 – 140 by 5, that is, [10, 15, 20, etc.] Note: If you previously worked 20 to 30 problems, make sure you have at least 25 completed and do not be concerned about problems having multiples of five.
- 6.2: 3 – 42 by 3, that is [3, 6, 9, etc.] Please read 6.2 and especially look at examples 6.2.14 and 6.2.15 including the example on a power. I have updated the notes web page and you can click on the following notes at:
- Multiply, Divide and Powers [pdf]
- Please look at 6.3 and 6.4.
Week 6:
Finish up chapter six on operations on polynomials and start factoring in chapter seven
- 6.7: 3 – 114 by 3
- 7.1: 21 – 48 by 3.
- 7.2: 18 – 36 by 3.
- Read 7.4 as we will start with that in Week 7. Especially look at the table and factors and sum.
Week 7:
HW #7
More Factoring in Chapter Seven
- 7.4: 9 – 78 by 3: 9, 12, 15, …
- 7.3: 12 – 105 by 3: 12, 15, 18, …
- 7.5: 15 – 51 by 3: 15, 18, 21, …
Please check odd answers.
Please do a multiplication check of at least 10% of the problems.
Read over 7.5
Week 8:
Study for Test by working as many problems as possible from sections
- 6.7: 1 – 114
- 7.5: 69 – 110
- 7.6: 7 – 168
HW #8:
Please read 8.1, 8.2 and 8.3. Please copy the following notes into your notebook:
Solve a Quadratic Equation by Factoring.
Problems:
- 8.1: 15 – 55 by 5. Solve and check.
- 8.1: 69 – 71
Week 9:
Read 8.2 – 8.5
Please read over the following notes. You do NOT need to write them in your notes since we did the notes in class.
Problems for HW #9:
- 8.2: 32, 33, 35, 36
- 8.2: 77 – 84
- 8.3: 3 – 18 by 3.
- 8.3: 21 – 30 by 3
- 8.3: 34 – 37
- 8.3: 47 [Draw a diagram and then draw a right triangle.]
- 8.4: 12 – 45 by 3 and worded problems 59, 60, 63.
- Note: Please follow instructions carefully on 8.4. Some of these problems must be solved by the quadratic formula and others you need to choose factoring, square root property or the quadratic formula.
- The guidelines are the following when solving quadratic equations.
- If there is a binomial or trinomial that can be factored, use the factoring method.
- If there is just an x squared term and a constant or a ( ) squared and a constant, use the square root property method.
- In all other cases use the quadratic formula.
Week 10:
Review of chapter 8 and cover 8.5 on complex numbers. Cover chapter 9.
Problems:
- Please rework all problems on tests one and two. (You do not need to turn these in.)
HW #10
- 8.7: 3, 4, 43, 49, 52, 58, 67, 77
- 9.1: 5, 11, 21, 45, 49, 53
- 9.3: 37, 53