Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Math 9 final study guide
Transcript
MATH 9 FINAL EXAM STUDY GUIDE - June 2009 Your final exam will include 50 questions in both Multiple Choice and Numerical Response format. The following concepts may be included on the exam: Rational Numbers Definitions Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Principle Square Root Positive Square Root Negative Square Root Evaluate Estimate Simplify Repeating Decimal Terminating Decimal Non-repeating Decimal Non-terminating Decimal Key Concepts Identify if a number is rational or irrational Number of roots for a principle root e.g. 25 Number of roots for an equation e.g. x 2 25 Classify numbers N , W , I , Q, Q, R Evaluate roots Evaluate expressions with multiple roots Evaluate formulas with radicals Solve word problems Estimate roots between 1-100 Estimate large and small roots (use even powers of ten) * Memorise the first 13 perfect squares Exponents Definitions Simplify Evaluate Exponential Form Expanded Form Standard Form Power Exponent Base Key Concepts Identify the base, exponent, power Write a power in exponential, expanded and standard form Understand the difference 24 2 4 24 Exponent Laws Multiplication Law a m a n a mn Must have the m n m n same base Division Law a a a a0 Power of a Power a m a mn Negative Exponent Law a n n 1 an Zero Exponent Law a 0 1 a 0 a0 Use exponent laws to simplify and evaluate expressions Simplifying and evaluating expressions by changing bases Write numbers in scientific notation Write scientific notation in standard form Multiply numbers in scientific notation by grouping Multiply numbers in scientific notation by using a calculator Algebra Definitions you need to know Constant Distributive Property Numerical Coefficient Variable Literal Coefficient Term Like Terms Expression Factor Polynomial Monomial Inequalities Binomial Trinomial Degree Standard Form Additive Inverse Greatest Common Factor Difference of Squares Perfect Square Rational Expressions Restrictions x R, x I Operations that you need to be able to do Operation Adding polynomials (with tiles as well) Subtracting polynomials (with tiles as well) *Additive Inverse Multiplying and Dividing Monomials Multiplying Polynomials by a Monomial (with tiles as well) Dividing Polynomials by a Monomial Binomial Products (with tiles as well) Multiply any polynomials Use all these operations to simplify expressions Factoring Greatest Common Factor Factoring Trinomials in the form x bx c 2 Factoring Trinomials in the form ax bx c by factoring a GCF first Factoring Perfect Squares and Difference of Squares Rational Expressions Solving Equations Solving multiple step equations Solving Quadratic Equations Solving Rational Equations Isolating A variable in a formula Graph an inequality on a number line Restrictions x R, x I Solve inequalities Word Problems Number, Age, Value, Rate, And Distance d vt 2 Transformations Definitions that you need to know: Congruent Scale Factor Coordinate Pair Vertices Translation Notation (A→A’→A’’) Mapping Rule Vector Translation Arrow Centre of Rotation Counter Clock Wise (CCW) Clock Wise (CW) Cartesian plane Line of Reflection Centre of Dilatation Four Types of Translations: Translation (Slide) – You need to be able to do the following Write a translation using the 4 possible ways (Translation Arrow, Word Statement, Mapping Rule, Vector) Apply a translation to a figure and determine the coordinates of its new position Determine the coordinates of the original position of a figure given its final position and translation. (Working backwards) Identify a translation and write it in anyone of the 4 possible ways Rotation (Turn) – You need to be able to do the following Apply a 900, 1800, 2700 (CW or CCW) Rotation to a figure and determine the coordinates of its new position. (You may use tracing paper on the unit test) Determine the coordinates of the original position of a figure given its final position and rotation. (Working backwards) Identify a rotation and give answer in degrees and direction Reflection (Flip) – You need to be able to do the following Reflect a figure in the x-axis or in the y-axis and determine the coordinates of its new position Reflect a figure in a vertical or horizontal line that is not the x-axis or y-axis and determine the coordinates of its new position Reflect a figure in diagonal line and determine the coordinates of its new position Determine the coordinates of the original position of a figure given its final position and line of reflection. (Working backwards) Identify a reflection and determine its line of reflection Dilatation (Enlarging Reducing) Apply a dilatation to a figure and determine the coordinates of its new position when the centre of dilatation is the origin. * Tip – short cut use mapping rule (e.g. if scale factor = 2 use x, y 2 x,2 y ) Apply a dilatation to a figure and determine the coordinates of its new position when the centre of dilatation is not origin. (you can not use short cut “ mapping rule”) Im age Identify a dilatation and determine the scale factor S .F . original Identify a dilatation and determine the centre of dilatation Combined transformation Apply 2 translation on a figure and determine its final position. Find the original position given the final position and the translations applied (Working backwards) Tip – The last translation done to the figure must be done backwards first to get back to the original) Probability Study Guide Definitions Experimental Probability Theoretical Probability Relative Frequency Event Outcome Independent Events Dependent Events Sample Space You should be able to… Calculate Theoretical Probability P( A) Favourable Outcomes Total Number of Outcomes Calculate Experimental Probability (Relative frequency) Create sample spaces by making a table or by a tree diagram. Use a sample space to determine probabilities. Determine if events are Dependent or Independent and be able to calculate probability P( A and B) P( A) P( B) Independent P( A and B) P( A) P( B A) Dependent Probability of B given that A has occurred Determine the number of outcomes (or combinations) using the Fundamental Counting Principle Determine probabilities of events using the Fundamental Counting Principle. STATISTICS UNIT STUDY GUIDE Definitions: Population Sample Census Questionnaire Random Sample Bias Tally Frequency Interpolate Extrapolate Survey Research Interview Range Median Mean Mode Graphing Definitions: Dependent Variable (Responding) Scatter plots: Independent Variable (Manipulative) Positive Correlation (Increasing trend) Negative Correlation (Decreasing trend) No Correlation Strong and Weak Correlations Describe the relationship Example Weak Positive Correlation Correlation Strong Negative Correlation No You must be able to do the following 1. Be able to design and properly label a scatter plot, draw on the line of best fit, and decide whether your graph has positive, negative or no correlation and why. Also, be able to make predictions about data on the graph as well as data not directly on the graph. 2. Be able to gather information into a tally chart and figure out the frequency for each Range. Then take this information and properly design and label a histogram. 3. Calculate the four measures of central tendency - mean, median, mode, and range.
