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ANSWERS
Screening Test
4.
1. C 2. H 3. B 4. H 5. C 6. J 7. A 8. F 9. C
10. G 11. C 12. F 13. B 14. H 15. C 16. J
17. D 18. H 19. B 20. J 21. C 22. H 23. C
24. J 25. B 26. H 27. D 28. G 29. D 30. F
31. C 32. F 33. C 34. J 35. C 36. G 37. D
38. F 39. B 40. J 41. C 42. J
Benchmark Test 1
1. C 2. J 3. C 4. F
10. G 11. D 12. F
17. B 18. H 19. D
24. H 25. C 26. G
31. A 32. G 33. A
5. D 6. J 7. B 8. H 9. A
13. C 14. G 15. B 16. J
20. G 21. A 22. J 23. C
27. D 28. G 29. C 30. G
10 in.
6 in.
2 in.
5. Your friend will be on the honor roll. 6. x 5 3
7. 25
8.
L
M
Benchmark Test 2
9. Subtraction Property
1. D 2. G 3. B 4. F 5. C 6. J 7. A 8. H 9. C
10. G 11. A 12. H 13. C 14. H 15. B 16. G
17. C 18. H 19. A 20. H 21. B 22. G 23. C
24. G 25. C 26. H 27. D 28. F 29. C 30. H
31. D 32. G 33. D
10.
Benchmark Test 3
1. A 2. G 3. A 4. J 5. B 6. J 7. A 8. G 9. A
10. G 11. C 12. F 13. A 14. F 15. D 16. H
17. B 18. G 19. A 20. H 21. C 22. H 23. B
24. F 25. B 26. G 27. C 28. H 29. B 30. G
31. C 32. G 33. B
Benchmark Test 4
1. C 2. G 3. D 4. F 5. C 6. H 7. C 8. G 9. B
10. H 11. A 12. J 13. B 14. J 15. D 16. J 17. B
18. H 19. C 20. J 21. A 22. F 23. B 24. H
25. B 26. F 27. C 28. J 29. B 30. G
Benchmark Test 5
Fro
1. 13, 21 2. Answers may vary. Sample: a tiger
has four legs but it is not a dog. 3. y 5 2x 2 4
ht
nt
Rig
11. 70 12. Line b is parallel to line c by the
Transitive Property of Parallel Lines. 13. 29
14. Suppose that 2x 1 4 5 6. Subtract 4 from both
sides of the equation by the Subtraction Property.
This gives an equation of 2x 1 4 2 4 5 6 2 4,
which reduces to 2x 5 2. Now divide both sides
of the equation by 2 by using the Division
Property. This gives an equation of
* )
2x
2
5 ,
2
2
which simplifies to x 5 1. 15. AC 16. 12p m
17. Answers may vary. Sample: A student can
drive if and only if he or she is over the age of
sixteen. If a student can drive, then he or she is
over the age of sixteen. If a student is over the age
of sixteen, then he or she can drive.
18.
1. C 2. G 3. C 4. H 5. D 6. G 7. B 8. H 9. C
10. H 11. B 12. J 13. B 14. J 15. D 16. G
17. C 18. F 19. B 20. F 21. C 22. H 23. A
24. J 25. B 26. H 27. D 28. F 29. D 30. G
31. C 32. G 33. A 34. F 35. C 36. G
Quarter 1 Test, Form G
2 in.
10 in.
C
A
P
B
/
19. (1, 2.5) 20. y 5 3x 1 1 21. /2 > /4 by the
Converse of the Corresponding Angles Theorem
or /2 1 /3 5 180 by the Converse of the
Same-Side Interior Angles Theorem 22. 2 "17
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ANSWERS (CONTINUED)
23. The intersection is a point, or there is no
intersection. 24. Two lines must not intersect and
be in the same plane to be parallel. 25. 40
26. 50 27. 90 28. hypothesis: if you are not at
school; conclusion: you are at home 29. If you are
at home, then you are not at school. 30. Transitive
Property
25. Answers may vary. Sample:
6
4
4
9
6
6
6
9
Quarter 2 Test, Form G
26. x 5 3, y 5 3"2 27. x 5 2, y 5 4
28. 具3, 2 9典 29. 12 in. 30. 8
1. RS 2. 20 3. 3 4. 50 5. 40; 82 6. SSS
Postulate 7. SAS Postulate 8. (c 2 a, b) 9. 45
10. /R, /P, /Q 11. AAS, nABC > nABD
12. 133; 47 13. Answers may vary. Sample: You
Quarter 4 Test, Form G
can use the distance formula to find the lengths
of the diagonals AC and DB. If the lengths are
equal, then the diagonals are congruent, so the
parallelogram is a rectangle. 14. 4 15. Answers
may vary. Sample: The diagonals must be
perpendicular bisectors of each other, or all sides
must be congruent. 16. The orthocenter is the
intersection of the three altitudes of a
triangle. 17. 2 18. PN . MN 19. HypotenuseLeg Theorem 20. 9 21. BC > BD 22. Suppose
that a triangle had more than one right angle.
If this were true, then two of the angle measures
alone would add up to 180, and the third angle
would have a measure that would contradict the
Triangle Angle-Sum Theorem. 23. AB, BC, AC
24. 90; 30 25. rhombus 26. 65 27. c, e, b, a, d or
e, c, b, a, d 28. No; the midsegment is not half
the length of the third side. 29. a kite 30. /R
Quarter 3 Test, Form G
1. 14 2. nABC , nJKL by SSS , Theorem
3. nTUV , nWXY by AA , Postulate 4. obtuse
5. 56.3 6. 10.7 7. reflectional symmetry and 180°
rotational symmetry (point symmetry)
8. 2 "26 9. sin A 5
8
15
8
; cos A 5 ; tan A 5
17
17
15
10. A9(7, 2), B9(11, 2), C9(10, 21), D9(6, 21)
11. A9(25, 4), B9(29, 4), C9(28, 1), D9(24, 1)
12. A9(23, 24), B9(27, 24), C9(26, 21),
D9(22, 21) 13. 53.9 mi/h; 21.8° south of east
2
14. (3, 3) 15. A 16. Yes; 42 1 62 5 Q 2"13 R , so
it is right triangle by the Converse of the
Pythagorean Theorem. 17. 4"3 18. 38
19. 6 20. 18.4 21. Check students’ work.
22. No; there will be gaps when the pattern is
repeated. 23. A9(22, 6), B9(0, 14), C9(8, 4)
24. 48 ft
1. 268.1 cm3 2. 66.3 cm2 3. 25 4. 32
5. 128 cm2 6. Answers may vary. Sample: Draw
d1, a diagonal of the kite that divides it into two
congruent triangles. Let d1 represent the base of
1
2
each triangle. The area of one triangle is d1h1.
1
The area of the other triangle is d1h2. Because
2
the triangles are congruent, h1 5 h2. The other
diagonal, d2, is the sum of h1 and h2. Therefore,
1
the area of a kite is d1d2. 7. 14.14 cm2 8. 12.5
2
9. a circle with center (22, 23) and radius 5 units
10. 113.1 m2 11. 28p m3 12. 81 m2 13. 6
14. center: (5, 6); radius: 4
10
8
6
4
2
2
2
4
y
x
2 4 6 8 10
15. 73.7 16. 92 17. 400 ft3 18. 164 in.3 19. 30
20. 60 21. 270 22. b, c, a, d 23. 310.4 in.2
24. 8 25. (x 2 2)2 1 (y 2 2)2 5 4 26. 188.1 in.2
* )
* )
27. 2p in. 28. Answers may vary. Sample: QR is
tangent to (P. QR is perpendicular to a radius of
(P. 29. 284.7 cm2 30. 4%
Mid-Course Test, Form G
1. 63; 127 2. 86 3. 19 4. 7 5. parallelogram
6. 12 7. Division Property of Equality 8. /B, /A,
/C 9. 36, 36 10a. If it is summer, then it is
sunny. 10b. If it is not sunny, then it is not
3
2
summer. 11. y 5 2 x 1 2 12. 26 13. 125°;
obtuse 14. 60 15. nCAB > nBDC by SAS.
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128
ANSWERS (CONTINUED)
11. 14.0 in. 12. 8.9 13. 47.0 cm2 14. 1280 m3
15. two parallel, horizontal lines, one 3 units
16. (a 2b, c) 17a. /3 and /5 or /4 and /6
17b. /1 and /5, /2 and /6, /3 and /7, or
/4 and /8 18. 67°
above and one 3 units below y 5 22
19.
3
1
y
5
Right
2
Front
4 2
20. 115; 65 21. The circumcenter of a triangle is
the point of concurrency of the perpendicular
bisectors of the triangle. 22. The orthocenter of a
triangle is the point of concurrency of the lines
that contain the altitudes of the triangle.
23. /1 > /3 or /2 > /4 or m/1 1 m/4 5 180°
or m/2 1 m/3 5 180° 24. Line / is parallel to
line p; since lines / and n are both perpendicular
to line m, they are parallel to each other. Since
lines / and p are both parallel to line n, line / and
p are parallel to each other by Transitive Property
of Parallel Lines.
25. AC > CF; CB > FD; BA > DC;
/ACB > /CFD; /CBA > /FDC;
/BAC > /DCF
26. Answers may vary. Sample: A rectangle always
has opposite sides parallel, making it a
parallelogram. A parallelogram doesn’t always have
four right angles, so it is not always a rectangle.
27. AD . CD 28. rectangle 29. rhombus
30. square 31. trapezoid 32. rectangle
33. rhombus 34. 6 35. 48; 90; 42; 57; 33
36. x 5 25; y 5 31 37. (2.5, 1) 38. Soccer
practice will be canceled. 39. 118; 34 40. 7.2
41. area 5 452.4 in.2; circumference 5 75.4 in.
42. 74 43. HL 44. not possible 45. SSS
46. AAS 47. not possible 48. SAS
49. ASA or AAS 50. SSS or SAS
Final Test, Form G
* )* )
1. 36 2. (2.5, 1) 3. AB 6 CD ; Converse of the
Same-Side Interior Angles Theorem
4. Hypotenuse-Leg Theorem; ^ABC > ^EDC
5. (6, 25) 6. 128 cm2 7. 96 in.2 8. reflectional
and rotational symmetry 9. D
10.
2
x
4
y 2 2
4
16. 144"3 in.2 17. 15.0 18. F 19. 6.5 20. 7.5
21. 54 cm2 22. 63 m 23. 64 ft 24. 53.2 mi/h;
41.2° west of north 25. 11 26. (22, 22) 27. /A,
/C, /B 28. a, c, e, b, d or c, a, e, b, d 29. never
30. sometimes 31. sometimes
32. SAS; ^ACD > ^CAB 33. Yes; the length of
AB is half the length of DE. 34. 18 35. 34
36. 92.3 in.2 37. 100 38. 466.5 ft2 39. 199.0 cm2
40. 6
41.
42.
5
< 55.6% 43a. 1809.6 cm2 43b. 7238.2 cm3
9
44a. If two angles have the same measure, then
they are congruent. 44b. If two angles are not
congruent, then they do not have the same
measure. 45a. PQ 45b. /F 46. 13.0
47. MW < 43.5, MX < 34.3 48. 58° 49. 113
1
50. y 5 2 x 1 1 0
3
Quarter 1 Test, Form K
1. 21, 25 2. Answers may vary. Sample: a frog
swims, but it is not a fish. 3. y 5 3x 2 2
4. C 5. You will have piano lessons after school.
6. 5 7. 9
8.
12 cm
A
B
5 cm
5 cm
p cm
10p
9. Addition Property
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129
ANSWERS (CONTINUED)
10.
3
1
11. X9(2, 21), Y9(3, 25), Z9(6, 22)
12. X9(22, 21), Y9(23, 25), Z9(26, 22)
13. 40.3 mi/h; 29.7° north of west 14. (10, 0)
15. Yes; the preimage and image are congruent.
16. Yes; 82 1 152 5 172, so it is right triangle by
Right
2
Front
the Converse of the Pythagorean Theorem.
17. 5"7 18. x 5 9, y 5 15 19. y 5 14 20. 45°
21. Check students’ work.
22. yes
11. 138 12. Line a is parallel to line b by the
following theorem: In a plane, if two lines are
perpendicular to the same line, then they are
parallel to each other. 13. 90° 14. Substitution
Property 15. BF 16. 10p m 17. You live in
Tallahassee. You live in the capital of Florida.
18.
J
23. X9(0, 23), Y9(3.5, 22), Z9(3, 1) 24. 88 ft
/
H
25. Check students’ work. 26. 5"2 27. 6"3
28. ,3, 8. 29. 12 in. 30. J
Quarter 4 Test, Form K
19. (22, 4) 20. 23 21. G 22. 5 23. a line or no
intersection 24. noncoplanar lines that do not
intersect 25. 90 26. 60 27. 85 28. hypothesis:
1. 904.8 in.3 2. 63.4 in.2 3. 90 4. 75 5. 4 : 7, 16 : 49
6. 24 square units 7. 150.80 cm3 8. 8 9. a circle
two angles have a sum of 180°; conclusion: the
angles are supplementary angles 29. B 30. J
with center (24, 6) and radius 8 units
10. 245.0 ft2 11. 90p ft3 12. 40 cm2 13a. 5
13b. 9 14. center: (0, 0); radius: 5
y
Quarter 2 Test, Form K
4
1. XZ 2. 4 3. 4 4. 56° 5. x 5 85, y 5 60
6. SAS Postulate 7. SSS Postulate 8. (c 1 a, b)
9. 45 10. /C; /A; /B 11. ASA Postulate
12. x 5 142, y 5 38 13. Answers may vary.
2
x
Sample: show that the slope of diagonal AC is the
negative reciprocal of the slope of diagonal BD.
14. 4 15. D 16. circumcenter 17. 5
18. m/QTR , m/RTS 19. HL Theorem
20. 10 21. /CAB > /DAB 22. Suppose a
triangle has more than one obtuse angle. Since
the sum of two obtuse angle measures is greater
than 180°, the sum of the measures of the angles
in the triangle would be greater than 180°.
This contradicts the Triangle Angle-Sum
Theorem. 23. AB; AC; BC 24. 56° 25. rectangle
1
26. 55° 27. CPCTC 28. Yes; AB 5 MN
2
29. parallelogram 30. /X
Quarter 3 Test, Form K
3. nAYM , nXQH by AA , Postulate 4. obtuse
5
12
5
9. sin A 5 ; cos A 5 ; tan A 5 ;
13
13
12
2
4
2
4
15. 90° 16. 104° 17. 128 cm2 18. 114 in.3
19. 133° 20. 133° 21. 180° 22a. 184 in.2
22b. 201.1 ft2 23. 192.5 in.2 24. 11 25. B
7
3
26. 259.8 in.2 27. pft 28. Yes; since
32 1 42 5 52, ^PQR is a right triangle, and
PQ ' QR. Therefore, QR is a tangent to the circle.
29. 188.5 cm2 30. 10%
Mid-Course Test, Form K
1. D 2. nBRG , nNDK by SAS , Theorem
5. 32.2 6. 12.8 7. line symmetry 8. 4 "5
4 2
1. 29, 211 2. 95 3. 12 4. 16 5. rectangle 6. 11
7. A 8. /T, /R, /S 9. 30 10. Hypothesis: a
transversal intersects two parallel lines;
conclusion: alternate interior angles are
congruent.
10. X9(4, 6), Y9(5, 10), Z9(8, 7)
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130
ANSWERS (CONTINUED)
11.
4
15. circle with center (1, 0) and radius 3
y
y
4
2
2
x
4
2
2
(1, 0)
4
24 22
2
24
12. 14 13. 60°; acute 14. 45
15. nLRT and nLMN; /RLM 16. (0, b)
17a. /2 and /3 or /6 and /7 17b. /2 and /6
or /3 and /7 18. 5
16. 40 m2 17. 12.5 18. H 19. 6.4 20. 8 22. 110 ft
23. 44m 24. ,9, 1. 25. 7 26. (21, 26) 27. /C,
/B, /A 28a. vertical angles 28b. CPCTC
29. always 30. Never 31. sometimes 32. SAS
33. 1 34. 5.5 35. 32.5 36. 24.6 cm2 37. 80
38. 200p cm3 39. 28.5 cm2 40. 9.7
19.
2
x
4
22
4
2
2
2
Right
1
41.
Front
20. x 5 100, y 5 80 21. incenter 22. centroid
23. J 24. Line l is parallel to line n by the
Transitive Property of Parallel Lines. 25. A
26. G 27. MN . QS 28. rhombus 29. kite
30. trapezoid 31. rectangle 32. trapezoid
33. rhombus 34. 7 35. m/1 5 34°, m/2 5 68°
36. 13 37. (1, 2) 38. I have dance lessons.
39. m/1 5 40°, m/2 5 95°, m/3 5 45° 40. 10
41. C < 100.5 in., A < 804.2 in.2 42. m/1 5 54°,
m/2 5 63° 43. HL 44. not possible 45. SSS
46. AAS 47. ASA 48. SAS 49. AAS 50. HL
Final Test, Form K
1. 45 2. (5, 8) 3. Converse of the Corresponding
Angles Postulate 4. Hypotenuse-Leg Theorem
5. (21, 1) 6. 24 ft2 7. 48 cm2 8. rotational and
reflectional symmetry 9. B
10.
5 cm
6 cm
11. 13.6 ft 12. 4 13. 120 cm2 14. 1296 cm3
1
5 25% 43a. 282.7 m2 43b. 314.2 m3 44. If
4
two angles are congruent, then they are vertical.
45a. BC 45b. /H 46. 7.1 47. AC < 41.3,
CD < 33.4 48. 50° 49. 113 50. y 5 3x 2 10
42.
Test-Taking Strategies
Writing Gridded Responses
1. 6 2. 5 3. 11.4 4. 326.7 5. 615.75 6. 2.5 7. 12
8. 51 9. 87 10. 690 11. 552.9 12. 13.30
Writing Short Responses
1a. 2 points; all parts are solved, work is shown,
and answers are correct. 1b. 0 points; no work
shown and answer is incorrect. 1c. 1 point; error in
work, but problem is set up correctly, incomplete
answer 2a. 0 points; incorrect and incomplete
response 2b. 2 points; the measure of each angle is
found, all work is shown, and a diagram is
complete and correct. 2c. 1 point; correct answer,
but did not complete a drawing. 3a. 0 points;
incomplete and incorrect response 3b. 1 point;
work is shown, however it contains a math error
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131
ANSWERS (CONTINUED)
Writing Extended Responses
Interpreting Data
1a. The work shows all steps but there is a minor
computational error where 80 is added to 180
instead of subtracted from 180. 1b. Even though
the final answer is correct, the problem is not set
up correctly as the diagram shows /1 and /3 as
alternate interior angles, not corresponding
angles. 2. The answer is correct, but there is little
work shown. 3. Answers may vary: Sample:
1. C 2. G 3. C 4. J
A
1. 108, 78, and 94 2. 40, 60, and 80 3. (6.5, 0)
7
1
, 0) 5. 8, 12, or 16 6. 40 7. 60 8. 22
19
2
1
9. 4 in. 10.
11. 3 12. 7 13. 4 14. 108°
2
4. (2
Drawing a Diagram
B
(4x 30)
Using a Variable
1. rhombus 2. BE 5 ED 5 8 and AE 5 EC 5 24
3. Two sides are 22, and two sides are 14
2x
D
C
4. Y(28, 2); Z(2, 6) 5. 35°, 35° 6. 79, 79
7. (0, 1), (3, 0) 8. (5, 5) 9. (26, 26), m 5 1
F
BD bisects /ABC, therefore m/CBD 5 m/ABD.
2x 5 4x 2 30
x 5 15
m/CBD 5 2(15)° 5 30°
m/BDC 5 (4(15) 2 30)° 5 90°.
10. 12 1 6"2 or 20.49 11. x 5 1; each diagonal
is 8 12. 120° 13. Two sides are 12 and two
sides are 32
Finding Multiple Correct Answers
1. C 2. J 3. C 4. F 5. B 6. G
The measure of an exterior angle is the sum of
the two remote interior angles. Therefore,
m/BCF 5 m/CBD 1 m/BDC
5 30° 1 90°
5 120°.
Testing Multiple Choices
4. Answers may vary. Sample: Find the slope of
1a. Answers may vary. Sample: D can be
eliminated because 142 5 196 and the length of
the side will be less than 14. A can be eliminated
because the length of the side will be longer
than 7. 1b. C 2a. The angle is just a bit larger
than a 30° angle, so using the special right
triangle relationships you can eliminate F. The
hypotenuse is the longest side so you can
eliminate J. 2b. G 3a. The angle is just a little bit
smaller than a 30° angle, so using the special
right triangle relationships you can eliminate
A and D. 3b. B 4a. H and J are obtuse
angles. 4b. G 5a. A and B are too small since the
1
area will be greater than ? 7 ? 48. 5b. C
2
6a. The first coordinate has to be 29 so choices
G and J can be eliminated. 6b. F
1. B 2. G 3. C 4. F 5. B 6. J 7. C 8. G
9. B 10. F
Eliminating Answers
the line.
123
2
1
m5
52 52 .
3 2 (23)
6
3
Parallel lines have the same slope.
1
1
y 1 1 5 2 (x 1 1) Substitute m 5 2 and
3
3
(21, 21) in the point-slope
formula.
1
1
y1152 x2
3
3
1
4
y52 x2
Subtract 1 from both sides
3
3
to write the equation in
slope-intercept form.
(3, 3) y
2
(3, 1)
x
2
(1, 1)
2
O
2
Choosing “None of These”
1. D; A 5 pr 2 5 60, so r ^ 4.37 cm.
C 5 2pr ^ 27.5 cm. 2. J; /2 is a right angle, /3 is
complementary to /1, so m/3 5 50°, /4 is
supplementary to /1, so m/4 5 140°. Therefore,
they are not congruent to /1. 3. C 4. J; only one
pair of corresponding sides are shown to be
congruent, so SSS and SAS cannot be used. While
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132
ANSWERS (CONTINUED)
two pairs of corresponding angles are shown to
be congruent, the corresponding congruent pair
of sides are not between the angles, so SAS
cannot be used. Only ASA can be used to show
that the triangles are congruent. 5. B 6. C
7. J; for all three sets of side lengths,
a2 1 b2 , c2, so all three triangles are obtuse.
8. D; the lengths of the legs are 3 and 3"3,
so A 5
1 Q
9"3
(3) 3"3 R 5
. 9. G
2
2
Answering Open-Ended Questions
1a. The figure incorrectly shows the two
triangles share a common side, not a
common angle. All subsequent work is done
correctly. 1b. The figure correctly shows two
congruent triangles with a common angle,
but no work is shown to justify the congruence
and the congruence statement and the
correspondence of parts is missing.
2. Answers may vary. Sample:
Choosing “Cannot Be Determined”
B
E
1. C 2. G 3. D; need lateral surface area, total
surface area, or volume. 4. G 5. B 6. J; need the
dimensions of the garden. 7. A 8. J; need the
radius. 9. C
A
Using Estimation
3. Answers may vary. Sample:
1. A 2. F 3. C 4. G 5. B 6. H
Let the lines intersect at (1, 1) and let the slope of
1
one line be . The slope of the other line is 22.
2
Equation of the first line:
1
y 2 1 5 (x 2 1)
2
1
1
y215 x2
2
2
1
1
y5 x1
2
2
Equation of the second line:
Answering the Question Asked
1. the sum of the x- and the y-coordinates of the
reflected point; D 2. the y-coordinate of the
reflected point; J 3. the distance of the
translated point to the x-axis; B 4. the vector of
the translation; G 5. the sum of the x- and
y-coordinates of the rotated point; D 6. the
difference between the y-coordinate and the
x-coordinate of the image after translation; H
7. The length A9B9; B 8. lines of symmetry in the
figure; H 9. a false property of a reg. hexagon; C
10. image of (8, 25); G
y 2 1 5 22(x 2 1)
y 2 1 5 22x 1 2
y 5 22x 1 3
Using Mental Math
1. 4x 1 8 2. 50° 3. 100° 4. m/1 5 115°,
m/2 5 65°, m/3 5 65° 5. m/1 5 130°,
m/2 5 50° 6. BC 5 10, CE 5 5, DE 5 4
7. 4 8. AC 5 12, m/ABC 5 70° 9. 12
10. 4, 4 "3 11. 30
D
C
3
y
(1, 1) x
23 21
O
3
23
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F
A N S W E R S : S AT / A C T P R A C T I C E T E S T
Multiple Choice
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Student-Produced Responses
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