MHF Mastery Test 2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Simplify x - 2y - 1 -2x +y -3
a. / -x - y - 4 / b. / -3x - 3y - 4 / c. / -2xy - 4 / d. / -x - y - 2____ 2. Simplify 3x + 2y -1 -2x -y -3
a. / x + y - 2 / b. / x - 3y - 2 / c. / x +y - 4 / d. / x + 3y - 4____ 3. Which method would be easiest to solve the system:
a. / graphing / b. / substitution / c. / elimination____ 4. Which method would be easiest to solve the system:
a. / graphing / b. / substitution / c. / elimination____ 5. If then
a. / / c. /b. / / d. /
____ 6. Use a TI-83 to find the equation of the parabola of best fit and the value of R2 (rounded to 2 decimal places) for the following data:
a. / y = -0.31x2 + 20.88x - 157.50 and R2 = 0.94b. / y = -0.17x2 + 13.52x - 62.73 and R2 = 0.96
c. / y = -0.43x2 + 27.06x - 239.32 and R2 = 0.99
d. / y = -0.09x2 + 8.01x + 21.14 and R2 = 0.98
____ 7. The equation of the parabola shown is
a. / / b. / / c. / / d. /____ 8. A function is defined by . Its range is
a. / {y | y 0, y } / c. / {y | y -3, y }b. / {y | y > 0, y } / d. / {y | y -3, y }
____ 9. The equation of the image of after a translation of 3 units right is
a. / / b. / / c. / / d. /____ 10. If - 3x - 4 then its zero(s) are at
a. / 4 and –1 / b. / 4 and 1 / c. / –4 and 1 / d. / –4 and –1____ 11. The period of the function graphed below is closest to ...
a. / 4.5 / b. / 1.5 / c. / 7.5 / d. / 2____ 12. Complete the identity
a. / 2 / b. / / c. / / d. / + 1____ 13. The period of the function graphed below is closest to ...
a. / 7 / b. / 10.5 / c. / 8 / d. / 1.5____ 14.
The diagram shows the unit circle with points equally spaced around its circumference.Which point on the unit circle lies on the terminal arm of ? /
a. / O / b. / U / c. / C / d. / I
____ 15. The input/output diagram illustrates a number of transformations to y=cos(x).
The correct sequence of horizontal transformations applied to y=cos(x) is...
a. / a horizontal translation of 1 units right, followed by a hor. stretch of factorb. / a horizontal stretch of factor , followed by a hor. translation of 1 units right
c. / a horizontal translation of 1 units left, followed by a hor. stretch of factor 3
d. / a horizontal stretch of factor 3 , followed by a hor. translation of 1 units left
____ 16. The input/output diagram illustrates a number of transformations to y=sin(x).
The correct sequence of horizontal transformations applied to y=sin(x) is...
a. / a horizontal translation of 6 units right, followed by a hor. stretch of factor 3b. / a horizontal stretch of factor 3 , followed by a hor. translation of 6 units right
c. / a horizontal translation of 6 units left, followed by a hor. stretch of factor
d. / a horizontal stretch of factor , followed by a hor. translation of 6 units left
____ 17. If where 0 q 360, then
a. / q = -60 or q = -120 / c. / q = 120 or q = 240b. / q = 240 or q = 300 / d. / q = 150 or q = 210
____ 18. If then ?
a. / 0.0234375 / b. / 10 / c. / 19683 / d. / 0.01171875____ 19. What is the next number in the sequence ?
a. / 768 / b. / –432 / c. / –144 / d. / 153____ 20. Evaluate
a. / / b. / 25 / c. / / d. / -25____ 21. Evaluate
a. / 4 / b. / / c. / -4 / d. /____ 22. Simplify . Assume
a. / / b. / / c. / / d. /____ 23. After the graph of has been translated horizontally 3 units to the left, and translated vertically 1 units up, the resulting equation of the function would be...
a. / / b. / / c. / / d. /____ 24. The tables below shows the concentration of CO2 in the air in a room over time. The best estimate of the average rate of change of the CO2 level over the first 3 seconds is...
a. / -12.6 / b. / -6.3 / c. / -2.1 / d. / 0 / e. / 8.4____ 25. The tables below shows the concentration of CO2 in the air in a room over time. The best estimate of the average rate of change of the CO2 level over the first 5 seconds is..
a. / -12.6 / b. / -6.3 / c. / -2.1 / d. / 0 / e. / 8.4____ 26. Given the graph of y=f(x) shown below. Tangent lines to the graph are also shown.
The average rate of change of y with respect to x between x=0 and x=6 is ...
a. / 2 / b. / 0.5 / c. / 3 / d. / 1.5____ 27. Given the graph of y=f(x) shown below. Tangent lines to the graph are also shown.
Which of the following is most likely to be true?
a. / The instantaneous rate of change of f at x=-1 is 0b. / The instantaneous rate of change of f at x=1 is
c. / The instantaneous rate of change of f at x=6 is 3
d. / The instantaneous rate of change of f at x=4 is 1
____ 28. Given the graph of y=f(x) shown below. Tangent lines to the graph are also shown.
Which of the following is most likely to be true?
a. / The instantaneous rate of change of f at x=-1 is 1b. / The instantaneous rate of change of f at x=0 is
c. / The instantaneous rate of change of f at x=4 does not exist
d. / The instantaneous rate of change of f at x=6 is 3
____ 29. Given the graph of y=f(x) shown below. Tangent lines to the graph are also shown.
Which of the following is most likely to be true?
a. / The instantaneous rate of change at x=-1 is2b. / The average rate of change between x= -2 and x= 2 is 0
c. / The instantaneous rate of change at x=4 is 1
d. / The average rate of change between x= -1 and x=4 is 0.5
____ 30. A man kept track of his weight and daily food consumption every day for several months. He drew a graph with weight on the vertical axis and time on the horizontal axis. What units could be used for instantaneous rate of change on this graph?
a. / kg/day / c. / cal/dayb. / years/kg / d. / kg/cal
MHF Mastery Test 2
Answer Section
MULTIPLE CHOICE
1. A
The illustration of x - 2y - 1 -2x +y -3 is below. Note that x and y tiles are similar ... just different lengths: Simplifying, we get or -x - y - 4.
2. C
The illustration of 3x + 2y -1 -2x -y -3 is below. Note that x and y tiles are similar ... just different lengths: . Simplifying, we get or just x + y - 4.
3. B
Both equations are linear and one equation has a variable isolated already, so substitution would be easiest.
4. C
Both equations are linear and are already set up so that adding the equations would eliminate a variable, so elimination would be easiest.
5. D
The quadratic formula:
6. B
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=-.1704545455
b=13.52272727
c=-62.72727273
=.96003996
The (rounded) equation is y = -0.17x2 + 13.52x - 62.73 and R2 = 0.96.
7. D
The vertex is at (3,0), and it opens downward so the correct choice is .
8. A
In the real numbers, will always give an answer which is greater or equal to 0 (the square root symbol actually means the ‘principal’ or positive square root). It is also possible for to produce any real number greater or equal to 0 (e.g., if x = 3, = 0)
Therefore 0
So ... y 0
9. D
This is a vertical transformation, so it is applied after the base function (square root). To translate 3 units right, we want to add 3 to the ‘old’ values of x to get the ‘new’ values of x. This means that we must subtract 3 from the ‘new’ values of x to get the ‘old’ values of x, so we can draw an input/output diagram as follows. To get the equation, just apply the operations in sequence to x.
10. A
The easiest way to do this problem is probably to just sub in x=4 ,or x=–4 and then x=–1 or x=1 to find out which ones ‘work’.
OR
On the TI-83, type in the equation into the y= screen, and the look at the graph or table to see what its zeros are.
or factor the expression ...
so... (x - 4) (x + 1), and its zeros are at 4 and –1.
or ... complete the square or use the quadratic formula.
11. A
The graph crosses the y-axis very close to 3 and then it appears that one full cycle is graphed between here and (4.5,3), so the period is 4.5.
12. D
We know that for all q. If we separate the , we get
Another method is to substitute into the given expression to get:
13. A
The graph crosses the y-axis very close to 3.4 and then it appears that one full cycle is graphed between here and (7,3.4), so the period is 7.
14. A
Angles are measured starting at A(1,0) and rotating counter clockwise. There are 6 divisions in each quadrant, so each mark is past the last one. From A to G is , from A to M is , and from A around to S is . All other angles can be measured relative to those.
, so we have to move 2 marks past M, to get to O.
15. A
The input/output diagram for the function is shown below.
Horizontally, we have to work backwards from the base function, so the first operation that we have to undo is “subtract 1”, so the first horizontal transformation is a translation of 1 units right.
The second operation we have to undo, working away from the base function, is “multiply by 3”, so the second horizontal transformation is a horizontal stretch of factor