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Pre-Calculus 11 Date: _____________________ Page 1 of 3 Section 2.1: Absolute Value Recall: In section 1.5 (when we learned about Infinite Geometric series), you learned a formula to find the sum of an infinite Geometric series... and the restrictions on the formula were… We can rewrite ____________________ as an ABSOLUTE VALUE: _________________ because the absolute value can be used to represent the distance of a number from ZERO in the real-number line, REGARDLESS OF THE DIRECTION… Notice that for a real number “a”, the ABSOLUTE VALUE of “a” is written as ________ and is always a ____________________ number. (that’s why some people just think that the absolute value is just the positive of a negative number, or that an absolute value makes all numbers positive) Example 1: Evaluate the following. a) |123| b) |−49| e) |−4 + 13| − |3 − |−8|| c) |2 − 7| + 3 d)| 5 − (2)(3 − 9)2 | f) |5(−2)2 + |4(−3) + 7|| Treat the absolute value bars like brackets in the order of operation. Pre-Calculus 11 Date: _____________________ Page 2 of 3 Section 2.1: Absolute Value Recall: Principal Square Root: The non-negative square root of a non-negative real number, a, is called the principal square root of a and is written√𝑎. The distance between two real numbers, A and B is 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = |𝐴 − 𝐵|. |𝑥| = √𝑥 2 Example 2: Determine the distance between 9.8 and -10.5. Example 3: Determine the length of the horizontal or vertical line segment using the absolute value symbols. Then calculate the length. a) A(9,2) and B(4, 2) b) E(m, n) and F(m,p) Example 4: Evaluate: √(7 − 10)2 Hint: Use |𝑥| = √𝑥 2 . c) C(-2, 6) and D(-2, 11) Pre-Calculus 11 Section 2.1: Absolute Value Date: _____________________ Page 3 of 3 Page 89: 2,4,5,6b,7,8c, 9, 10, 11cd, 12d-f, pg 94, mc #1 Higher level 13ac, 15, 16 (show all your work), pg 94, MC #2 Word Problems Example 5: Mr. Lee checks his bank account online each day. On Monday, his account balance was $250, on Tuesday, it was $196. On Wednesday, it was $225. On Thursday, the balance was $240 and on Friday, the balance was down to $190. a) Use an absolute value expression to determine the TOTAL CHANGE in Mr. Lee’s bank balance during this period. b) Calculate the NET CHANGE in his bank balance and explain how this is different from the TOTAL CHANGE you calculated above. Example 6: A trading stock opens the day at a value of $20 per share, drops to $17 by 10 am and then rises to $19 by noon. It then falls to $18 by 1 pm and suddenly rises to $22 by 3 pm. The stock finally falls to an unknown amount to close the trading day. If the absolute value of the total change for this stock is $15, determine the amount that the stock dropped in the afternoon before closing.