Grade 9 Math Units 1-9 June Exam Outline Unit 1 Square roots and surface area
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1 Grade 9 Math Units 1-9 June Exam Outline Unit 1 Square roots and surface area 1. What is a perfect square and list the perfect squares from Determine whether a whole number, fraction or decimal is a perfect square ( ie. Can it be written as the product of 2 equal factors) 3. Show that a number is a perfect square by using: a) diagram (use the area of a square) b) a list of factors ( odd # of factors give a perfect square) c) Can it be written as the product of 2 equal factors. 5. What does square root mean? 4. Determine the square root of a whole #, decimal or fractional perfect square. 5. Side length of a square can be found by taking the square root of the area. Area can be found by squaring the side length. 6. Estimate the square root of a number( whole #,decimal, fraction) by using bench marks and using a calculator. 7. Be able to determine if the original number is a perfect square if the square root is given. ( ie. If square root is a terminating decimal the original # is a perfect square. If square root is non-terminating and non repeating then original # is not a perfect square). 8. Identify a # that has the square root between 2 given numbers. Ex. 50 has a square root between 7 and Be able to calculate the number whose square root is given. Ex. What # gives a square root of 2/3. Answer: 2/3 x 2/3 = 4/ Know the Pythagoras Theorem and be able to apply it to find missing sides of right triangles. 11. Be able to find the surface area of rectangular prisms, triangular prisms and cylinders. 12. Be able to find the total surface area of composite figures made from rectangular prisms, triangular prisms and cylinders( Remember to subtract the area that overlaps). 13. Be able to recognize the error and fix the mistake to get the right answer in a question. Note: pages are good practice. Check answers in back of book. Unit 2 POWERS AND EXPONENT LAWS 1. Know what the base, exponent and power is. Be able to write a power as repeated multiplication and vice versa. 2. Know that squared is referred to a base with exponent 2 and can be modelled using the area of a square. 3. Know that cubed is referred to a based with exponent 3 and can be modelled using the volume of a cube. 4. Change a power of 10 to standard form ( the regular #) and vice versa Know the difference between 2, 2, Any base to the exponent zero equals one. Know the difference between and Follow order of operations to evaluate expressions with powers. 8. Know the laws of exponents on the right including #6 above and be able to evaluate expressions. 9. Be able to express answers as a single power using the law of exponents Ex Be able to recognize the error and fix the mistake to get the right answer in a question. Note: pages are good practice. Check answers in back of book.
2 Unit 3 RATIONAL NUMBERS 1. Know the difference between rational and irrational numbers. 2. Be able to compare and order rational #s (integers, decimal and fractions) from least to greatest and place on a number line. 3. Be able to name a number between two given numbers. 4. Be able to add, subtract, multiply and divide integers, decimals and fractions (rationals). 5. Be able to solve word problems involving the operations with rationals. 6. Be able to calculate expressions using the order of operations with and without the calculator. 7. Be able to recognize the error and fix the mistake to get the right answer in a question involving rational numbers. Note: pages are good practice. Check answers in back of book. Unit 4 Linear Relations Outline 1. Know the difference between an algebraic expression and an equation 2. Be able to draw the next diagrams to continue a pattern given the first 2 or 3 diagrams. 3. Be able to represent the pattern in these diagrams using: - words, table of values, graph, expression or equation. 4. Be able to identify the independent (input) and dependent (output) variables. 5. Use the expression or equation to predict missing values of the independent or dependent variables. 6. Know what a linear relation is. ( Note: it always occurs when there is a constant change in the independent and independent variables.) 7. Obtain the linear equation based on the table of values. 8. Be able to determine if a relation is linear by looking at the graph and by looking at the table of values. 9. Be able to describe a real situation for a linear equation.( Ex. P = 3h +20 Sally is paid 20$ to start a job and then paid $3 per hour) 10. Be able to write an equation from a situation. The cost of a cab is initially $3.50 plus $ 1.50 per km -> C = 1.50d ) 11. Be able to determine whether discrete (dotted line) or continuous data (solid line) is used in a situation. 12. Be able to graph horizontal, vertical and oblique lines. 13. Be able to write the equation for a vertical and horizontal line by looking at the graph. 14. Given an equation be able to determine whether it is vertical, horizontal or oblique. 15. Match given linear equations with their corresponding graph. 16. Know the difference between interpolation and extrapolation and use it to find the missing variable given the other. 17. Determine whether an ordered pair satisfies an equation. Ex. Does ( 2,5) satisfy y = 2x + 1. Sub x = 2 and see if the y value will equal 5. y = 2(2) + 1 = = 5 yes. 18. Be able to recognize the error and fix the mistake to get the right answer in a question. Note: pages are good practice. Check answers in back of book.
3 Unit 5 Polynomials 1. Know the terminology and be able to recognize them in an expression: variable, variable expression, constant, like terms, unlike terms, polynomial, monomial, binomial, trinomial, degree, and number of terms. 2. Be able to model a given expression using algebra tiles and also be able to write the polynomial given a model Be able to recognize equivalent expressions ( 5x 3x 7and 7 5x 3x ). 4. Simplify polynomial expressions by combining like terms. 5. Be able to add and subtract polynomials by using models and symbolically (grouping like terms). This can be done use the horizontal or vertical method. Note: when subtracting you can use the add your opposite rule. 6. Identify the error(s) in a given simplification of a given polynomial expression. 7. Be able to multiply and divide polynomial expressions by a monomial. Be able to show these using a model ( algebra tiles or area model) and symbolically. 8. Apply your knowledge of polynomials to area and perimeter of a figure. Note: pages are good practice. Check answers in back of book. Unit 6 Linear Equations and Inequalities 1. Solve linear equations (and SHOW PROPER STEPS) of the form: ax = b x ba, 0 a ax + b=c x b c, a 0 a ax =b + cx a(x +b) = c ax + b = cx + d a(bx + c)=d(ex + f ) a bx, 0where a, b, c, d, e and f are rational numbers. x 2. Be able to model the solving of linear equations. 3. Determine, by substitution, whether a given rational number is a solution to a given linear equation ( ie. Check or verify). 4. Identify and correct and error in a given incorrect solution of a linear equation. 5. Represent a given problem using a linear equation and solve. 6. Know what an inequality is and what the symbols:,,, represent. 7. Be able to translate a given problem into a single variable linear inequality using the symbols,,,. 8. Determine if a given rational number is a possible solution of a given linear inequality (ie. Check and verify). 9. Be able to graph the solution of a given linear inequality on a number line. 10. Be able to solve inequalities and show the proper steps. Note: If you multiply or divide both sides by a negative then switch the inequality sign to its opposite. 11. Understand difference between equations and inequalities, equations only have 1 solution, inequalities can have many. Note: pages are good practice. Check answers in back of book.
4 Unit 7 Similarity and Transformations 1. Know what a scale diagram is ( enlargements and reductions). newlength 2. Be able to determine the scale factor of a scale diagram = originallength. 3. Be able to draw an enlargement or a reduction of a figure given the scale factor. 4. Give real life examples of scale diagrams. 5. Determine if two figures are proportional ( ie. Examples of a scale diagram) 6. Determine the missing length in a scale diagram using proportions and the scale factor. 7. Convert lengths into the same units. ( 1km = 1000 m, 1m =100 cm, 1cm = 10 mm, 1km = cm) 8. Know what is meant by corresponding angles and sides are. 9. Know what is meant by similar polygons (have the same shape but not necessarily the same size). 10. Know the properties of similar polygons: a) Their corresponding angles are equal b) Their corresponding sides are proportional ( have the same ratio) 11. Be able to show why two figures are similar. 12. Draw a polygon similar to a given figure and explain why they are similar. 13. Use properties of similar figures to find missing sides and angles. Be able to right the proper notation to show what figures are similar and the sides that are in AB BC AC proportion. ( ex. ABC DEF and ) DE EF DF 14. Know what line of symmetry( reflection line) or reflective symmetry is. 15. Determine how many lines of symmetry an object has. ( Note: The number of lines of symmetry in a regular polygon is equal to the number of vertices. Ex. A regular pentagon has 5 sides and 5 vertices, therefore it has five lines of symmetry). 16. Be able to draw the other half of an object given the original half and the line of symmetry. 17. Know what rotational symmetry is and be able to determine the order of rotation and the angle of rotation. 18. Be able to rotate an object clockwise or counter clockwise about a given rotation center and draw the resulting image. 19. Know what a tessellation is and be able to recognize line symmetry, rotational symmetry, order of rotation and the angle of rotation. 20. Be able to create or provide a piece of artwork and recognize line symmetry, rotational symmetry, order of rotation and the angle of rotation 21. Be able to perform a translation, reflection or rotation of a pre-image and be able to label the image vertices and write the ordered pairs ( co-ordinates). Also, be able to recognize any lines of symmetry or rotational symmetry Note: pages are good practice. Check answers in back of book. Unit 8 Circle Geometry 1. Know the terms and be able to recognize them and draw a sketch: center of a circle, radius, diameter, circumference, major and minor arc, tangent, point of tangency, chord, perpendicular, perpendicular bisector, inscribed angle, central angle and subtended. 2. Know some basic facts to help find missing angles and sides in diagrams drawn in a circle. a) The sum of the angles in a triangle equal 180 degrees. b) all radii in a circle are equal. c) In an isosceles triangle, the base angles ( angles across from the equal sides) are equal. d) Use Pythagoras to find a missing side in aright triangle if 2 sides are known. 3. Know and be able to apply the properties a) A radius drawn to a tangent at the point of tangency forms a right angle. b) The perpendicular from the center to a chord will bisect the chord.
5 Unit 8 Circle Geometry continued c) A line that joins the center of a circle to the midpoint of a chord will be perpendicular to the chord ( form 90 degree angles). d) The perpendicular bisector of a chord will always pass through the center of the circle. e) The measure of the central angle is twice the size of the inscribed angle that subtends the same arc. f) The measure of the inscribed angle is half the size of the central angle that subtends the same arc. g) An inscribed angle that subtends a diameter ( or semi-circle) is equal to 90 degrees. h) All inscribed angles that subtend the same arc are equal. Note: pages are good practice. Check answers in back of book. Unit 9 Probability and Statistics 1. Be able to show an understanding of probability in real life. ( Ex. Weather- 40 % chance of rain). 2. Be able to identify assumptions associated with a given probability and explain the limitations of each assumption. 3. Explain how a single probability can be used to support opposing positions. ( ex. 90% chance of getting 25 cm of snow will cause different reactions from society). 4. Explain, using examples, how decisions based on probability may be a combination of theoretical probability, experimental probability and subjective judgment. ( Ex. People will make decisions picking lottery numbers, playing Poker or Black Jack based on the 3 terms above.) 5. Describe the effect of: bias, use of language, ethics, cost, time and timing, privacy, cultural sensitivity on the collection of data. Be able to identify problems in the above mentioned areas in a given case study. 6. Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity may influence the data. 7. Select and defend the choice of using either a population or a sample of a population to answer a question. 8. Identify whether a given situation represents the use of a sample or a population. 9. Provide an example of a question where a limitation precludes the use of a population and describe the limitation, ex. too costly, not enough time, limited resources. 10. Identify and critique a given example in which a generalization from a sample of a population may or may not be valid for the population. ( Surveying one class of grade 9 s for choice of a song for their school leaving ceremony may not be representative of all grade 9 students) 11. Be able to collect, display and analyze data by: formulating a question for investigation, choosing a data collection method that includes social considerations, selecting a population or a sample, collecting the data, displaying the collected data in an appropriate manner, drawing conclusions to answer the question. Note: pages are good practice. Check answers in back of book. Study for your June exam by going over notes, tests, assignments, chapter reviews and tests for practice in book. Remember to practice, practice, practice!!! Your exam will be the PROVINCIAL ASSESSMENT (CRT) written by the government. We will mark it for our final exam mark before we send it to them. The assessment has a total score of 50 and is composed of: Section 1 25 selected response questions (multiple-choice). Value: 25 Section 2 Constructed response questions requiring students to write or draw an answer. Value: 25 (The value of each item will range from 1, 2 or 3 marks and partial marks will be awarded for each question).
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