Download Mastery Grade 10 Sept 11 A

Mastery Grade 10 Sept 11 A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
1. Select the table of values for the equation 3x + 2y = -2
a.
b.
c.
d.
2. Solve 2x + 3y = -4 for x
a.
b.
c.
d.
3. Simplify
a.
c.
d.
b.
____
4. Simplify
____
a.
b.
c.
d. 2
5. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
____
____
a. add 4 to both sides b. add 2 to both sides c. add 3x to both
sides
d. divide both sides
by 3
a.
d.
6.
b.
7. The graph of x - y = 1 is
c.
a. Line 2
b. Line 5
c. Line 1
d. Line 4
e. Line 3
____
8. Simplify
a. 4x
b.
c.
d.
____ 9. Express 23.1 as a percentage.
a. 2310%
b. 231%
c. 0.0231%
d. 0.231%
____ 10. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
a. divide both sides b. add x to both sides c. add 2 to both sides d. subtract 2x from
by 2
both sides
____ 11. A line has equation 3x + 2y = 5. Its y-intercept is
a.
b.
____ 12. Simplify 3x + 2y -1 -2x -y -3
a. x + y - 2
b. x +y - 4
c.
d.
c. x - 3y - 2
d. x + 3y - 4
____ 13. Which of the following diagrams illustrates that
a.
____ 14. The graph of y = -2 is
b.
?
c.
d.
a. Line 4
b. Line 2
c. Line 1
____ 15. 40% of _____ is 80.
a. 50
b. 200
c. 32
____ 16. A line has equation 3x - 2y = 5. Its slope is
a.
b.
d. Line 5
e. Line 3
d. 0.5
c.
d.
____ 17. The graph of x + 6y = 6 is
a. Line 4
b. Line 3
c. Line 2
____ 18. If x = -4, then evaluate
a. 4
b. -20
____ 19. If x = -3, then evaluate
a. -15
b. 15
____ 20. Solve 3x - 2y = 4 for x
a.
b.
____ 21. Which of the following diagrams illustrates that
d. Line 5
e. Line 1
c. 12
d. -12
c. 39
d. 21
c.
d.
?
a.
b.
c.
d.
____ 22. A line has equation 2x - 3y = 5. Its x-intercept is
a.
b.
c.
d.
____ 23. The graph of y=-1 is
a. Line 3
b. Line 4
c. Line 5
____ 24. The number marked on the number line is
a.
b. -2.5
d. Line 2
c. -1.5
e. Line 1
d.
____ 25. The graph of 2x - y = -1 is
a. Line 1
b. Line 3
c. Line 2
d. Line 5
e. Line 4
____ 26. The following diagram illustrates an equation. Which of the following is a reasonable first step in order to
solve the equation?
a. add 2x to both
sides
____ 27. Simplify
a.
b. subtract 2x from
both sides
c. divide both sides
by -2
d. add x to both sides
b.
c.
d.
____ 28. The graph of y = - x + 3 is
a. Line 4
b. Line 2
c. Line 3
d. Line 1
e. Line 5
____ 29.
a.
b.
c.
d.
a.
b.
c.
d.
____ 30.
Mastery Grade 10 Sept 11 A
Answer Section
MULTIPLE CHOICE
1. ANS: D
If x = -2 and y=2 then
3x + 2y
= 3(-2) + 2(2)
= -6 + 4
= -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=-7 then
3x + 2y
= 3(4) + 2(-7)
= 12 - 14
= -2
is correct.
PTS: 1
2. ANS: A
Add -3y to both sides to isolate 2x
Divide both sides by 2 to isolate x
Divide each term by 2
PTS: 1
3. ANS: A
The illustration of
If we combine what we can, we get
PTS: 1
4. ANS: D
is as follows:
or just
.
means
If we were simply dividing 6 by 3, we would ask how many groups of 3 are there in
6, or what multiplied by 3 is 6? In this case, we ask "what multiplied by
is
?" or " how many groups
of
are there in
?". We can easily see that
is 2 groups of
from the drawing below. This means
that
. Another way to say this is that
.
Another way to approach this question is to express any powers as multiplication and remember that
multiplication and division are inverse operations (i.e., they undo each other). So ...
which is equivalent to
is the same as
or just 2.
PTS: 1
5. ANS: B
The basic strategy for solving an equation is to get the x's on one side and the units on the other side by
adding (or subtracting) the same thing to/from both sides. You would normally decide on the side of the
equation the x's should be on first. It is easier to try to make sure the x's are positive as well, so we usually try
to eliminate x's from the side of the equation that has the smallest number of x's (i.e., if both are positive, big
the smaller one to eliminate, if one is negative and one is positive, eliminate the negative one, and if both are
negative, eliminate the one that is the 'most' negative.)
In this case, there is a +3x on the left and a +x on the right, so we choose to eliminate the +x by adding -x to
both sides.
While this is probably the best strategy, it would also be acceptable to eliminate the 3x from the left side by
adding -3x to both sides, or adding 2 to both sides to eliminate the -2 on the left, OR add -4 to both sides to
eliminate the +4 on the right. The only correct answer listed is c. add 2 to both sides.
So the algebraic solution should look like one of the following:
PTS: 1
6. ANS: B
To multiply fractions, just multiply the numerators and denominators to get
.
PTS: 1
7. ANS: C
We know the x-intercept is 1 (if we let y=0, we get x=1) and the y-intercept is -1 (if we let x=0, we get y=-1),
so it must be Line 1
We also could have solved for y and used slope and y-intercept to identify the line.
PTS: 1
8. ANS: D
We can think of
as
may have not looked at diagrams for
Two of the positive
. These are 'like terms', so they can be 'combined' to get
yet - but it is possible to illustrate this question as follows:
solids eliminate the two negative
solids. The answer is
. You
.
PTS: 1
9. ANS: A
23.1 means
or
. Therefore, 23.1 is 2310%. Another way to do this is to use the fact that 100% is the
same as the number 1. We know that if we multiply a number by 1 we don't change its value, so 23.1 = 23.1
100%. Multiplying the 23.1 by the 100 we get 2310% (the decimal place moves 2 units to the right when
you multiply by 100).
PTS: 1
10. ANS: B
The basic strategy for solving an equation is to get the x's on one side and the units on the other side by
adding (or subtracting) the same thing to/from both sides. You would normally decide on the side of the
equation the x's should be on first. It is easier to try to make sure the x's are positive as well, so we usually try
to eliminate x's from the side of the equation that has the smallest number of x's (i.e., if both are positive, big
the smaller one to eliminate, if one is negative and one is positive, eliminate the negative one, and if both are
negative, eliminate the one that is the 'most' negative.)
In this case, there is a -x on the left and a +x on the right, so we choose to eliminate the -x by adding +x to
both sides.
While this is probably the best strategy, it would also be acceptable to eliminate the +x from the right side by
adding -x to both sides, or adding -2 to both sides to eliminate the +2 on the left, OR add +3 to both sides to
eliminate the -3 on the right.
So the algebraic solution should look like one of the following:
PTS: 1
11. ANS: A
3x + 2y = 5
2y = 5 - 3x
Isolate y by subtracting 3x from both sides.
Divide both sides by 3
Simplify
or
Comparing
with y = mx + b, we see that the y-intercept,b, is .
PTS: 1
12. ANS: B
The illustration of 3x + 2y -1 -2x -y -3 is below. Note that x and y tiles are similar ... just different lengths:
or just x + y - 4.
. Simplifying, we get
PTS: 1
13. ANS: C
The corrct answer is
It has 4 out of 6 or
.
shaded on the left
It also has 3 out of 6 or
shaded on the top.
The overlapping area is 12 squares out of the 36 or
.
This diagram shows that
.
PTS: 1
14. ANS: A
We know the y-coordinate of every point on the line is -2, so it must be line 4.
PTS: 1
15. ANS: B
If 40% of the unknown number is 80, then 10% of the number would be 20 (divide both parts by 4). This
means that 100% of the number is 200 (multiply both parts by 10), and 100% of the number IS the number!
The number is 200.
This question is equivalent to 40 out of 100 is the same as 80 out of _____. Once you understand this
meaning, it is easy to see that the answer is 200.
PTS: 1
16. ANS: C
3x - 2y = 5
3x - 5 = 2y
Isolate y by adding 2y to both sides and subtracting 5 from both sides.
Divide both sides by 2
Simplify
or
Comparing
with y = mx + b, we see that the slope, m, is .
PTS: 1
17. ANS: C
We know the x-intercept is 6 (if we let y=0, we get x=6) and the y-intercept is 1 (if we let x=0, we get y=1),
so it must be Line 2.
We also could have solved for y and used slope and y-intercept to identify the line.
PTS: 1
18. ANS: B
if x = -4 then
=
= -4 - (16)
= -4 - 16
= -20
First, replace x with -4 in brackets. The
brackets group the negative sign with the 4.
Next, we must square -4 to get 16. Finally
subtract to get -20.
PTS: 1
19. ANS: D
if x = -3 then
=
= 2(9) + 3
= 18 + 3
First, replace x with -3 in brackets. The
brackets group the negative sign with the 3.
Next, we must square -3 to get 9 and change
subtract -3 to add +3. Multiply next and
then add to get 21
= 21
PTS: 1
20. ANS: B
Add 2y to both sides to isolate 3x
Divide both sides by 3 to isolate x
This cannot be simplified (3 would have to divide into
both terms)
PTS: 1
21. ANS: C
The corrct answer is
It has 1 out of 6 or
.
shaded on the left
It also has 2 out of 6 or
shaded on the top.
The overlapping area is 2 squares out of the 36 or
This diagram shows that
PTS: 1
22. ANS: D
2x - 3y = 5
2x - 3(0) = 5
2x = 5
.
.
To find the x-intercept, let y=0
Simplify
Therefore the x-intercept is .
PTS: 1
23. ANS: D
We know that the y-coordinate of every point on the line is -1, so it must be line 2.
PTS: 1
24. ANS: B
If -3 was marked on the number line we could see that the number marked is halfway between -2 and -3, so it
is -2.5. If we look elsewhere on the number line we can see that
is
spaces is 0.5 units. The marked number
spaces to the left of -2, so it is -2.5.
PTS: 1
25. ANS: A
We know the x-intercept is
(if we let y=0, we get x=
) and the y-intercept is 1 (if we let x=0, we get
y=1), so it must be Line 1.
We also could have solved for y and used slope and y-intercept to identify the line.
PTS: 1
26. ANS: A
The basic strategy for solving an equation is to get the x's on one side and the units on the other side by
adding (or subtracting) the same thing to/from both sides. You would normally decide on the side of the
equation the x's should be on first. It is easier to try to make sure the x's are positive as well, so we usually try
to eliminate x's from the side of the equation that has the smallest number of x's (i.e., if both are positive, big
the smaller one to eliminate, if one is negative and one is positive, eliminate the negative one, and if both are
negative, eliminate the one that is the 'most' negative.)
In this case, there is a -2x on the left and a +x on the right, so we choose to eliminate the -2x by adding +2x to
both sides.
While this is probably the best strategy, it would also be acceptable to eliminate the +x from the right side by
adding -x to both sides, or adding -1 to both sides to eliminate the +1 on the left, OR add +3 to both sides to
eliminate the -3 on the right.
So the algebraic solution should look like one of the following:
PTS: 1
27. ANS: B
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
so
could be written as
. Rearranging, we get
which is
.
PTS: 1
28. ANS: E
We know the slope is - and the y-intercept is 3, so it must be line 5 (that is the only line with y-intercept 3).
You can check the equation for two points:
If x = 0, then y= - (0) + 3
If x = 2 then y = - (2) + 3
=0+3
= -3 + 3
=3
=0
The points at (0,3) and (2,0) are on the line, so it must be line 5.
PTS: 1
29. ANS: C
=
=
To subtract fractions, get a common denominator (12) by multiplying
the numerator and denominator of the first fraction by 3 and then the
numerator and denominator of the second fraction by 2.
Now that we have a common denominator, subtract the numerators
and keep the same base.
PTS: 1
30. ANS: A
=
=
PTS: 1
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.