* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Math 150 Practice Problems – Rule of Four, Number System, Sets
Survey
Document related concepts
History of mathematical notation wikipedia , lookup
Law of large numbers wikipedia , lookup
Infinitesimal wikipedia , lookup
Location arithmetic wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Positional notation wikipedia , lookup
Ethnomathematics wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Non-standard analysis wikipedia , lookup
Surreal number wikipedia , lookup
Hyperreal number wikipedia , lookup
Large numbers wikipedia , lookup
Transcript
F12-M150 Rule of four, No. Sys, Sets, Abs. val 9/3/2012 Math 150 Practice Problems β Rule of Four, Number System, Sets, Absolute Value The Rule of Four: 1. Given π¦ = 2π₯ 3 a) Which form of representation is this out of the four rules to describe a mathematics problem? b) What are the other forms? Write the names and appropriate representation for the given problem. c) Sketch the graph for = 2(π₯ β 1)3 . 2. Anna and Sana are two sisters. Sana is three years older than Anna. a) Which form of representation is this out of the four rules to describe a mathematics problem? b) What are the other forms? Write their names and appropriate representation for the given problem. Make the necessary assumptions. (Let π₯ represent Annaβs age, and let π¦ represent Sanaβs age). c) What are the slope and π¦ βintercept of the line. d) How would the graph be if they were both the same age. e) What are the slope and π¦ βintercept of the new graph. 1 F12-M150 Rule of four, No. Sys, Sets, Abs. val 9/3/2012 Number System 3. Consider the following numbers. Which sets of the number system do these numbers belong to : Natural numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real 107 29575 2 3 6 -5 0 οΏ½οΏ½οΏ½οΏ½ 2.31572β¦ 3.5123 Sets 4. Write the inequality and/or interval notation as applicable: a) π₯ β (β5, β1) βͺ [0,7] b) π₯ β (ββ, 1) βͺ (2, 5] c) π₯ β (0, β) d) Set of real numbers less than 10 AND greater than -5 e) Set of real numbers less than or equal to 10 AND greater than or equal to -5. f) Set of real numbers greater than 10 and less than -5. g) 0 β€ π₯ β€ 25 h) β7 β€ π₯ β€ 7 i) Set of real numbers greater than 2 and greater than or equal to 10. j) Set of all real numbers 2 F12-M150 Rule of four, No. Sys, Sets, Abs. val 9/3/2012 Absolute Value 5. Find the solution to the equations : a) π₯ 2 = 16 b) |π₯ + 4| = 3 c) |π₯| = π₯ β 1 d) 4|π₯ β 3| = 2 e) 3|π₯ β 5| + 1 = 7 f) |π₯ β 1| = 2π₯ + 3 g) |2π₯ + 4| = β3π₯ β 1 h) (π₯ β 1)2 = 9 6. For the following, recognize the βcβ and βdβ , find the solution, sketch and write the solution in interval and inequality notation. a) |π₯ + 3| > 4 b) |π₯ + 4| < 2 c) |π₯ β 5| β₯ 3 d) |π₯ β 4| < 3 e) |π₯ + 3| = 2 7. For each of the following, sketch the solution and write it in the form of absolute value inequality equation: a) π₯ β (1,7) b) π₯ β [β3,5] c) 2 β€ π₯ β€ 8 d) π₯ > 5 π΄ππ· π₯ < β1 3