Mathematics 10 Final Exam Review This is not the “definitive review”!! This is a guide. You main review should be to go through old tests, comprehension questions, assignments and the review section of the textbook (at the end of each chapter). Do not just read over notes, practise, practise practise!!!
Patterns, Relations, Equations, and Predictions 1. Be able to solve linear equations, including those with brackets and fractions: a 1 a 1 1 3 2x 5 a) 26d 3 18 316 3d b) c) 4x 1 2x 3 2 4 3 2 3 6 2. Be able to solve an inequation. Know that the inequality reverses when you multiply or divide by a negative. a) 2 3x 20 b) 2 3x 20 3. Know how to find the intersection point of two lines (solve a system of equations) using each method: a) Graphing b) Substitution Solve this system graphically: Solve this system by substitution 2y x 8 0 x 2y 5 3 y x 4 y 4x 7 2 4. Given an equation, be able to draw its graph 3 a) Draw the graph of y x 4 4 b) Change x 2y 1 3 to y mx b form and graph it. c) Find the x and y intercepts of 2x 3y 18 and use the intercepts to draw the graph. 5. Given a graph, be able to write an equation. Write equations for these graphs.
L1 :______
L2 : ______
L3 : ______
6. Given a context (story) be able to make a table of values, write an equation or draw a graph. Julie rents a jet ski and is charged an initial flat fee of $5 plus $2 for every litre of fuel consumed. a) Draw a graph of this relationship b) Complete the table of values c) Write an equation for the Fuel (L) Charge ($) relationship. Use c to 1 represent the charge and f to 2 represent the number of litres 3 consumed. 4 5
7. Change a table of values into a graph, equation or story (context)/ On weekends, Gina operates a window cleaning Hours Charge business. The table shows how her fee depends on worked ($) hours worked. 1 15 a) What is her hourly rate? 3 35 b) What is her flat fee (initial charge)? 5 55 c) How much would Gina charge for a 10 hour job? 7 75 d) Write an equation for the relationship. e) Graph the relationship.
8. Make sure you can rewrite an equation so it is in y mx b form. 9. Find the equation of a line given: a) The slope and a point: Find the equation of the line with a slope of -½ that passes through the point 4,5. b) Two points: Find the equation of the line which passes through 1, 2 and 3, 4 c) The x and y intercepts: The x intercept of a line is 4. Its y intercept is 6. Find the equation of the line.
10. Know that a slope of zero means the line is horizontal and that an undefined slope means the line is vertical. Modeling Functional Relationships 11. For graphs of functions and relations: a) Identify whether the graph represents a function or not b) State whether the graph is continuous or discrete c) State the domain and range of the relation Answer questions a, b and c for each graph. i) ii) iii) iv)
12. Be able to change an algebraic expression from a sum to a product and from a product to a sum. A. Expand and simplify: a) x 42 b) 2a2a 2 m c) y 3y 3 d) 2x 34x 7 B. Factor completely: a) a 2 25 b) y 2 5y 4 c) x 2 7x d) x 2 10x 25 e) 2x 2 x 10 f) x 2 16 g) 2x 2 7x 6 h) 2x 2 18 13. Be able to use factoring to simplify algebraic fractions. Simplify: 3x 6 x 2 7x 12 x 2 1 a) b) x 2 4 x 2 3x x 2 3x 4 14. Be able to solve quadratic equations by factoring. Solve each quadratic equation: a) x 2 8x 15 0 b) x 2 5x 0 c) 2x 2 x 6
15. Be given a situation defined by a quadratic graph ( a baseball, a rocket flight etc), factor to solve for the roots to find the landing point, or discuss the significance of the y intercept. 16. Use transformations to graph quadratic and absolute value functions. a. Given an equation in transformational form, identify the transformations of y x 2 or y x which have occurred. b. Write a mapping rule. c. Graph the function. Do a, b, and c for each of the following functions. 2 2 1 2 i) y 3 x 1 ii) y x 2 iii) 2 y 2 x iv) y 1 x 2
17. Given a graph, write the equation for the translation of y x 2 18. Write the equation for each graph: a) b) c)
19. Be able to work with function notation when the graph of a function is given. Given the graph of a function, f , determine each of the following: a) f 3 b) f 0 c) f 2 d) x if f x 4 e) x if f x 0
20. Be able to work with function notation when the function is given as an equation. Given f x 3x 2 , gx x 2 3x and hx 3x 1 , determine the following: a) f 5 b) f 1 c) f 0 d) g3 e) g 2 f) h2 g) h0 Find x if h) f x 11 i) f x 16 j) gx 4 k) hx 10 21. Be able to interpret graphs. a. Explain the meaning of the following: i) positive slope ii) flat section iii) y-intercept iv) x-intercept b) Write a story to fit the graph.
22. Be able to use the graphing calculator to Page 209 – 210 determine functions that can represent a set #12 of data and use the model to make #15 predictions.
Trignometry: How Far? How Tall? How Steep? 23. Know how to use the three trig ratios (SOH CAH TOA) to solve for missing angles and sides in right triangles, be able to draw the diagram and solve The dancer is 1.4m tall. She is standing 2.5m from a projector. What is the angle of depression from her line of sight to the projector?
2.5m 24. Use the Pythagorean Theorem to solve problems. a) How long must a ladder be to reach the top of a 6.2 m wall if the foot of the ladder must be 2.3 m from the wall? b) Find the missing value. a
13 18
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25. Perform operations on expressions involving radicals and simplify radicals. Simplify each of the following, leaving final answers in simplest radical form: a) 5 10 b) 3 65 2 c) 3 12 4 3 d) 6 24 5 54 26. Be able to define the trigonometric ratios and use them to solve problems involving right angled triangles. Solve for the indicated variable: a) b) c) d)
7 θ x 42 8.9 29º 17 33 63º 35º x 52º x e) A tree casts a shadow 11.3 m long when the angle of elevation of the sun is 68º. Find the height of the tree. Linear Programming 27. Be able to plot points that satisfy a Page 334-335 condition #6 a, d, f 28. Write constraints as inequalities and graph #7, 8 the inequalities #9 29. Find a feasible region #10a, c 30. Use profit lines to find maximum profit #11
The Geometry of Packaging 31. Be able to use formulas and apply Page 303 - 304 relationships for area, perimeter of 2 #4, 5 dimensional shapes. #7, 8 32. Be able to use formulas and apply relationships for surface area and volume of prisms, pyramids, cylinders, and cones. 33. Find the Economy Rate of several shapes and compare them.
Data Management
34. Masses in kilograms of a sample of suitcases at an airport are listed in the following table.
a. Using technology construct a histogram (bin = 4) of the data, and describe its shape. b. Determine the mean and standard deviation. Why might this information be useful to the airport?
35. The mean salary of all employees at the Brown Corporation is $30,000.00. Make up an example to show how this statistic may be misleading.
36. Last night when temperature dropped to -2 Celsius and it started to snow. After 3 hours there were 9 cm of snow on the ground. Give the dependent variable in this relationship. [a] amount of snow [b] 9 cm [c] 3 hours [d] time
37. Bill is asked to find the average of the following set of numbers: {18, 25, 32, 44, 51}. He claims the average is 34. Which of the following measures of central tendency did he use? [a] mean [b] median [c] mode [d] standard deviation
38. A truck is carrying books packaged in boxes. The number of books in each box is recorded as shown. a. Use technology to construct a box and whisker plot to represent the data and sketch it on paper with correct labeling. b. What do you think is a "typical" number of books in a box? Justify your answer. c. Are their outliers? Explain.
39. The following data shows the average amount of tar (in mg) and the average amount of nicotine (in mg) per cigarette in 12 different brands, as found by the FTC.
a. Draw a scatterplot on the grid provided above. b. Draw the median-median line of best fit. c. Predict the amount of tar in a cigarette with 0.7 mg of nicotine. d. Predict the amount of nicotine in a cigarette with 19 mg of tar.
40. An Intel group employs 50,000 people, with the average term of employment being 18 years with a standard deviation of 5 years. Assuming a normal distribution. a. Draw and label the curve b. How many employees will work longer than 23 years?