First Math Review - Past Paper PDF

# EQAO Questions that stumped students in 9 Academic in 2015-2016 ## #6 - LINEAR RELATIONS - THINKING - Board 47% correct Answer - C Two golf courses offer student memberships. Information about the linear relationships between the total cost, C, in dollars, and the number of games played, n, at t...

# EQAO Questions that stumped students in 9 Academic in 2015-2016 ## #6 - LINEAR RELATIONS - THINKING - Board 47% correct Answer - C Two golf courses offer student memberships. Information about the linear relationships between the total cost, C, in dollars, and the number of games played, n, at these two golf courses is given below. ### First Golf Course | Total cost ($) | Number of games | |---|---| | 10 | 0 | | 20 | 1 | | 30 | 2 | | 40 | 3 | | 50 | 4 | ### Second Golf Course | Total cost, C ($) | Number of games, n | |---|---| | 51 | 3 | | 85 | 5 | | 153 | 9 | | 204 | 12 | Which of the following statements correctly describes the two relationships? a) They are both direct variations. b) The first is a direct variation, and the second is a partial variation with an initial value of $17. c) The first is a partial variation with an initial value of $10, and the second is a direct variation. d) The first is a partial variation with an initial value of $10, and the second is a partial variation with an initial value of $17. ## #16 - ANALYTIC GEOMETRY - Thinking - Board 45% correct - Answer - B Which graph shows a line that is perpendicular to the line y = x - 4? ## #9OR - NUMBER SENSE AND ALGEBRA - APPLICATION - AVERAGE SCORE 56% ### Floored Areas The diagram of the floor shown below has algebraic expressions for the lengths of its sides, in meters.  Determine an unsimplified expression for the total area of the floor, A, in m². A = Simplify your expression fully. Show your work. ## #15 - ANalytic Geometry Students had trouble determining the rate from tables & graphs, all students picked C but answer was d. Information about four different linear relationships between C and n is shown below. **Relationship 1:** (0,50) and (8,90) **Relationship 2:** | n | C | |---|---| | 0 | 50 | | 8 | 90 | | 16 | 130 | **Relationship 3:** (10,30) and (12,35) **Relationship 4:** | n | C | |---|---| | 10 | 30 | | 12 | 35 | | 14 | 40 | How many of the linear relationships have a rate of change of 5? a) 4 b) 3 c) 2 d) 1 ## #1MC - NUMBER SENSE - ANswer A - Board average 57% A ball is dropped from a height of 25 m. The ball's height, H, in meters, after n bounces is represented by the equation below. H = 25($\frac{1}{2}$)^n What is the height of the ball after 4 bounces? a) 25/16 m b) 25/8 m c) 25/4 m d) 25/2 m ## Exam Review 1) 9² + x² = 14² Find x 2) For the polynomial $\frac{5}{7}$x²yz + $\frac{2}{5}$x²yz² + 1 a) special name b) coefficient of and term c) degree d) constant 3) Expand 12x⁴y² (2xy³ - 3x²y + 6) 4) Solve 7x - 9 = 2x - 5 - 5x 5) Evaluate 3⁷ / 3⁴ . 3² 6) Factor 25a²b²c⁴ - 10a²b³c³ 7) Simplify (y⁵) / (y⁴)² 8) A father is now three times as old as his son. Eight years ago the father's age was five times that of his son. Find their present ages. 9) Solve for x : $\frac{3}{2}$ = x - $\frac{7}{6}$ 10) Evaluate if x = 0, y = 1 3(x - 2)² + y - 4(x + 3) 11) a) Find perimeter b) Find area 12) y = 30 3y = 30 13) Simplify (4x²y³)⁶ 14) Find the area of a circle if radius is 7cm. (Use 3.14 for π) A = πr² 15) Factor 21a²b⁶ + 49a⁴b⁶ - 6² 16) Find the mean, median, mode & range. 1, 13, 7, 2, 9 , 4, 1 15, 2, 4, 7, 9, 1, 3 17) Simplify 5 - √72 + 4√288 - 3√7 18) (√2)(-8√7)(9√2) ## MORE Exam Review 1. Two numbers differ by seven, if their sum is 65, what are the numbers? Let one # be x, the other # be x+7 (larger) 2. a) Find y² 3. a) Perimeter = b) Area = 4) Solve 4(j + 9) = 6(j + 2) 5) Find the equation of a line with slope of 3/2 and a y intercept of 3. (Final answer in standard form). y = mx + b 6) Find the x and y intercepts for the line 3x + 2y - 4 = 0 7) Simplify 3(2x - 9) - (5x - 1) 8) Simplify √148 - 4√32 + √12 9) Simplify $\frac{255}{65410}$ x $\frac{358}{12510}$ 10) Find slope if 2 points on a line are (5,-4) and (-3,-2) m = (y2 - y1) / (x2 - x1) 11. Simplify y⁷y⁴ y⁶y³y⁰/y¹⁵ 12. Simplify 81x⁵y⁴/36x⁴y⁻¹ 13) Factor 36j⁴k⁷l - 54j⁵k² 14) Solve $\frac{3}{7}$x - 2 = $\frac{4}{7}$ 15) For the polynomial x²y¹⁷ + x⁴y² - 1 a) degree b) constant c) coefficient of first term d) The equation of a horizontal line going through (5,-3)? 16) The point (7,2) is in the quadrant 17) In the graph below when is the person running the fastest? a) b) When has he stopped? c) 18) Make an equation if it costs $30 to rent a bike and $5 for every hour you have it. y = mx + b 19) Make the line on the graph. | x | y | |---|---| | 0 | 30 | | 1 | 35 | | 3 | 45 | 20) How would the line change if it costs only $3 for every hour the person has the bike? y = mx + b 21) Would these lines ever intersect? Explain. 22) Six less than five times a number is twenty-four. Find the number Let x be the number. 5x - 6 = 24 23) Julie has ten more dimes than nickels in her pocket. She has a total of $2.05. How many of each coin does she have? # of dimes x+10 # of nickels x Value of 10(x+10) + 5x ## Solving Linear Inequalities in Two Variables by Graphing Sketch the graph of each linear inequality 1) 3x - 5y ≤ 30 2) 5x + 4y > 12 3) -8x - 7y > -21 4) -4x + y ≥ 0 5) -3y - 4x ≥ 15 6) 2y + 2 ≤ -5 Is (3,2) a solution for any of the questions above? ## 7 y ## 8 y Is (-5,4) a solution? Is (-5,2) a solution? Hilaria works two part time jobs in order to earn enough money to meet her obligations of at least $240 a week. Her job in food service pays $10 an hour and her tutoring job on campus pays $15 an hour. How many hours does Hilaria need to work at each job to earn at least $240? Let x be the number of hours she works at the job in food service and let y be the number of hours she works tutoring. Write an inequality that would model this situation. Graph the inequality. Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Hilaria. Hugh works two part time jobs. One at a grocery store that pays $10 an hour and the other is babysitting for $13 hour. Between the two jobs, Hugh wants to earn at least $260 a week. How many hours does Hugh need to work at each job to earn at least $260? Let x be the number of hours he works at the grocery store and let y be the number of hours he works babysitting. Write an inequality that would model this situation. Graph the inequality. Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Hugh.