Second Trimester Exam: STUDY GUIDE: KEY 1. Coordinate Plan - Quadrants: a. The coordinate plane below labels the four quadrants, the origin, x-axis, y-axis, and show how to plot points. b. Quadrant I 2. Integers: a. -5 degrees b. 18 yards c. $37 d. a height of 75 yards 3. Coordinate Plan: 8 in 4. Ordering Integers: a. -37, -12, 0, 1, 7, 21 b. -10 (East), -3 (South), -1 (West), 3 (North) 5. Prime factorization: a. 29 is prime. b. 240 = 2 4 x 3 1 x 5 1 c. 450 = 2 1 x 3 2 x 5 2
6. Expressions: 65 miles per hour 7. Absolute Value: a. Define absolute value, it is in your workbook! b. Evaluate: 1. 20 = 20 c. -16 2. -2 = 2 3. 0 = 0 8. Coordinate Plan - Quadrants: a. (3, -4) b. (-4,1) c. (2,4) 9. Terminating and Repeating Decimals: a. Define terminating decimal it is in your workbook! Example: 0.6 b. Define repeating decimal it is in your workbook! Example: 0.333 = 0.3 c. 1. 2 9 = -0.2 = repeating decimal 2. 18 25 = 0.72 = terminating decimal 3. 7 = -0.63 = repeating decimal 11 10. Operations with Fractions: a. 2 3 4 b. 16 7 8 cups c. 4 25 d. 18 students e. 12 sections
11. Conversions: 68.67 yards (I rounded my answer to the nearest hundredth place) 12. GCF and LCM: a. Define GCF (greatest common factor), it is in your workbook! b. 7 c. Define LCM (least common multiple), it is in your workbook! d. 108 13. Algebra - Properties: Property: Definition: Example: Commutative Property The order in which two numbers are added or multiplied does not change their sum or product. a + b = b + a ab = ba Associative Property The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. a + (b + c) = (a + b) + c a (b c) = (a b) c Identity Property The sum of an addend and 0 is the addend. The product of a factor and 1 is the factor. a + 0 = a a 1 = a Inverse Property The additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation. The multiplicative inverse property states that when you multiply any number by its opposite, the result is always 1. -a + a = 0 b + -b = 0 a ( 1 a ) = 1 b c (c b ) = 1 Distributive Property To multiply a sum by a number, multiply each addend by the number outside the parentheses. a(b + c) = ab + ac
14. Distributive Property: c. 12 + 8x 15. Coordinate Plane: F(2,-3) 16. Integers and Absolute Value: Answers can vary. One example is{-3,3}. 17. Powers and Exponents: a. 3.2 4 = 104.8576 b. ( 1 4 )3 = 1 64 18. Comparing Rational Integers: 9 16 < 0.8282... 10 30 = 0.3 0.98 > 9 10 19. Ordering Rational Integers: (least to greatest) a. { 4.6, 4 1, 4.2, 4 3 } b. { 7 2, 7. 3, 7.23, 7 3 } 9 8 3 4 c. { 9 8 9, 9.7, 9.87, 9 7 8 } d. { 5 4 5, 5.42, 5.34, 5 5 6 }
20. Coordinate Plane: W(4,-1) W 21. Expressions: a. Let d represent he number of marbles Dakota has. d-4 b. Let p represent the volume of the pool. 1 3 p c. Let b represent the cost of a baseball. 9b d. Let c represent the cost for each game ticket. 8+50c 22. Variables and Expressions: a. 5x + 7 = 57 b. x + 6 = 27 c. 2x + 12 = 54 23. Distributive Property: a. 49 + 14 = 7(7+2) b. 25 + 15 = 5(5+3) c. 9 + 21 = 3(3+7)
24. Order of Operations: a. 20 4 + 17 (9-6) = 56 b. 2 8 2 + (3-1) 2 = 12 c. 3 6 2 + 7 = 115 d. 4 2 + 5 2 1 = 25 *The Order of Operations is PEMDAS. The Order of Operations is just an agreement that allows us all to do a problem the same way so we get the same answer. Without the Order of Operations, one person might simplify 3 + 4 x 5 as 35 by adding first. Another person might simplify 3 + 4 x 5 as 23 by multiplying first. Having two answers for the same problem would be very confusing. So as we make arrangement to all drive on the right side of the road, to wear wedding bands on our left hand, to list home teams last in sports, we make agreements in math for consistency as well. The agreement is to do from left to right all groupings first, followed by exponentials, then multiplication and division third, and finally all additions and subtractions. Example: 3 + 12 2 x 3 = 21. Since there were no groupings or exponentials, we started with multiplications or divisions from left to right. That resulted in us dividing 12 by 2 before multiplying.