MPM2D - Practice Mastery Test #5 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2. If, then x = a. -4 b. -3 c. 1 d. 2 3. Simplify 4. Select the table of values for the equation 3x - 2y = 2 5. Solve a. a=2 & b=-1 b. a=-4 & b=1 c. a=5 & b=-2 d. a=-3 & b=-1 6. d represents the number of dimes and q represents the number of quarters. Choose the equation corresponding to the statement "There are 3 fewer dimes than quarters". a. d - 3 = q b. q - d = 3 c. 10d = 25q + 3 d. d - q = 3 7. Given points A(6,3) and B(4,-1). The distance between A and B is approximately a. 4.5 b. 5 c. 7 d. 2.6 8. Given points A(6,3) and B(4,-1). The slope of AB is a. 2 b. -0.5 c. -2 d. 0.5 9. What does it appear that the missing number in the table should be? a. b. 4 c. 3 d. 10. is equal to... 11. is equal to... 12. Which curve best fits the data shown?
a. curve1 b. curve 2 c. curve 3 d. curve 4 13. Which curve best fits the data shown? a. curve1 b. curve 2 c. curve 3 d. curve 4 14. Which curve best fits the data shown? a. curve1 b. curve 2 c. curve 3 d. curve 4 15. Use a TI-83 to find the equation of the parabola of best fit and the value of R 2 (rounded to 2 decimal places) for the following data:
a. y = -0.31x 2 + 20.88x - 157.50 and R 2 = 0.94 b. y = -0.17x 2 + 13.52x - 62.73 and R 2 = 0.96 c. y = -0.43x 2 + 27.06x - 239.32 and R 2 = 0.99 d. y = -0.09x 2 + 8.01x + 21.14 and R 2 = 0.98 16. The first relationship is defined A second relationship is defined by its by the table of values: table of values: Which of these relationships is linear or quadratic? a. 1st is linear and the 2nd is quadratic b. 1st is linear and the 2nd is neither c. 1st is neither and the 2nd is quadratic 17. The first relationship is defined by the table of values: table of values: d. some other combination A second relationship is defined by its Which of these relationships is linear or quadratic? a. 1st is neither & the 2nd one is linear b. 1st is quadratic & the 2nd is linear c. 1st is quadratic & the 2nd is neither d. some other combination 18. A parabola has zeros at -7 and 1. The equation of the axis of symmetry is a. x = 3 b. x = -6 c. x = -3 d. x=-4 19. The graph of a parabola is shown below. Its minimum value is
a. -2 b. -1 c. 1 d. -3 20. The following diagram illustrates that a. c. b. d. 21. Expand and simplify 3x(x - 2) 22. Expand and simplify 2x(3x - 1) 23. Expand and simplify (2x - 1)(x + 3) 24. Factor completely: 25. Factor completely: 26. Factor completely: 27. Factor completely: 28. Factor completely:
29. Factor completely: 30. Solve for x: a. or b. or c. or d. or
MPM2D - Practice Mastery Test #5 Answer Section MULTIPLE CHOICE 1. ANS: D = = To add fractions, get a common denominator (15) by multiplying the numerator and denominator of the first fraction by 5 and then the numerator and denominator of the second fraction by 3. Now that we have a common denominator, add the numerators and keep the same base. 2. ANS: A Since this is multiple choice, the easiest thing to do might be to just check each of the answers (avoiding the fraction at first!). We discover that x=-4 satisfies the equation; i.e.,. Another way is to think... 6 divided by something is equal to -2. This means that x + 1 must be equal to -3, and x=-4. Of course, an algebraic solution is possible. In this case, having the variables in the denominator makes an algenraic solution quite a bit more difficult (and grade 9 students do NOT have to know how to do this algebraically). However, one possible algebraic solution is shown below. 3. ANS: A There is no written operation between the terms in brackets. This means it is multiplication. So, is the same as. We already know that is the same as and is the same as, so could be written as. Rearranging, we get which is.
You can also remember the laws of exponents - to multiply powers with the same base, (in this case, add the exponents and leave the base unchanged, so is the same as, which is.. and is equal to or, so the answer is or just 4. ANS: B If x = -2 and y=-4 then If x = 0 and y=-1 then If x = 4 and y=5 then 3x - 2y = 3(-2) - 2(-4) = -6 + 8 = 2 3x - 2y = 3(0) - 2(-1) = 0 + 2 = 2 3x - 2y = 3(4) - 2(5) = 12-10 = 2 Each of these points is on the line. is correct. 5. ANS: B While it is reasonable to solve the system algebraically, probably the easiest thing to do is to just check each pair of values in both equations. (-4) +3(1) 2(-4) + (1) = -4 + 3 = -8 + 1 = -1 = -7 We notice that a=-4 and b=1 satisfy both equations, so it is the solution. 6. ANS: B the number of dimes is three less than the number of quarters the number of dimes is the number of quarters - 3 d = q - 3 or q - d = 3 (subtract d and add 3 to both sides) 7. ANS: A distance = = = 8. ANS: A slope =
= = 2 9. ANS: A As you move through the table from left to right each y value is multiplied by 4 to get the next term, so it must be (the missing number comes right before 1, and multiplied by 4 is 1) 10. ANS: A To multiply powers with the same base, keep the base (in this case 4), and add the exponents, so the answer is 11. ANS: A To take the power of a power, keep the base (in this case 3), and multiply the exponents, so the answer is 12. ANS: B Curve 2 best fits the trends shown in the data 13. ANS: C Curve 3 best fits the trends shown in the data 14. ANS: D Curve 4 best fits the trends shown in the data 15. ANS: A Clear the screen by pressing CLEAR a couple of times. Make sure the diagnostics are on by pressing 2nd 0 to choose CATALOG. Use the down arrow button to scroll down until the arrow is pointing at DiagnosticOn and press ENTER. This should paste the command DiangnosticOn onto your home screen with the cursor flashing beside it. Press ENTER and it should say Done. Now to enter the data. Use the list editor on the TI-83 (push STAT and then choose 1. Edit. If lists 1 and 2 are not shown, press teh STAT button again and then 5. SetUpEditor. Clear lists 1 and 2 by moving the cursor up to L1, press CLEAR and then the down scroll button (arrow pointing down). If you push delete by accident, you will lose L1 (you can fix this by using 5.SetUpEditor).
Enter the lengths in L1 by pressing ENTER after each one. Enter the heights in L2. Return to the home screen by pressing 2nd MODE (to QUIT). Clear your screen. Press STAT, use the right arrow button to select CALC, press 5:QuadReg to choose line of best fit. Your screen should now say QuadReg with the cursor flashing to the right. Entre L1 by pressing 2nd 1. Push the comma button (,) and then enter L2 by pressing 2nd 2. This tells the calculator where to find the data you entered. Press the comma button again and then VARS and the right arrow button to select Y-VARS. Select 1:Function by pressing ENTER and then ENTER again to select Y1. This tells the calculator where to store the equation of the line. At this point, you should have: QuadReg L1, L2, Y1 at the top of your screen with the cursor flashing in the next line. Press ENTER. The following should appear: y=ax+b a=-.3125 b=20.875 c=-157.5 =.9352941176 The (rounded) equation is y = -0.31x 2 + 20.88x - 157.50 and R 2 = 0.94. 16. ANS: D In the first table, the 1st differences (in C values) are not all the same (2,4,2,2) so it is not linear, and the 2nd differences are (2,-2,0) so it is not quadratic. In the second table, the differences are -8, -4, -2,-1., so it is not linear and the 2nd differences are 4,2,1, so it is not quadratic. 17. ANS: B In the first table, the 1st differences are -7,-3,1, and 5, and the 2nd differences are 4,4, and 4, so it is quadratic. In the second table, the differences are all -2, and the value of n also increases by a constant value, so it is linear. 18. ANS: C The axis will be mid-way between -7 and 1. 19. ANS: D The vertex is at (-1,-3). The minimum value of a function is the minimum value for y - in this case -3. 20. ANS: A The two expressions that are multiplied are 2x-1 and 3x+4, and the product is simplifies to which 21. ANS: B
We can think of this multiplication using tiles... but it is not necessary to draw the tiles every time. The following diagram illustrates the multiplication (as long as you understand that 3x multiplied by x is 3x.) or... 22. ANS: C We can think of this multiplication using tiles... but it is not necessary to draw the tiles every time. The following diagram illustrates the multiplication (as long as you understand that 3x multiplied by x is 3x.) or... 23. ANS: B We can think of this multiplication using tiles... but it is not necessary to draw the tiles every time. The following diagram illustrates the multiplication (as long as you understand that 2x multiplied by x is 2x.) or... 24. ANS: C The expression has a common factor of x. x must multiply by 2x and by -1 to give. 25. ANS: D Arrange the tiles into a rectangle: So 26. ANS: A Arrange the tiles into a rectangle:
So 27. ANS: D Arrange the tiles into a rectangle: So 28. ANS: D Arrange the tiles into a rectangle: So 29. ANS: A Arrange the tiles into a rectangle:
So 30. ANS: B If then or, so or