Gateway Quiz #1 Results: Average class score: x.x% Number of students who passed: x (Passing the Gateway requires a perfect score of 8/8, and very few students score 100% on the first try…) Common errors on the Gateway: Not simplifying fractions. Misplaced negative signs. Not following the order of operations. The next Gateway will be given in class in about 2 weeks. (Those who have scored 8/8 on the first one don’t have to take it again.)

Next Gateway: The next Gateway will be given in class about 2 weeks from now. Before that day, each student who did not score 8/8 on the first Gateway must go over that online quiz and the paper worksheet you get back today one-on-one with a teacher or TA and get a signature from them on the bottom of the second page of the quiz. This can be done either in the open lab or in any class session after lecture. After reviewing that worksheet, the TA or teacher will give you a paper copy of another practice Gateway to take in the lab at that session. They’ll grade it for you when you finish and then they’ll review with you any questions you missed. You must show your classroom teacher the signed quiz before you will be allowed to take the next version. You should also take the online practice Gateway again before the next in-class Gateway. You can do this as many times as you want to, so work on it until you can score 100%.

Grade Scale Online Quiz #1 Results: Average class score after partial credit: xx.x% Commonly missed questions: # x, x, x, x

Make sure you review all problems you got wrong on Quiz 1. (Do this by clicking on Gradebook, then click Review, and go over your quiz and your paper answer sheet.) TAs in the open lab can help you understand how to do any problems you got wrong. These sections will be tested again on Test 1 and on the final, and you’ll need to continue using these skills on upcoming homework sections.

Quiz # 2 will be given in class the next class session after Gateway Try 2. Quiz 2 will cover sections 2.1 – 2.3. Calculators will not be allowed on this quiz.

NOW PLEASE CLOSE YOUR LAPTOPS and prepare to take notes.

Section 2.1 A term in an algebraic expression is the product of a real number and variables (or variables raised to powers), or a real number by itself. The number part at the front of the term is called a coefficient.

Examples of Terms: 5x 3 (coefficient is 5) 4xy 2 (coefficient is 4) z 2 (coefficient is 1) -10x(coefficient is -10) -y(coefficient is -1) 7 (coefficient is 7) NOTE: If a variable does not have a power after it, the power is understood to be 1. Example: In the term 4xy 2, the coefficient is 4, the power (or exponent) of the x term is 1 (x = x 1 ), and the power of the y term is 2.

In the algebraic expression 7x 5 + x 2 y 2 – 4xy + 7, there are 4 terms: 7x 5, x 2 y 2, -4xy and 7. The coefficient of term 7x 5 is 7, The coefficient of term x 2 y 2 is 1, The coefficient of term –4xy is –4 and The coefficient of term 7 is 7. 7 is called the constant term. (no variable part, like x or y)

Like terms are terms that contain exactly the same variables raised to exactly the same powers (i.e. the variable parts are “alike”.) To combine like terms, add or subtract the numerical coefficients (the numbers in front of the letters), then put that combined number in front of the variable (letter) part. Examples: 3x + 5x = 8x 10y 2 – 6y 2 = 4y 2 Note: The coefficients of unlike terms cannot be combined to make one term. Examples: 3x + 3y (cannot be combined into one term) 10y 2 – 6x 2 (cannot be combined into one term)

6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2 -11xy Can’t be combined (since the terms are not like terms) Examples of Combining Terms: Terms Before Combining:After Combining Terms:

Problem from today’s homework:

Example: Simplify 4(2x + 3) – 2(3x – 1) Solution: 4·2x + 4·3 – 2·3x – 2·(-1) = 8x + 12 – 6x + 2 = 8x – 6x = 2x + 14

Problem from today’s homework:

Example: Subtract 4x – 7 from 8x + 10 Solution: 8x + 10 – (4x – 7) = 8x + 10 – 4x + 7 = 8x – 4x = 4x + 17

Problem from today’s homework:

Note that this problem requires skills from several different Gateway problems. Make sure you combine like terms and simplify all fractions in your final answer!

Example: Simplify 0.4y – y – 0.3 – 2.6y Solution: 0.4y + 1y – 2.6y – 6.7 – 0.3 = ( – 2.6) y – 7.0 = -1.2y – 7.0 or -1.2y - 7

Problem from today’s homework:

Example: Simplify 2x 2 – 3x + 5 – (5x 2 + 4x – 7) Solution: 2x 2 – 3x + 5 – 5x 2 – 4x + 7 = 2x 2 – 5x 2 – 3x – 4x = -3x 2 – 7x + 12

3a 2 – 6a + 11 Example Add or subtract each of the following, as indicated. 1) (3x – 8) + (4x 2 – 3x +3) = 4x 2 + 3x – 3x – = 4x 2 – 5 2) 4 – (-y – 4) = 4 + y + 4 = y = y + 8 3) (-a 2 + 1) – (a 2 – 3) + (5a 2 – 6a + 7) = -a – a a 2 – 6a + 7 = -a 2 – a 2 + 5a 2 – 6a = = 3x – 8 + 4x 2 – 3x + 3

Example: Write the following phrase as an algebraic expression, then simplify: The sum of 2, three times a number, -9, and four times a number Solution: Let x stand for the number. Then the sum is: 2 + 3x + (-9) + 4x = 3x + 4x + 2 – 9 = 7x - 7 Now simplify:

Problem from today’s homework:

Example: Write and simplify an algebraic expression for the perimeter of a rectangle whose length is 3x feet and whose width is 2x + 1 feet. Solution: Remember that the perimeter of a figure is the sum of all the sides of the figure. A rectangle has four sides: two sides equal to the length and two sides equal to the width. Therefore the perimeter is 2 lengths + 2 widths = 2(3x) + 2(2x + 1) = 6x + 4x + 2 = 10x + 2 NOTE: It always helps to draw a picture!

Homework for Section 2.1 is due before the start of the next class period. Reminder: You should be doing this homework without using a calculator, because calculators can’t be used for Quizzes 1 or 2, Test 1, or the Gateway Quiz. DON’T FORGET TO GO OVER YOUR GATEWAY QUIZ WITH A TEACHER OR TA AND HAVE THEM SIGN OFF ON PAGE 2.