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Course Review Package Unit 1 – Number Systems Unit 2 – Polynomials Unit 3 – Equations & Inequalities Unit 4 – Linear Relations Unit 5 – Measurement Unit 6 – Statistics & Probability Unit 1 – number systems Powers What is a power and what does it mean? Power – Expanded Form – Standard Form A power with an exponent of zero Exponent Laws: a0 1 o Product Law o Quotient Law o Power of a Power o Power of a Product o Power of a Quotient Order of Operations with Powers (BEDMAS) Square Roots Square roots of Perfect Squares i.e. 36 6 1, 4, 9, 16, ____, ____, ____, ____, ____, ____, ____, ____, ___, ___, ___ Approximate Square Roots of Non-perfect Squares i.e. 20 4.5 Rational Numbers Comparing and ordering rational numbers (number line) Problem solving that involve arithmetic operations with rational numbers Irrational Numbers – non-repeating, non-terminating decimal numbers. π = 3.14.15965 . . . . . . . . . . 5 2.236067 . . . . . . . . . Unit 2 – Polynomials What is a polynomial? o Create a concrete model or a pictorial representation for a polynomial Algebra Tiles: Black is positive, White is negative ie. Use algebra tiles to model 2 x 2 3 x 5 o Write an expression for a given model of a polynomial represents o Classify polynomials as a monomial, binomial or trinomial o Identify the variable, degree, number of terms, coefficients and constant term 7 y 4 3n 8 3x 2 5 x 6 o Describe a situation for a first degree polynomial expression o Match equivalent polynomial expressions 5v + v2 – 7 and -7 + 5v + v2 Addition & Subtraction o Concretely: using algebra tiles (zero principle) o Pictorially: o Symbolically: 4m2 4m 5 2m2 2m 1 3x 7 2x 2 Multiplication & Division: o Concretely: using algebra tiles (area = length x width) o Pictorially: o Symbolically: 5x 3 = 24 x 2 = 6 3 2 s 2 7 s 4 = 8n 4 = 2 2w 3w 5 = 40 x 2 16 x = 8x Unit 3 – Equations & Inequalities Linear equations: Model the solution of a given linear equation, using concrete or pictorial representations. Verify by substitution whether your answer (x = ) is a solution to a linear equation. i.e. Indicate whether the following values of x are solutions to 4 x 5 7 x = -2, 0, 3 Solve a linear equation symbolically. o Various forms: 5x 15 x 11 2 3x 6 18 x 27 4 6x 14 x 6 x 8 72 3x 4 2x 9 2 3x 1 4 x 5 8 2 x Identify and correct an error in a given incorrect solution of a linear equation. Represent a given problem, using a linear equation. o Kevin is planning to rent a car for one week. Company A charges $200 per week, With no charge for the distance driven. For the same car, Company B charges $25 administration fee plus $0.35 per kilometre. Linear Inequalities: Translate a given problem into a linear inequality using the symbols ≥, >, ≤, or <. o A coffee maker can hold not more than 12 cups of water. o You must be at least 14 years old to obtain a learner’s permit to drive. Solve a linear inequality algebraically. o o o o 2x 8 3x 2 10 7 y 14 4x 3 2x 9 Graph the solution of a linear inequality on a number line. Solve a given problem involving a linear inequality, and graph the solution. i.e. The cost of a prom is $400 to rent a hall, and $30 per person for the meal. The prom committee has $10 000 to spend. How many students can attend? Unit 4 – Linear Relations Write a linear expression representing a given pictorial or written pattern. ie. Here is a pattern made with toothpicks. The pattern continues. Write a linear expression that relates the number of toothpicks (t) and the number of houses (h) Write a linear equation to represent a situation. ie. Clint has a window cleaning service. He charges a fixed cost of $12, plus $1.50 per window. a) Write an equation that relates the total cost to the number of windows cleaned. b) Clint charged $28.50 for a job. How many windows did he clean? Solve, using a linear equation, a given problem that involves a pictorial or written pattern. ie. The cost to print brochures is the sum of a fixed cost of $250, plus $1.25 per brochure. a) Write an equation that relates the total cost, C dollars, to the number of brochures, n. b) What is the cost of printing 2500 brochures? c) How many brochures can be printed for $625? Write a linear equation representing the pattern in a given table of values. Verify the equation by substituting values from the table. Describe a pattern found in a given graph. Graph a linear relation, including vertical lines (x = ) and horizontal lines (y = ). Match a given equation of a linear relation to its graph. Interpolate the approximate value of one variable on a graph, given the value of the other variable. Extrapolate the approximate value of one variable on a graph, given the value of the other variable. Unit 5 – Measurement Surface Area Determine the surface area of a 3D object o cylinders, rectangular prisms, triangular prisms Determine the surface area of a composite 3D object o area of overlap (overlap shape x 2) o cylinders, rectangular prisms, triangular prisms Solve problems with composite 3D objects Similarity Determine if the polygons in a given set are similar and explain why. Draw a polygon similar to a given polygon given the scale factor Solve a problem, using the properties of similar polygons i.e A rectangular door has height 200 cm and width 75 cm. It is similar to a door in a doll’s house. The height of the doll’s house door is 25 cm. a) Sketch and label both doors. b) Calculate the width of the doll’s house door. Determine the scale factor for a given diagram drawn to scale s.f. enlargement (s.f. > 1) or a reduction (s.f. < 1) Solve a problem that involves the properties of similar triangles i.e. Jaquie is 1.6 m tall.When her shadow is 2.0 m long, the shadow of the school’s flagpole is 16 m long. How tall is the flagpole, to the nearest tenth of a metre? length on scale diagram length on original Symmetry Line symmetry – a reflection about a horizontal, vertical or oblique line. Rotation symmetry o Order of rotation symmetry – number of times a rotation coincides with itself 360 o Angle of rotation symmetry = order of rotation Rotate a given 2-D shape about a vertex, and draw the resulting image – tracing paper. Identify the type of symmetry from a given transformation on a grid Identify and describe the types of symmetry created in a given piece of artwork Determine whether or not two given 2-D shapes on a grid are related by either rotation or line symmetry. Translation an object on a grid – right 2, and up 3 Circle Properties Perpendicular from the centre of a circle to a chord bisects the chord Central angle is equal to twice the measure of the inscribed angle subtended by the same arc Inscribed angles subtended by the same arc are equal The inscribed angle on a semi-circle is a right angle. A tangent to a circle is perpendicular to the radius at the point Solve problems involving the application of one or more of the circle properties Unit 6 – Statistics & Probability Experimental Probability, Theoretical Probability, Subjective Judgement Describe the effect of: o Bias o use of language o ethics o cost o time and timing o privacy o cultural sensitivity on the collection of data. Select and defend the choice of using either a population or a sample of a population to answer a question. o Identify whether a given situation represents the use of a sample or a population. i.e. To determine the favourite TV show of grade 9 students in a school, all grade 9 students in the school are surveyed. o Describe some of the limitations of using a population – (too costly, not enough time, limited resources) o Describe when a generalization from a sample of a population may nor may not be valid for the population. i.e. Courtney surveys her friends and finds that 68% of them have an MP3 player. She reports that 68% of the grade 9 students have an MP3 player. James surveys the entire grade 9 population and discovers that 51% have an MP3 player. a) Whose conclusion is more likely to be valid? Explain. b) Why might the other student’s conclusion not be valid? Practice o Significance of a sample size in interpreting data. Common Sampling Methods: o o o o o o Simple Random Sample Systematic or Interval Sampling Cluster Sampling Self-Selected Sampling Convenience Sampling Stratified Random Sampling