MPM2D - Practice Mastery Test #5
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
a.
____
2. If
b.
c.
d.
b. -3
c. 1
d. 2
, then x =
a. -4
____
3. Simplify
____
a.
b.
c.
4. Select the table of values for the equation 3x - 2y = 2
a.
b.
c.
____
5. Solve
____
6.
____
7.
____
8.
____
9.
____ 11.
d.
a. a=2 & b=-1
b. a=-4 & b=1
c. a=5 & b=-2
d. a=-3 & b=-1
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
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
Given points A(6,3) and B(4,-1). The slope of AB is
a. 2
b. -0.5
c. -2
d. 0.5
What does it appear that the missing number in the table should be?
a.
____ 10.
d.
a.
is equal to...
b. –4
c. –3
d.
b.
c.
d.
c.
d.
is equal to...
a.
b.
____ 12. Which curve best fits the data shown?
a. curve1
b. curve 2
____ 13. Which curve best fits the data shown?
c. curve 3
d. curve 4
a. curve1
b. curve 2
____ 14. Which curve best fits the data shown?
c. curve 3
d. curve 4
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 R2 (rounded to 2 decimal places)
for the following data:
a. y = -0.31x2 + 20.88x - 157.50 and R2 = 0.94
b. 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
____ 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?
b. 1st is linear and
c. 1st is neither and d. some other
a. 1st is linear and
the 2nd is
the 2nd is neither
the 2nd is
combination
quadratic
quadratic
____ 17. 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?
b. 1st is quadratic & c. 1st is quadratic & d. some other
a. 1st is neither &
the 2nd one is
the 2nd is linear
the 2nd is neither
combination
linear
____ 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
____ 20. The following diagram illustrates that
a.
b.
c. 1
d. -3
c.
d.
____ 21. Expand and simplify 3x(x - 2)
a.
b.
____ 22. Expand and simplify 2x(3x - 1)
b.
a.
____ 23. Expand and simplify (2x - 1)(x + 3)
a.
b.
____ 24. Factor completely:
a.
c.
d.
c.
d.
c.
d.
b.
c.
d.
____ 25. Factor completely:
a.
b.
c.
d.
____ 26. Factor completely:
a.
b.
c.
d.
____ 27. Factor completely:
a.
b.
c.
d.
____ 28. Factor completely:
a.
b.
c.
d.
____ 29. Factor completely:
a.
b.
____ 30. Solve for x:
a.
or
b.
c.
or
c.
d.
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.
=
PTS: 1
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.
PTS: 1
3. ANS: A
There is no written operation between the terms in brackets. This means it is multiplication. So,
is the same as
the same as
, so
. We already know that
could be written as
which is
.
is the same as
and
is
. Rearranging, we get
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
.
and
is the same as
is equal to
or
, so the answer is
, which is
or just
.
PTS: 1
4. ANS: B
If x = -2 and y=-4 then
3x - 2y
= 3(-2) - 2(-4)
= -6 + 8
=2
If x = 0 and y=-1 then
3x - 2y
= 3(0) - 2(-1)
=0+2
=2
Each of these points is on the line.
If x = 4 and y=5 then
3x - 2y
= 3(4) - 2(5)
= 12 - 10
=2
is correct.
PTS: 1
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.
PTS: 1
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)
PTS: 1
7. ANS: A
distance =
=
=
PTS: 1
8. ANS: A
slope =
=
=2
PTS: 1
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)
PTS: 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
PTS: 1
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
PTS: 1
12. ANS: B
Curve 2 best fits the trends shown in the data
PTS: 1
13. ANS: C
Curve 3 best fits the trends shown in the data
PTS: 1
14. ANS: D
Curve 4 best fits the trends shown in the data
PTS: 1
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 = -0.31x2 + 20.88x - 157.50 and R2 = 0.94.
PTS: 1
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.
PTS: 1
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.
PTS: 1
18. ANS: C
The axis will be mid-way between -7 and 1.
PTS: 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.
PTS: 1
20. ANS: A
The two expressions that are multiplied are 2x-1 and 3x+4, and the product is
simplifies to
PTS: 1
21. ANS: B
which
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...
PTS: 1
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...
PTS: 1
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...
PTS: 1
24. ANS: C
The expression has a common factor of x. x must multiply by 2x and by -1 to give
PTS: 1
25. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
26. ANS: A
Arrange the tiles into a rectangle:
.
So
PTS: 1
27. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
28. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
29. ANS: A
Arrange the tiles into a rectangle:
So
PTS: 1
30. ANS: B
If
PTS: 1
then
or
, so
or