Download Questions # 26-30

AIMS PRACTICE QUESTION #26: Absolute value functions
5. What are the values of x in the equation shown?
1. What are the values of x in the equation shown?
4x + 6 + 8 = 3
x =3
a.
b.
c.
d.
−11 1
,
4 4
11 −1
b.
,
4 4
−11 −1
c.
,
4 4
d. ∅
a.
0,3
3,6
0,6
-3,3
2. What are the values of x in the equation shown?
x−2 =3
a.
b.
c.
d.
1,5
-1,5
1,-5
-1,-5
6. What are the values of x in the equation shown?
3x + 2 = 4 x + 5
a.
b.
c.
d.
−3, −1
1, −3
−1
−3
3. What are the values of x in the equation shown?
4 x +1 = 8
a.
b.
c.
d.
7. A machine fills Quaker Oatmeal containers with 32 ounces of oatmeal. After the
containers are filled, another machine weighs them. If the container's weight
differs from the desired 32 ounce weight by more than 0.5 ounces, the container
is rejected. Write an equation that can be used to find the heaviest and lightest
acceptable weights for the Quaker Oatmeal container. Solve the equation.
0,1
-3,2
1,2
-3,1
4. What are the values of x in the equation shown?
2 5 x − 3 = 24
−9
,3
5
9
b.
, −3
5
12
c. 3,
5
3
'− 3
d.
4
a.
answers:
1. d
2.b
3.d
4.a
5.d
6. c
Name_______________
PRACTICE AIMS QUESTION #27
Patterns
7. Solution: Let x = the weight of the container.
Figure
Case 1:
Case 2:
Answer: x = 31.5 ounces (lightest)
x = 32.5 ounces (heaviest)
Number of triangles
1
2
3
6
Perimeter
3
4
7
12
1. Based on the pattern shown, which conjecture is valid?
a) A figure with 15 triangles has a perimeter of 31
b) A figure with 12 triangles has a perimeter of 23
c) A figure with 15 triangles has a perimeter of 30
d) A figure with 12 triangles has a perimeter of 25
Figure
When setting up a word problem involving absolute value, remember that
absolute value can represent "distance" from a given point.
The difference between the answer (x) and the desired point (32) is placed
under the absolute value symbol. This absolute value is then set equal to the
desired "distance" (0.5).
Number of squares
1
2
3
6
Perimeter
4
6
8
10
2. Based on the pattern shown, which conjecture is valid?
a) A figure with 4 squares has a perimeter of 8
b) A figure with 9 squares has a perimeter of 12
c) A figure with 4 squares has a perimeter of 7
d) A figure with 9 squares has a perimeter of 18
3.
a)
b)
c)
d)
Find the missing numbers
64,192, 576
64, 128, 256
96, 192, 256
96, 192, 576
1
2
3
4
5
2
4
8
16
32
6
7
8
4. Find the pattern ¼, 1/9, 1/16, 1/25, 1/36
a) add 5 then 7, then 9, then 11 to the denominator
b) There is no pattern to this problem
c) I have no idea how to find the pattern
d) the pattern is 1/x squared where x begins with 2, then 3, then 4, etc.
Name_______________
PRACTICE AIMS QUESTION #28
Dilations
5. Find the pattern for the given set of ordered pairs.
(-2,2) (-1,4) (0,6) (1,8)
a) switch the x and y coordinate and subtract the numbers
b) add 4 to the x coordinate and change the sign
c) double the y coordinate and add 1 to get the x coordinate
d) there is no pattern for the ordered pairs
Answers: 1.a
2. b
3. b
4. d
5.c
1. What are the coordinates of the image of point B under a dilation with center at the origin of
scale factor 1/2?
a) (-3/2,-3/2) b) (-3/2, -3) c) (-6,-6)
d) (-3,-3/2)
2. What are the coordinates of the image of point B under a dilation with center at the origin of
scale factor 3?
a) (-1,-1)
b) (-1, -3)
c) (-9,-3)
d) (-9,-9)
3. The graph at the left is an example of a which
transformation?
a) dilation
b) translation
c) reflection in origin
d) none
Name_______________
PRACTICE AIMS QUESTION #29
Simplifying Radical Expressions
1. What is the value of the expression?
64x12 y 8
a) 8x 6 y 4
b) 8x12 y 8
c) 32x 6 y 4
d) 32x12 y 8
2. What is the value of the expression?
1024x14 y 20
4. Under a dilation of scale factor 4 with the center at the origin, what will be the coordinates of the
image of point B?
a) (8,3)
b) (8,12)
c) (2,12)
d) (6,7)
5. Under a dilation of scale factor 1/3 with the center at the origin, what will be the coordinates of
the image of point B?
a) (2/3,1)
b) (2/3, 3)
c) (2,1)
d) (2,3)
6. Give the coordinates of point B after a dilation of scale factor 3 with the center at the origin, and
a reflection across the y-axis.
a) (6,9)
b) (-6,9)
c) (6,-9)
d) (-6,-9)
7. Give the coordinates of point B after a dilation of scale factor 3 with the center at the origin, and
a reflection across the x-axis.
a) (6,9)
b) (-6,9)
c) (6,-9)
d) (-6,-9)
a) 2 x14 y 20 512
b) 32x 7 y10
c) 512x 7 y10
d) 32 x 7 y10
3. What is the value of the expression?
20x 9 y10
b) 2 x 4 y 5 5 x
a) 2 5x 9 y10
c) 5 x 2 x 4 y 5
d) 5 2x9 y10
4. What is the value of the expression?
3
a) 8x 6 y 9
64x 6 y 9
b) 4x 3 y 4 y
c) 8 3 x 6 y 9
d) 4x 2 y 3
5. What is the value of the expression?
2 3 216x13 y 24
a) 6x 4 y 8 3 x
b) 12x 4 y 8
c) 12x 4 y 8 3 x
Answers: 1.a
Answers: 1.a 2.d
3. d
4. b
5. a
6. b
7. c
2. b
d) 2 x 4 y 8 3 6 x
3. b
4. d
5.c
Name______________
AIMS Review Problems similar to #30 in packet
Recall: When solving radicals get the radical by itself, then square both sides!
1. What is the solution to the equation
shown?
6 = 4 x + 20
a.
b.
c.
d.
3
-4
4
14
2. Solve the following equation for a.
2 a − 6 = 18
a.
b.
c.
d.
87
262
75
68
3. Find the solution for the following
equation.
d. 3
DOK Problems:
6. When solving the equation
−4 = x + 6 explain why the correct
answer is “no solution.”
a. When you square both sides and
subtract 6 the resulting statement is
false.
b. After squaring both sides the answer
becomes positive.
c. When squaring both sides of an
equation, you introduce an
extraneous solution.
d. You cannot take the square root of a
negative number.
7. The owner of a health foods store
determines that the demand equation for
selling a nutritional supplement is
p = 18 −
2 x − 2 + 7 = 11
a.
b.
c.
d.
0.5
11
-9
9
4. What is the solution to the equation
below?
−4 + x + 6 = 4
a.
b.
c.
d.
58
60
-6
10
where p is the price in dollars and x is the
number of bottles demanded per week.
Solve the equation for x and then determine
how many bottles of the supplement were
sold if the company made $100. Then
determine if the demand for this supplement
is high or low.
a.
b.
5. Solve the following equation for y.
c.
6 = 3 3y − 8
a. 12
b. 4
c. 17/3
Answers: c. a. d. a. b. d. d.
1
x−4
2
d.
(−2 p + 36) 2 = x − 4, x = 100,
demand is low.
4 p 2 + 1300 = x, x = 4130,
demand is fairly high.
4 p 2 − 144 p + 1300 = x, x = −12, 700,
demand is low.
4 p 2 − 144 p + 1300 = x, x = 26,900,
demand is high.