Algebra, Functions
and Patterns
AIMS Prep
The Jones family is planning to average 55
mph on their vacation. The travel time (t) is
determined by the distance (d) traveled
each day. What is the dependent variable?
a) distance
b) time
c) rate
d) none of the above
The Jones family is planning to average 55
mph on their vacation. The travel time (t) is
determined by the distance (d) traveled
each day. What is the dependent variable?
a) distance
b) time
c) rate
d) none of the above
A radioactive isotope has a half life of 1682 years and decays exponentially. Which of
the following graphs represent the amount (a) of isotope left after t years?
A radioactive isotope has a half life of 1682 years and decays exponentially. Which of
the following graphs represent the amount (a) of isotope left after t years?
What equation best represents the
graph shown?
a) y = (x - 3)2 - 2
b) y = -(x - 3)2 - 2
c) y = (x + 3)2 - 2
d) y = -(x + 3)2 - 2
What equation best represents the
graph shown?
a) y = (x - 3)2 - 2
b) y = -(x - 3)2 - 2
c) y = (x + 3)2 - 2
d) y = -(x + 3)2 - 2
Over which of the following intervals can
the following graph be considered a
function?
a) between a and c
b) between a and d
c) between d and e
d) between c and d
Over which of the following intervals can
the following graph be considered a
function?
a) between a and c
b) between a and d
c) between d and e
d) between c and d
Determine the slope and intercepts of
the equation 3x - 4y - 8 = 0
a) slope = 3/4 with intercepts (0,-2) and (8/3,0)
b) slope = -3/4 with intercepts (-2,0) and (0,8/3)
c) slope = 4/3 with intercepts (-2,0) and (8/3,0)
d) slope = -4/3 with intercepts (0,-2) and (0,8/3)
Determine the slope and intercepts of
the equation 3x - 4y - 8 = 0
a) slope = 3/4 with intercepts (0,-2) and (8/3,0)
b) slope = -3/4 with intercepts (-2,0) and (0,8/3)
c) slope = 4/3 with intercepts (-2,0) and (8/3,0)
d) slope = -4/3 with intercepts (0,-2) and (0,8/3)
Which of the following lines is
perpendicular to y = 5/9 x + 2 ?
a) y = -(5/9) x + 2
b) y = (5/9) x - 2
c) y = -(9/5) x
d) y = -(5/9) x
Which of the following lines is
perpendicular to y = 5/9 x + 2 ?
a) y = -(5/9) x + 2
b) y = (5/9) x - 2
c) y = -(9/5) x
d) y = -(5/9) x
Given triangle ABC, what is the
cosine of angle B?
a) 24/25
b) 7/25
c) 24/7
d) 25/7
Given triangle ABC, what is the
cosine of angle B?
a) 24/25
b) 7/25
c) 24/7
d) 25/7
Simplify:
[ 4(6 - 22 + 5) - 6(5 - 4)2 ] /2
a) 11
b) 8
c) 27
d) 15
Simplify:
[ 4(6 - 22 + 5) - 6(5 - 4)2 ] /2
a) 11
b) 8
c) 27
d) 15
If you simplify the expression
3(x - 2) - 6(x + 2) , the result is:
a) -3x - 18
b) -3x + 6
c) -3x
d) -21x
If you simplify the expression
3(x - 2) - 6(x + 2) , the result is:
a) -3x - 18
b) -3x + 6
c) -3x
d) -21x
Simplify
36𝑥 16 𝑦 4
a) 18x8y2
b) 6x4y2
c) 6x8y2
d) 18x4y2
Simplify
36𝑥 16 𝑦 4
a) 18x8y2
b) 6x4y2
c) 6x8y2
d) 18x4y2
Multiply (x3y2z)(x4yz3)
a) x12y2z3
b) x7y2z3
c) x7y3z4
d) x12y3z3
Multiply (x3y2z)(x4yz3)
a) x12y2z3
b) x7y2z3
c) x7y3z4
d) x12y3z3
−3 2
𝐵=
5 −6
2
3
𝐴=
−4 −1
The sum of A & B is:
a)
b)
c)
d)
−3 2
𝐵=
5 −6
2
3
𝐴=
−4 −1
The sum of A & B is:
a)
b)
c)
d)
2
3
𝐴=
−4 −1
−3 2
𝐵=
5 −6
Determine -3A.
a)
b)
c)
d)
2
𝐴=
−4
3
−1
−3 2
𝐵=
5 −6
Determine -3A.
a)
b)
c)
d)
Solve for 𝑙 in the equation 𝑃 = 2𝑙 + 2𝑤
a) 𝑙 = 𝑃 − 2𝑤
c) 𝑙 =
𝑃−2𝑤
2
b) 𝑙 =
𝑃
2
d) 𝑙 =
𝑃−2𝑙
2
− 2𝑤
Solve for 𝑙 in the equation 𝑃 = 2𝑙 + 2𝑤
a) 𝑙 = 𝑃 − 2𝑤
c) 𝑙 =
𝑃−2𝑤
2
b) 𝑙 =
𝑃
2
d) 𝑙 =
𝑃−2𝑙
2
− 2𝑤
Solve the equation
a)
9
7
b)
7
9
c)
7
−
9
d)
3
7
Solve the equation
a)
9
7
b)
7
9
c)
7
−
9
d)
3
7
Solve the system for x & y (Show
Your Work)
Solve the system for x & y (Show
Your Work)
2y = -2
y = -1
2x - 3(-1) =
2x - (-3) =
2x + 3 =
2x =
x=
7
7
7
4
2
Solution: (2, -1)
The solutions to the system of equations
in the graph are approximately:
a) { (1,-3) , (-2,-6) }
b) { (-1,3) , (2,6) }
c) { (-1,3) , (2,4) }
d) {(1,3) , (2,6) }
The solutions to the system of equations
in the graph are approximately:
a) { (1,-3) , (-2,-6) }
b) { (-1,3) , (2,6) }
c) { (-1,3) , (2,4) }
d) {(1,3) , (2,6) }
The data in the table shows the startup costs and the per unit cost
for a new company that will make watches. Write an algebraic
equation that describes the situation where X = the number of
watches produced.
# of watches
production costs
startup costs
total
0
$0
$10,000
$10,000
1
$10
$10,000
$10,010
10
$100
$10,000
$10,100
100
$1000
$10,000
$11,000
a) Total = $10x + $1000
c) Total = $10,000x + $10
b) Total = $10x + $10,000
d) Total = $10x + $10
The data in the table shows the startup costs and the per unit cost
for a new company that will make watches. Write an algebraic
equation that describes the situation where X = the number of
watches produced.
# of watches
production costs
startup costs
total
0
$0
$10,000
$10,000
1
$10
$10,000
$10,010
10
$100
$10,000
$10,100
100
$1000
$10,000
$11,000
a) Total = $10x + $1000
c) Total = $10,000x + $10
b) Total = $10x + $10,000
d) Total = $10x + $10
Given the graph below, what is the
maximum height reached?
a) 3.5 meters
b) 7 meters
c) 60 meters
d) 50 meter
Given the graph below, what is the
maximum height reached?
a) 3.5 meters
b) 7 meters
c) 60 meters
d) 50 meter
A basketball court is approximately twice as
long as it is wide. If the width is z, which of
the following equations describes the
approximate area of the basketball court?
a) 𝐴 = 6𝑧
b) 𝐴 = 6𝑧 2
3
c) 𝐴 = 𝑧
2
2
𝐴
=
2𝑧
d)
A basketball court is approximately twice as
long as it is wide. If the width is z, which of
the following equations describes the
approximate area of the basketball court?
a) 𝐴 = 6𝑧
b) 𝐴 = 6𝑧 2
3
c) 𝐴 = 𝑧
2
2
𝐴
=
2𝑧
d)
Which is the graph of 𝑦 = 𝑥 2 + 2
Which is the graph of 𝑦 = 𝑥 2 + 2