Final Exam Review 2

Fall Final Exam Practice 1
Name: ________________________ Period ______ 1
1. Given the function, f ( x) =
A) x = 4
x
, what is the value of x when f ( x) = 16 ?
4
B) x = -4
C) x = 64
1. _____
D) x = 8
2. Which diagram is a NOT a One to One Function?
2. _____
A)
B)
C)
D)
3. If you have a rotational symmetry angle of 18°°, then your order is:
A) 2
B) 5
C) 10
4. This shape has:
A) Only Rotational Symmetry
3. _____
D) 20
B) Only Reflectional Symmetry
4. _____
C) Both Rotational & Reflectional Symmetries
symmetry
D) Neither
5. AB is rotated 87°° about point T. Which of the following statements is false?
A) T = T’
B) AT = A’T
C) AA’ = BB’
D) m∠ATA’ = 87°
5. _____
6. If RO ,167° ( ∆ABC ) = ∆DEF then:
A) m∠BOD = 167°
B) m∠OAD = 167°
C) m∠AOE = 167°
D) m∠FOC = 167°
6. _____
Determine whether the following are (T)rue or (F)alse.
7. T ( x, y) − − − − > (3x, y + 2) is an isometric transformation.
T or F
8. A rotational symmetry of order 2 means that the angle of the order is 90°°.
9. A rotation of 180°° reverses the orientation of the shape.
10. The isometric transformations are rotation, reflection, dilation and translation.
T or F
T or F
T or F
11. Given coordinate rule, T ( x, y) − − − − > ( x + 2, y − 6) determine the pre-image of A’(-2,2)?
12. Given the shape, shade it so that it has reflectional symmetry.
a) 1 line of symmetry
b) 2 lines of symmetry
c) Order 4
d) Order 4
2
13. ∆ABC is mapped by a single isometric transformation to ∆A’B’C. Name ALL of the isometric
transformations that could have performed this? Explain why you chose the one(s) you did.
14. Determine whether the following are (T)rue or (F)alse.
a) F (x,y) -------> (x + 3,y) is a translation of 3 units to the right.
b) RO ,180 = Rx axis R y axis
T or F
T or F
c) A composite transformation of a rotation followed by translation reverses the
orientation of the shape.
d) A double reflection over y = 3 followed by y = 4, translates all points up 2 units.
e) R y = 11 R y = 6 = T< 0,10 >
T or F
T or F
T or F
6
15. Perform the following on the grid.
a)
A
D
RM ,90° ( NOPQ)
4
C
H
b) RF ,180° ( ∆GHI )
10
T〈 3,2〉 ( ∆JKL)
M
N
B
c) RAB (∆CDE )
d)
2
E
G
I
O
J
5
5
K
F
2
Q
P
L
4
16. Determine the smallest positive angle of rotation that would perform the same rotation as the given
one.
a)
R0,−50° = R0,_______ °
b)
R0,400° = R0,_______ °
c)
R0,−730° = R0,_______ °
17. Use your rules to solve these.
a)
Rx axis A(5, 4) = A '(_______, _______)
b)
Ry axis Rx axis A(−5,1) = A ''(______, ______)
c)
Rx axis R y axis A(_______, _______) = A ''(4, −3)
d)
T〈−3,5〉 A(_______, _______) = A '(9, −3)
e)
T〈−2, −1〉 R y axis A(5,3) = A ''(_______, _______)
f)
Rx axis A( −1, 6) = A '(_______, _______)
g)
RO ,90 A(3, 2) = A '(_______, _______)
h)
RO ,90° A(_______, _______) = A '(8,3)
3
18. _____
18. If two triangles are congruent, then:
A) they have the same side lengths B) isometric transformation(s) map one onto the other
C) they have the same angle
D) all of the above are true
19. _____
19. A student believes that he can prove these two triangles to be congruent using SSS
because he knows that BD ≅ BD . What would be his reason for
knowing this?
C
D
B
A) The triangles are congruent
B) The Reflexive Property
C) It can’t be SAS because no angle is given D) The Substitution Property
E
20. To be able to prove that ∆ABD ≅ ∆CBD by HL, using the two given congruent
corresponding sides, one piece of information is missing. Which of the
following would be that piece of information?
20. _____
B
C
A) Base angles of an isosceles are congruent
B) BD ≅ BD
C) BD bisect ∠ABC
D) ∠ADB is a right angle
D
A
21. Quadrilateral FHJK is congruent Quadrilateral MNPO. Complete the following congruent statements.
b) NP ≅ ______
a) ∠J ≅ ∠ ______
c) ∠M ≅ ∠ ______
d) KF ≅ ______
B
22. Which triangle congruence criteria will determine congruence for
given diagram?
E
C
A) SSS
B) SAS
C) ASA
D) AAS
A
E) HL
D
22. _____
Choose whether they are (T)rue or (F)alse.
23. Given ∆ABC & ∆RTS and ∠A ≅ ∠R, ∠B ≅ ∠T, ∠C ≅ ∠S then ∆ABC ≅ ∆RTS.
T or F
24. Determine the following for any point P.
k
a) R_________
R_________ ( P ) would result in a rotation of 82°.
b) R_________
R_________ ( P ) would result in a rotation of -174°.
c) R_________
R_________ ( P ) would result in a rotation of 256°.
l
m
87°
41°
A
E
25. Three of the four items listed can be used to establish congruence by ASA.
Determine which one is NOT needed to prove ∆BCA ≅ ∆DCE by ASA?
A) ∠DCE AND ∠BCA are vertical ∠’s
B) AB ≅ ED
C) C is the midpoint of AE
D) ∠A ≅ ∠E
B
C
D
24. ________
A
26. If isosceles ∆ABC has a base angle, ∠B, with a measure of 45°°, then ∆ABC is
A) an acute ∆
B) a right ∆
C) an obtuse ∆
D) a scalene ∆
25. ________
4
27. Which of the following is NOT a characteristic of all rectangles?
A) Consecutive angles are supplementary
B) Opposite angles are congruent
C) Diagonals bisect each other
D) Diagonals are perpendicular
26. ________
28. Which of the following group of quadrilaterals have diagonals that are perpendicular?
A) Rhombus, Square
B) Rhombus, Parallelogram, Square
C) Rectangle, Square
D) Rectangle, Rhombus, Square
27. ________
Determine whether the following are (T)rue or (F)alse.
29. ∆ABC has m∠
∠C = 71°° and m∠
∠B = 71°°, then AB ≅ AC .
T or F
30. A rhombus has four congruent angles.
T or F
31. Consecutive sides are congruent in a rectangle.
T or F
32. What are the missing measures in Parallelogram SRQP?
m∠9 = 66˚
m∠2 = 14˚
m∠1 = 16˚
Q
3
m∠6 = ________
9
m∠10 = ________
m∠11 = ________
m∠3 = ________
33) GIVEN:
CB || ED & CA ≅ DA
PROVE:
BA ≅ EA
STATEMENT
REASON
1
6
T
10
2
P
5
4
11
8
7
S
R
5
34. Solve for the unknown values.
a) x = ___________
b) x = ___________
c) x = ___________
9x - 11
5x + 25
7x + 15
d) x = ________
e) x = ________
126°
x
f) x = ________
41°
89°
g) x = ________
x
165°
x
h) x = ________
35°
i) x = ________
x
x
32°
53°
x
Solutions
1. C 2. B 3. D 4. C 5. C 6. D 7. F 8. F 9. F 10. F 11. No, Different Sizes 12.
13. Translation or Rotation 14a. T 14b. T 14c. F 14d. T 14e. T 15a-d.
16a. 310 16b. 40 16c. 350 17a. (5,-4) 17b. (5, -1) 17c. (-4, 3)
17d. (12,8) 17e. (-7, 2) 17f. (-1, -6) 17g. (-2,3) 17h. (3, -8) 18. D 19. B
20. D 21a. P 21b. HJ 21c. F 21d. OH 22. C 23. F 24a. k,m
24b. k,l 24c. l,m 25. B 26. B 27. D 28. A 29. T 30. F 31. F
32a. 14 32b. 114 32c. 66 32d. 100 33.
34a. 23 34b. 13 34c. 11 34d. 36
34e. 76 34f. 76 34g. 74 34h. 74
34i. 60
x
x