Inequalities 1
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The document provides instructions on: 1) The meanings of the inequality symbols <, >, , and how to graph them using open or closed circles. 2) How to solve simple inequalities by using the same process as solving equations and boxing the variable. 3) How to graph the solutions of inequalities on a number line by placing open or closed circles above the solution number and drawing arrows in the appropriate direction based on making the inequality true.
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This document provides tips for acing the Additional Mathematics (AM) and Elementary Mathematics (EM) exams. It summarizes key statistics on topics that are highly tested, such as differentiation and integration making up 27.8% of the AM exam. It recommends focusing on the 11 chapters that make up 74.6% of the exam. Sample questions are provided for topics like trigonometry, logarithms, linear laws, and matrices. Strategies are outlined for solving different types of questions on these topics.Powerpoint for preparing students to take the GMAT Focus Edition
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This document discusses several mathematical concepts including integers, place values, number lines, inequalities, probabilities, exponents, and remainders. It explains that the absolute value of a number removes its negative sign, place values represent a number as sums of powers of 10, number lines can represent inequalities with open and closed circles, and inequalities on number lines evaluate to true if a number is within the given range. It also mentions exponents represent the number of times a base is multiplied by itself and remainders are what is left over when dividing two numbers.Additional Mathematics Revision
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This document provides a summary of topics related to algebra, functions, and calculus including: linear and quadratic expressions, simultaneous equations, completing the square, trigonometric ratios, differentiation, tangents, normals, and finding stationary points through higher derivatives. It outlines key steps and methods for solving various types of problems within these topics.Math Dictionary
Math Dictionarydmarsh1
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This document defines key math terms related to integers, the coordinate system, and rules for integer operations. It explains integers, absolute value, the x-axis, y-axis, quadrants, ordered pairs, and rules for addition, subtraction, multiplication, and division of integers. It also defines mean, commutative, associative, identity, multiplicative inverse, and distributive properties and includes example problems.Inequalities 1
- 2. Important Facts < means ____ than > means ______ than means ____________________________ means ____________________________ Use an _____circle for < and > when graphing Use a _______ circle for and when graphing
- 3. Important Facts < means less than > means greater than Use an open circle for < and > when graphing. Use a closed circle for and when graphing
- 4. How to solve an inequality There is only one difference between an equation and an inequality = versus <, >, ,
- 5. Solving inequalities 4 + x < 12 4 + x < 12 (draw T chart) 4 + x < 12(box in variable) 4 + x < 12 (minus 4 both sides) -4 -4 x<8
- 6. Graphing Why a closed circle for and ? If something is on your graph there is a dot or line on it. So, we use a regular dot or line to include numbers in our answer. Why an open circle for < and>? If something is not on our graph we do not put a dot or line on it. So, if 4 is not part of our answer but 3.9999999999 is we can graph that by putting an open circle to show we do not include 4 but we include numbers really really close to 4.
- 7. Now to graph the solution x<8 1. Draw a number line. Just need a few numbers on either side of the solution number. 2. Decide if open circle or closed circle. Place it above the solution number. 3. Determine which way your arrow goes by substituting a number in for the variable to make the statement true. Then draw the arrow pointing in that direction.
- 8. Solving inequalities 48 8 +m 48 8+m (draw T chart, box variable) -8 -8 (subtract 8 both sides) 40 m
- 9. Now to graph the solution 6m 1. Draw a number line. Just need a few numbers on either side of the solution number. 2. Decide if open circle or closed circle. Place it above the solution number. 3. Determine which way your arrow goes by substituting a number in for the variable to make the statement true. Then draw the arrow pointing in that direction.
- 10. 6u 36 u-6 36 +6 + 6 u 42 39 40 41 42 43 44
- 11. y15 y15 +1 +1 y6 3 4 5 6 7 8
- 12. Graph an inequality x < 12 1) Open circle or closed circle? 2) Which direction should the arrow go? 10 11 12 13 14
- 13. Graph an inequality 42 m 1) Open circle or closed circle? 2) Which direction should the arrow go? 40 41 42 43 44