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Practice Examination – MPM 1D1 This is a practice exam. It does not cover all the material in this course and should not be the only review that you do in preparation for your final exam. Your exam may contain questions that do not appear on this practice exam. Ideally, this should be completed after you have completed the final exam review so that you can get a feel for how long your exam will be. Answer all questions in the space provided. All work must be shown. Marks will be deducted for poor form. 1. Simplify. a) (-3)4 = _____________ b) -24 = _____________ 1,1 c) (y3)(y2)(y) = _____________ d) e) f) = _____________ 1,1 2,2 2. Expand and simplify. a) (2x2 – 3x + 1) + (4x2 + 6 – 3x) b) 3(x + 5) – 2(3x + 1) 2,2 3. Solve each equation. Show all steps. a) 2x - 4 = 8 b) 2x + 6 = 5x - 6 2,2 c) 3(x – 3) = 5 – 2(8 – x) 3, 4 d) 4. Graph the following lines using slope and y-intercept or x-y-intercepts. a) b) 2,2 5. Write the equation of the line that a) has a slope of 5 and y-intercept of 2 ______________________________ 2 b) passes through the points (5,4) and (7,3) 3 , and has a y-intercept of 1 ______________________________ c) is perpendicular to the line 2 6. Without making a graph, determine in the data in the table below is linear or non-linear. Give a reason for your answer. 2 x 0 y 8 Check one: Linear 2 4 Reason: 4 0 6 -4 8 -8 10 -12 or Non-linear 7. Find the value of each variable. Give justification for your answer. 28° 3 y z 54° x > Angle x = ______ > y = ______ z = ______ Justification 8. The manager of a movie theatre gathers data regarding the number of movie tickets sold and the number of buckets of popcorn sold. Here data is in the table below. Movie Tickets 54 63 88 125 143 160 171 189 201 225 Buckets of Popcorn 33 42 53 75 81 90 101 115 126 150 a) The independent variable is __________________________ 1 The dependent variable is __________________________ b) Create a scatter plot of number of movie tickets sold versus number of buckets of popcorn sold. Draw the line of best fit. 4 c) Classify the type of correlation: The correlation is strong / weak (Circle one) 2 The correlation is positive / negative (Circle one) d) Use the line of best fit to estimate the number of buckets of popcorn sold when 100 movie tickets were sold (answer here) 1 9. Find the area of the given shape. 3 _____________ 10. Thomas performs an experiment involving the mass of pennies in a cup. He adds pennies to the cup, and measures the mass after adding each penny. He created a scatter plot and then drew in a line of best fit. # Pennies 0 1 2 3 4 5 6 7 8 9 10 Mass (grams) 80.0 82.7 85.5 88.1 90.6 93.4 96.2 99.0 101.6 104.5 107.0 0 a) Calculate the slope of the line of best fit. Interpret the meaning of the slope. 3 b) What is the y-intercept of the line of best fit? Interpret the meaning of the y-intercept. 2 c) Write the equation of the line of best fit. _____________________________ 1 d) Use your equation to determine the mass of 18 pennies. 1 e) Use your equation to determine the number of pennies used but the mass is 300 grams. 2 f) Suppose that Thomas measured the mass of quarters instead of pennies. Explain how this would affect the y-intercept and slope of the line of best fit. 2 11. The GSS Graduating Class wants to have an “end of the school year celebration.” They must decide between Wild Water Works or Canada’s Wonderland. The cost of each trip is described below: Wild Water Works: $200 to rent a bus, and $15 per student for admission to the park Canada’s Wonderland: $800 to rent a bus, and $12 per student for admission to the park. Let “n” stand for the number of students who go on the trip. Let “C” stand for the TOTAL cost of the trip. 2 a) Write an equation for the total cost of each possible trip: Wild Water Works _____________________________________ Canada’s Wonderland ___________________________________________ 2 b) Find the total cost of each option if 150 students go on the trip. Wild Water Works 4 Canada’s Wonderland c) Graph each equation and determine the point of intersection Point of Intersection = _____________ 1 d) What does the point of intersection represent in the context of this problem? 12. What is the largest area that can be built with 30 m of fencing in the corner of the school? SCHOOL FENCE a) Complete the following table showing possible widths, lengths, areas and perimeters. W (metres) 1 2 3 4 6 10 12 15 3 L (metres) Area 2 (m ) Perimeter (metres) b) Explain your final solution. 3 13. Calculate the surface area and volume of the shape shown. 3 Surface Area 3 Volume