SOL Practice Items
1. Let m represent:
Angle A is obtuse.
Let n represent:
Angle B is obtuse.
What is the symbolic representation of the following argument?
Angle A is obtuse if and only if Angle B is obtuse.
Angle A is obtuse or Angle B is obtuse.
Therefore, Angle A is obtuse and Angle B is obtuse.
2. Lines a and b intersect lines c and d.
Which statement could be used to prove 𝑎 ∥ 𝑏 and 𝑐 ∥ 𝑑?
A. ∠1 and ∠2 are supplementary and ∠5 ≅ ∠6.
B. ∠1 ≅ ∠3 and ∠3 ≅ ∠5
C. ∠3 and ∠5 are supplementary, and ∠5 and ∠6 are supplementary
D. ∠3 ≅ ∠4 and ∠2 ≅ ∠6
3. Line a passes through points with coordinates (-4,5) and (2,-2).
What is the slope of a line perpendicular to line a?
Slope of perpendicular line =
4. Which construction represents a correct first step in constructing a line segment
perpendicular to ̅̅̅
𝐽𝐾 through point P?
5. Ben plans to bisect ∠𝐴𝐵𝐶 to create the congruent angles ABD and CBD.
Which angle is congruent to ∠𝐴𝐵𝐷 and ∠𝐶𝐵𝐷?
6. Given: Triangle ABC with vertices located at
A(1,1), B(2,-3), C (-1, -4)
Triangle ABC will be reflected over the line y = x. What will be the integral coordinates
of point C’ after this transformation?
C’ (
,
)
7. Given: Triangle ABC with AB = 42 and BC = 20
Which of the following are possible lengths for AC?
12
20
22
32
42
50
62
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅ , 𝐴𝐹
̅̅̅̅ ≅ 𝐹𝐷
̅̅̅̅
8. Given: 𝐴𝐵
Prove: ∆ABF ≅ ∆DCF
Construct a proof.
Statement
Reason
70
9.
Directions: Draw a line from the selected reason to the correct box.
Select the reasons for the last three statements of this proof.
Given: ∠𝑄𝑆𝑅 ≅ ∠𝑇𝑅𝑆; ̅̅̅̅
𝑃𝑅 ≅ ̅̅̅̅
𝑃𝑆
Prove ∆QSR ≅ ∆TRS
10. What value of x makes ∆STW ≅ ∆XYZ?
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅
11. Given: 𝐴𝐵
Prove: ∆ABF ~ ∆DCF
Construct a proof.
Statement
Reason
12. For what value of x is ∆ABC ~ ∆DEF?
13. What is the total number of lines of symmetry for this figure?
14. A ladder leans against a wall. The bottom of the ladder is 10 feet from the base of the
wall, and the top of the ladder makes an angle of 25° with the wall. Find the length, x, of
the ladder.
15. Which of these regular polygons could tessellate a plane?
Square
Pentagon
Octagon
Hexagon
Decagon
16. Quadrilateral QRST is to be reflected over the line y = -x
What are the coordinates of point T’ after this reflection?
⃗⃗⃗⃗⃗ and 𝐴𝐶
⃗⃗⃗⃗⃗
17. Given: Circle M with secants 𝐴𝐵
m ∠A = 30°
If the length of arc BC is 3 cm, what is the circumference of the circle?
18. In circle O, 𝑚∠𝑆𝑂𝑇 = 68°
What is 𝑚∠𝑆𝑅𝑇?
̂ = 30°, 𝑚𝐵𝐶
̂ = 120°, and ∠𝐽 ≅ ∠𝐾.
19. In circle O, 𝑚𝐹𝐺
̂?
What is 𝑚𝐸𝐻
20. Given: Three concentric circles with the center O
̅̅̅̅
𝐾𝐿 ≅ ̅̅̅̅
𝐿𝑁 ≅ ̅̅̅̅
𝑁𝑂
KP = 42 inches
Which is closest to the area?
A.
B.
C.
D.
231 sq. in.
308 sq. in
539 sq. in.
616 sq. in.
21. Bob divides his circular garden into 10 congruent sectors to plant different types of
flowers. The circumference of Bob’s garden is 50.5 feet. What is the area of one sector
of Bob’s garden?
22. Given: Circle T with WP = 36 centimeters.
Which best represents the area of the shaded sector?
23. The coordinate of the center of a circle are (-2,6). This circle has a diameter of 10 units.
a. What is the equation of the circle?
b. Give the integral coordinates of two points that lie on the circle.
24. Given:
Circle W
W(-4,6)
Radius = 10 units
Which point lies on circle W?
A. (0,4)
B. (2,10)
C. (4,0)
D. (6,16)
25. The equation of a circle is (𝑥 − 3)2 + (𝑦 + 4)2 = 16
a. What are the coordinates of the center of the circle?
b. What is the radius of the circle?
c. What is the diameter of the circle?
d. Give the integral coordinates of two points that lie on the circle.
26. Circle O is defined by the equation 𝑥 2 + (𝑦 − 2)2 = 25. Plot the center if circle O and
one point with integral coordinates that lies on circle O.
27.
Directions: Circle the two objects with the same volume.
Two cylinders, a sphere, and a cone are shown. Select the two objects with the same
volume.
28. A rectangular prism has a volume of 36 cm3
a. If the height of the prism is tripled and the other dimensions do not change,
what is the volume of the new rectangular prism?
b. If all dimensions of the original rectangular prism are tripled, what is the
volume of the new rectangular prism?
29. A cylinder has a surface area of 96 square inches. If all dimensions of this cylinder are
multiplied by ½ to create a new cylinder, what will be the surface area of the new
cylinder?
30. A company makes two similar cylindrical containers. The total surface area of the
smaller container is 0.81 times that of the larger container. The height of the larger
container is 60 centimeters. What is the height of the smaller container?
31.
Directions: Write your number choices in boxes provided
The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the
radii of these two spheres?
32. A cylinder has a volume of 300π cubic centimeters and a base with a circumference of
10π centimeters. What is the height of the cylinder?
1
33. If the height of a rectangular prism is decreased by 3, then which statement is true?
1
A. The volume would decrease by 3
1
B. The volume would decrease by 6
1
C. The volume would decrease by 9
1
D. The volume would decrease by 27
34. The heights of two similar triangles are in ratio 2:5. If the area of the larger triangle is
400 square units, what is the area of the smaller triangle?
35. Directions: Plot the point on the graph provided
below.
Line t contains the points (-4,7) and (5,-8).
Plot a point other than point P with integral coordinates that lie on a line that is
parallel to t and passes through point P.
36. Given: Quadrilateral ABCD.
Which expression proves that ABCD is a
rectangle?
A. Then length of each diagonal is √𝑟 2 + 𝑠 2
B. The common midpoint of the diagonals is
𝑟 𝑠
(2 , 2)
𝑠
−𝑠
C. The slope of ̅̅̅̅
𝐴𝐶 is 𝑟 and the slope of ̅̅̅̅
𝐵𝐷 is 𝑟
̅̅̅̅ and 𝐶𝐷
̅̅̅̅ is r and the
D. The length of both 𝐴𝐵
̅̅̅̅
̅̅̅̅
length of both 𝐴𝐷 and 𝐵𝐶 is s.
37.
Directions: Plot the point on the graph provided below.
The vertices of ∆ABC and the endpoints of ̅̅̅̅
𝐷𝐸 have integral coordinates. Plot point F
with integral coordinates so that ∆ABC ≅ ∆DEF.
38. Point A represents a vertex of an equilateral triangle inscribed in circle O.
Which other point is also a vertex of this equilateral triangle?
39.
Directions: Shade the area indicated.
This Venn diagram represent the set of cell phones in a store.
 Let P represent the cell phones that take pictures.
 Let I represent the cell phones that connect to the Internet.
 Let G represent the cell phones that have games.
Identify each region of the Venn diagram that represents the cell phones that only
take pictures and have games.
40.
Directions: Circle all the statements that must be true.
This figure models a gate that has been constructed using two parallel vertical boards
with a diagonal board connecting them. Identify all of the statements that must be true.