Name: ____________________
March 22, 2017
Math 1B/2A
Quarter 3 Test Review #3
Math 1b/2a - Review and Extension Problems for Quarter 3 Test
1. Sasha was copying two congruent quadrilaterals, WINS and ABLE.
However, when she copied the coordinate 𝐸(2,2), Tony spilled
coffee all over the first quadrant (if you don’t know what that is, you
can look at the diagram to the right).
a. If Tony’s spilled coffee covers the entire quadrilateral, label the other coordinates of
uadrilateral ABLE on the grid provided. We also know for a fact that the transformation
that maps WINS to ABLE is not a rotation.
b. In words, describe the transformation that occurred to WINS to create ABLE.
There is more than one correct answer here are two that work.:
1. Reflect over the line y = -1.
2. Reflect over the y axis and translate left 1.
c. In mapping notation, 𝑥, 𝑦 → , show what transformations occurred to point W to create
point E.
𝑥, 𝑦 → (𝑥 + 3, 𝑦 − 2)
a. q
Name: ____________________
March 22, 2017
Math 1B/2A
Quarter 3 Test Review #3
!
2. For this question, 𝑓 𝑥 = 2 𝑥 and 𝑔 𝑥 = 2𝑥 ! .
a. What is 𝑓 1 ? What is 𝑔(1)?
f(1)=2 and g(1) =2
b. What is 𝑓 −1 ? What is 𝑔(−1)?
f(-1)=-2 and g(-1) =-2
c. What happens graphically at the points 1,2 and −1, −2 ? Explain how you came to that
conclusion.
!
They are points of intersection on the graphs of 𝑓 𝑥 = 2 𝑥 and 𝑔 𝑥 = 2𝑥 !
d. Find the distance between 1,2 and −1, −2 in simplest radical form.
D = (−1 − 1)! + (−2 − 2)! = (−2)! + (−4)! = 20 = 2 5
Name: ____________________
March 22, 2017
Math 1B/2A
Quarter 3 Test Review #3
3. Below is a rectangle with radical side lengths 𝐴𝐷 = 27 and 𝐴𝐵 = 2 3.
a. Simplify 27 into its simplest radical
form.
27 = 3 3
b. Find the perimeter of the rectangle in simplest radical form
P = 3 3 + 2 3 + 3 3 + 2 3 = 10 3
c. Find the area of the rectangle.
Area = 3 3 ∗ 2 3 = 6 ∗ 3 = 18
d. Challenge: Find the length 𝐴𝐶.
Length of AC Calculation: 3 3
Length of AC = 39
!
+ 2 3
!
= 9 ∗ 3 + 4 ∗ 3 = 27 + 12 = 39
Name: ____________________
March 22, 2017
4. Below, several rational and radical expressions are given.
1
16
a. Rewrite
Answer:
!"
!"
!" !"
!"
!"
!
!!
,
13
13
,
!
Math 1B/2A
Quarter 3 Test Review #3
27 !
, 4! ,
8
such that it is simplest radical form.
= 13
b. Order the expressions from least to greatest. Show work to support your answer. (Hint:
simplify each as much as possible first!)
1
16
!"
!"
!
!!
=
1
1
16
!
!
1
= =4
1
4
!
27
=
8
!
= 13
4! =
Answer:
!
27
8
13
13
1
16
!
!!
5. In this problem, we are given point 𝑀 6,18 and 𝑇(12,10).
!
4!
!
27
!
4
8
!
=
3
2
=8
Name: ____________________
March 22, 2017
Math 1B/2A
Quarter 3 Test Review #3
a. Find the midpoint of 𝑀𝑇.
(9, 14)
b. Find a point that is collinear (on the same line) as the points 𝑀 and 𝑇. Explain how you
found your point.
One Method:
Graph the points, find the slope of 𝑀𝑇 which is -8/6 = -4/3, and use the slope to find the next
point in either direction.
Answers include: ( 9, 14) and (15, 6)
c. Find the equation of the line perpendicular to 𝑀𝑇 that goes through point 𝑀.
point 𝑀 6,18
slope of perpendicular line: ¾
!
Equation: 𝑦 − 18 = ! (𝑥 − 6)