Preparing for Algebra Chapter 0

0.1 Plan for Problem Solving Pg. P5-P6 Obj: Learn how to use the four-step problem- solving plan.

0.1 Plan for Problem Solving Four-Step Problem-Solving Plan ▫Understand the Problem  Read the problem and explore what the problem is about  Identify the information given  Identify what you need to find ▫Plan the Solution  Strategy example: write an equation ▫Solve the Problem ▫Check the Solution  Check your answer in the context of the original problem  Does your answer make sense?  Does it fit the information in the problem?

0.2 Real Numbers Pg. P7 – P10 Obj: Learn how to classify and use real numbers.

0.2 Real Numbers Positive Numbers – values greater than 0 Negative Numbers – values less than 0 Natural Numbers – 1, 2, 3, … Whole Numbers – 0, 1, 2, 3, … Integers - …, -3, -2, -1, 0, 1, 2, 3, … Rational Numbers – numbers than can be expressed as a fraction Square Root – one of two equal factors of a number

0.2 Real Numbers Principal Square Root – the nonnegative square root of a number Perfect Square – a number like 64, with a square root that is a rational number Irrational Numbers – numbers that cannot be expressed as a fraction (cannot be written as a terminating or repeating decimal) Real Numbers – irrational and rational numbers Graph – means to draw or plot the points named by those numbers on a number line

0.2 Real Numbers Coordinate – the number that corresponds to a point on a number line

0.3 Operations with Integers Pg. P11 – P12 Obj: Learn how to add, subtract, multiply, and divide integers.

0.3 Operations with Integers Absolute Value – the distance a number is from zero on the number line (always positive) Opposites – pairs of positive and negative numbers Additive Inverses – a number and its opposite

0.3 Operations with Integers Addition ▫Like Signs  Add and keep the sign ▫Different Signs  Subtract and keep the sign of the larger Subtraction ▫Change subtraction to addition and change the sign of the number immediately after ▫Follow addition rules

0.3 Operations with Integers Multiplication and Division ▫Like Signs  Positive Answer ▫Different Signs  Negative Answer

0.4 Adding and Subtracting Real Numbers Pg. P13 – P16 Obj: Learn how to compare and order; add and subtract rational numbers.

0.4 Adding and Subtracting Real Numbers Follow the same rules for adding and subtracting integers Adding and Subtracting Fractions ▫Like Denominators  Add or subtract the numerators  Simplify ▫Unlike Denominators  Find a common denominator  Rewrite the fractions using the common denominator  Add or subtract the numerators  Simplify

0.5 Multiplying and Dividing Rational Numbers Pg. P17 – P19 Obj: Learn how to multiply and divide rational numbers.

0.5 Multiplying and Dividing Rational Numbers Use the same rules for multiplying and dividing integers. Method ▫Cancel where possible ▫Multiply numerators and multiply denominators ▫Simplify if necessary Multiplicative Inverses or Reciprocals – two numbers whose product is 1

0.6 The Percent Proportion Pg. P20 – P22 Obj: Learn how to use and apply the percent proportion.

0.6 The Percent Proportion Percent – a ratio that compares a number to 100 Percent Proportion

0.7 Perimeter Pg. P23 – P25 Obj: Learn how to find the perimeter of two- dimensional figures.

0.7 Perimeter Perimeter – the distance around a figure Rectangle – P=2(l + w) or P=2l + 2w Parallelogram – P=2(a+b) or P=2a+2b Square – P = 4s Triangle – P = a + b + c Circle – the set of all points in a plane that are the same distance from a given point Diameter – the distance across the circle through its center

0.7 Perimeter Circumference – the distance around the circle – C=2 πr Center – the given point Radius – the distance from the center to any point on the circle

0.8 Area Pg. P26 – P28 Obj: Learn how to find the area of two- dimensional figures.

0.8 Area Area – the number of square units needed to cover a surface Rectangle – A=lw Parallelogram – A = bh Square – A = s² Triangle – A = ½ bh Circle – A = пr²

0.9 Volume Pg. P29 – P30 Obj: Learn how to find the volumes of rectangular prisms and cylinders.

0.9 Volume Volume – the measure of space occupied by a solid Rectangular Prism – V = lwh Cylinder - V = пr²h

0.10 Surface Area Pg. P31 – P32 Obj: Learn how to find the surface area of rectangular prisms and cylinders.

0.10 Surface Area Surface Area – the sum of the areas of all the surfaces, or faces, of a solid Prism – S = 2lw + 2lh + 2wh Cylinder – S = 2пrh + 2пr²

0.11 Simple Probability and Odds Pg. P33 – P36 Obj: Learn how to find the probability and odds of simple events.

0.11 Simple Probability and Odds Probability – the ratio of the number of favorable outcomes for the event to the total number of possible outcomes Sample Space – the list of all possible outcomes Equally Likely – when there are n outcomes and the probability of each one is 1/n Complements – the events for rolling a 1 and for not rolling a 1

0.11 Simple Probability and Odds Tree Diagram – a method used for counting the number of possible outcomes Fundamental Counting Principle Odds – the ratio that compares the number of ways an event can occur to the number of ways it cannot occur

0.12 Measures of Center, Variation, and Position Pg. P37 – P40 Obj: Learn how to find measures of central tendency, variation, and position.

0.12 Measures of Center, Variation, and Position Variable – a characteristic of a group of people or objects that can assume different values Measurement or Quantitative Data – data that have units and can be measured Categorical or Qualitative Data – data that can be organized into different categories Univariate Data – measurement data in one variable Measures of Center or Central Tendency – measures of what is average

0.12 Measures of Center, Variation, and Position Mean – the sum of the values in a data set divided by the total number of values in the set Median – the middle value of the mean of the two middle values in a set of data when the data are arranged in numerical order Mode – the value or values that appear most often in a set of data. A set of data can have no mode, one mode, or more than one mode.

0.12 Measures of Center, Variation, and Position Measures of Spread or Variation – describe how widely the data values vary Range – the difference between the greatest and least values Quartiles – common measures of position that divide a data set arranged in ascending order into four groups Lower Quartile – the median of the lower half (Q1) Upper Quartile – the median of the upper half (Q3)

0.12 Measures of Center, Variation, and Position Five-Number Summary – the three quartiles, along with the minimum and maximum values Interquartile Range – the difference between the upper and lower quartiles Outlier – data values that are beyond the upper or lower quartiles by more than 1.5 times the interquartile range

0.13 Representing Data Pg. P41 – P46 Obj: Learn how to represent sets of data using different visual displays.

0.13 Representing Data Frequency Table – uses tally marks to record and display frequencies of events Bar Graph – compares categories of data with bars representing the frequencies Cumulative Frequency – each event is the sum of its frequency and the frequencies of all preceding events Histogram – a type of bar graph used to display numerical data that have been organized into equal intervals

0.13 Representing Data Line Graph – usually shows how data change over a period of time Stem-and-leaf plot – the digits of the least place value usually form the leaves, and the rest of the digits form the stems Circle Graph – a graph that shows the relationship between parts of the data and the whole Box-and-Whisker Plot – a graphical representation of the five-number summary of a data set