# SAT Geometry Practice Quiz Questions And Answers

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The SAT Geometry Practice Quiz Questions and Answers is a valuable resource designed to help students prepare for the Geometry section of the SAT, a standardized test widely used for college admissions in the United States. Geometry is a crucial component of the SAT Math section, accounting for a significant portion of the test's math questions. This quiz features a comprehensive selection of geometry problems that mirror the types of questions students can expect to encounter on the actual SAT. Are you ready for these SAT geometry practice quiz questions and answers? The SAT exams can be a little Read moreunnerving, especially when one has not had enough practice before tackling them. If you have been having a hard time when it comes to solving some geometry problems, this quiz will help you get some practice.

Each question is thoughtfully crafted to assess a student's knowledge and problem-solving skills in these areas. Detailed explanations and step-by-step solutions accompany each question to aid in understanding and reinforce learning. This resource is an ideal study tool for students seeking to boost their geometry skills and enhance their SAT math scores. It allows test-takers to practice and refine their geometry proficiency, ultimately contributing to their overall SAT success. Whether you're a student gearing up for the SAT or an educator looking for geometry practice materials, this quiz provides a challenging yet supportive environment to sharpen your geometry skills. Do give it a try and see how much more practice you might need before

• 1.

### Which of the following points is not at a distance of 1 unit from the origin?

• A.

(0,1)

• B.

(1,0)

• C.

(1,1)

• D.

(0,-1)

• E.

(-1,0)

C. (1,1)
Explanation
The point (1,1) is not at a distance of 1 unit from the origin because the distance between the origin (0,0) and (1,1) can be calculated using the distance formula, which is the square root of ((1-0)^2 + (1-0)^2) = square root of (2) which is not equal to 1.

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• 2.

### If a circle has a radius of 4 inches, how many square feet is the area of half of the circle?

• A.

π/3

• B.

π

• C.

π/9

• D.

π/16

• E.

π/18

E. π/18
Explanation
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. In this question, the radius is given as 4 inches. To find the area of half of the circle, we divide the area formula by 2. So, the area of half of the circle is (π/2)(4^2) = 8π. However, the answer choices are given in square feet, so we need to convert inches to feet. Since 1 foot is equal to 12 inches, we divide 8π by (12^2) to get the area in square feet, which simplifies to π/18.

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• 3.

### If a triangle has sides of lengths 3 and 7, which of the following could not be the third side of the triangle?

• A.

14

• B.

5

• C.

8

• D.

9

• E.

11

A. 14
E. 11
Explanation
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, if the lengths of two sides are 3 and 7, the third side cannot be greater than 10 (3 + 7). Hence, the third side cannot be 14 or 11.

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• 4.

### Which of the following points is not on the graph of y = 2x + 3

• A.

(0, 3)

• B.

(1, 5)

• C.

(2, 7)

• D.

(-2, -7)

• E.

(-1, 1)

D. (-2, -7)
Explanation
The equation y = 2x + 3 represents a linear function with a slope of 2 and a y-intercept of 3. To determine if a point is on the graph, we substitute the x and y values into the equation and check if it is satisfied. For the point (-2, -7), when we substitute x = -2 into the equation, we get y = 2(-2) + 3 = -4 + 3 = -1, which is not equal to -7. Therefore, (-2, -7) is not on the graph of y = 2x + 3.

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• 5.

### How many 4 sqft. squares can fit onto the surface of a cube with sides of length 4 feet?

• A.

18

• B.

20

• C.

24

• D.

34

• E.

52

C. 24
Explanation
Each face of the cube has an area of 16 sqft. Since each 4 sqft. square can fit onto one face of the cube, the total number of squares that can fit onto the cube is equal to the total area of the cube divided by the area of each square. Therefore, 16 sqft. / 4 sqft. = 4 squares per face. Since a cube has 6 faces, the total number of squares that can fit onto the cube is 4 squares per face x 6 faces = 24 squares.

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• 6.

### Which of the following is not a true statement about the line y = x?

• A.

It is parallel to the line y = x + 5

• B.

It is perpendicular to the line y = -1/x

• C.

It has a slope of 1

• D.

It crosses the origin at the point (0,0)

• E.

It intersects the y axis exactly once.

B. It is perpendicular to the line y = -1/x
Explanation
The line y = x is not perpendicular to the line y = -1/x because the slopes of the two lines are not negative reciprocals of each other. The slope of y = x is 1, while the slope of y = -1/x is -1/x^2. Therefore, the statement that y = x is perpendicular to y = -1/x is not true.

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• 7.

### If a circle is divided into four sectors of areas x, 2x, 3x, and 4x, what is the angular measure of the smallest sector in degrees?

• A.

36

• B.

51

• C.

57

• D.

83

• E.

110

A. 36
Explanation
The smallest sector has an area of x. The total area of the circle is x + 2x + 3x + 4x = 10x. Since the area of a sector is proportional to its central angle, we can set up the equation (x/10x) * 360 = 36. Solving for x, we get x = 36. Therefore, the angular measure of the smallest sector is 36 degrees.

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• 8.

### A circle of radius r = 3 centered at the origin (0,0) will intersect the line y = 3 at how many points?

• A.

0

• B.

1

• C.

2

• D.

3

• E.

Infinitely many.

B. 1
Explanation
The circle with radius 3 centered at the origin will intersect the line y = 3 at only one point. This is because the line y = 3 is parallel to the x-axis and does not intersect the circle at any other point. Therefore, the correct answer is 1.

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• 9.

### What is the area of the square circumscribed by the circle with a radius of 10*sqrt(2) units?

• A.

100

• B.

400

• C.

900

• D.

40

• E.

25

B. 400
Explanation
The area of a square circumscribed by a circle can be found by squaring the diameter of the circle and dividing it by 2. In this case, the diameter of the circle is 2 times the radius, which is 20*sqrt(2) units. Squaring this value gives 800 units. Dividing it by 2 gives us 400, which is the area of the square.

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• 10.

### If the distance between the points (2,2) and (3, a) is 1, what is the value of a?

• A.

1

• B.

2

• C.

3

• D.

4

• E.

5

B. 2
Explanation
The question states that the distance between the points (2,2) and (3,a) is 1. The distance between two points is calculated using the distance formula, which is the square root of the difference of the x-coordinates squared plus the difference of the y-coordinates squared. In this case, the x-coordinate difference is 1 (3-2) and the y-coordinate difference is (a-2). Squaring these differences and adding them together should give us 1. If we square 1, we get 1. If we square (a-2), we get (a-2)^2. So, the equation becomes 1 = 1 + (a-2)^2. Simplifying this equation, we get (a-2)^2 = 0. Taking the square root of both sides, we get a-2 = 0. Solving for a, we add 2 to both sides and get a = 2. Therefore, the value of a is 2.

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• 11.

### How many diagonals does a hexagon have?

• A.

7

• B.

8

• C.

9

• D.

10

• E.

11

C. 9
Explanation
A hexagon has six sides, and each vertex can be connected to three other vertices to form a diagonal. Since there are six vertices in a hexagon, we can draw three diagonals from each vertex. However, we must divide the total count by 2 to avoid counting each diagonal twice. Therefore, the total number of diagonals in a hexagon is (6 * 3) / 2 = 9.

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• 12.

### At how many points do the graphs of y = x^2 + 3 and y = x^2 -3 intersect?

• A.

0

• B.

1

• C.

2

• D.

3

• E.

Many points

A. 0
Explanation
The two given equations are both quadratic functions, which means they represent parabolas. The first equation has a vertex at (0, 3) and opens upward, while the second equation has a vertex at (0, -3) and also opens upward. Since the parabolas open in the same direction and have different y-intercepts, they will never intersect. Therefore, the correct answer is 0.

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• 13.

### What is the radius, in inches, of a circle inscribed in a square with the area 400 sq. inches?

• A.

5

• B.

8

• C.

10

• D.

12

• E.

15

C. 10
Explanation
The area of a square is equal to the side length squared. In this case, the area of the square is 400 sq. inches. To find the side length of the square, we take the square root of the area, which is 20 inches. Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the radius of the circle is half of the diameter, which is 10 inches.

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• 14.

### If two different planes intersect, at how many points will they intersect?

• A.

0

• B.

1

• C.

2

• D.

3

• E.

Many points

E. Many points
Explanation
When two different planes intersect, they can intersect at many points. The number of points of intersection can vary depending on the orientation and position of the planes. If the planes are parallel, they will not intersect at any point. However, if the planes are not parallel, they can intersect along a line, a point, or even have multiple points of intersection. Therefore, the correct answer is "Many points".

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• 15.

### If the smaller angles in an obtuse triangle are x and 2x, what is a possible value for x?

• A.

24

• B.

32

• C.

34

• D.

36

• E.

44

A. 24
Explanation
In an obtuse triangle, one angle is greater than 90 degrees. Since the smaller angles are x and 2x, the sum of these angles must be greater than 90 degrees. If we assume x to be 24, then the smaller angles would be 24 and 48 degrees, which adds up to 72 degrees. This is less than 90 degrees, so x cannot be 24. Therefore, the possible value for x is not 24.

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• 16.

### A trapezoid has two bases in which one is five times the length of the other (x). If the area of the trapezoid is 50, what is the ratio height of the trapezoid to the smaller base?

• A.

50 : x

• B.

50 / x : x

• C.

50 / 3x : 3

• D.

50 / 3x : x

• E.

3 : 1

D. 50 / 3x : x
Explanation
The area of a trapezoid is given by the formula: A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the bases and h is the height. In this case, we are given that one base is five times the length of the other, so we can represent the bases as x and 5x. We are also given that the area is 50. Plugging in these values into the formula, we get 50 = (1/2)(x + 5x)h. Simplifying this equation, we get 50 = (3x)h. Dividing both sides by 3x, we get 50 / 3x = h. Therefore, the ratio of the height of the trapezoid to the smaller base is 50 / 3x : x.

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• 17.

### What is the angular measure of a sector of a circle of radius 6 if the area of the sector is 9*pi square units?

• A.

30 degrees

• B.

60 degrees

• C.

90 degrees

• D.

135 degrees

• E.

180 degrees

C. 90 degrees
Explanation
The area of a sector of a circle is given by the formula A = (θ/360) * π * r^2, where A is the area, θ is the central angle in degrees, π is a mathematical constant, and r is the radius of the circle. In this case, the area of the sector is given as 9π square units and the radius is given as 6 units. Substituting these values into the formula, we get 9π = (θ/360) * π * 6^2. Simplifying this equation, we find θ = 90 degrees. Therefore, the angular measure of the sector is 90 degrees.

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• 18.

### A man walks 5 miles North, 3 miles West, 8 miles South, and 7 miles East. What is his distance from his starting point?

• A.

Sqrt(2)

• B.

Sqrt(5)

• C.

3

• D.

5

• E.

13

D. 5
Explanation
The man walks a total of 5 + 3 + 8 + 7 = 23 miles. However, since he walked 5 miles North and 8 miles South, these distances cancel each other out. Similarly, the 3 miles West and 7 miles East cancel each other out. Therefore, the man's distance from his starting point is equal to the remaining distance he walked, which is 23 - 5 - 8 = 10 miles. However, the question asks for the distance, not the displacement. The distance is the magnitude of the displacement, which is the square root of the sum of the squares of the North-South and East-West distances. In this case, it is sqrt(5^2 + 3^2) = sqrt(34), which is approximately 5.

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• 19.

### An equilateral triangle is created by putting four small equilateral triangles together, three on the base forming a trapezoid and one on top. If the length of the smaller triangle side is 1, what is the length of the larger triangle side?

• A.

1

• B.

1.5

• C.

2

• D.

2.5

• E.

2*sqrt(2)

C. 2
Explanation
When four small equilateral triangles are put together, three on the base forming a trapezoid and one on top, they form a larger equilateral triangle. In the larger triangle, the length of the base is equal to the sum of the lengths of the bases of the small triangles. Since the length of the smaller triangle side is 1, the length of the base of the larger triangle is 3. Therefore, the length of each side of the larger triangle is also 3, making the correct answer 2.

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• 20.

### If a cylinder of volume V is doubled in height and tripled in radius, what will be the volume of the new cylinder?

• A.

3

• B.

6

• C.

9

• D.

12

• E.

18

E. 18
Explanation
When the height of the cylinder is doubled and the radius is tripled, the volume of the new cylinder can be calculated by multiplying the original volume by the ratios of the changes in height and radius. In this case, the height is doubled (2) and the radius is tripled (3). Therefore, the volume of the new cylinder will be 2 * 3 * V = 6V. So, the correct answer is 18.

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• 21.

### What is the distance between two opposite corners in the rectangular prism with length 2, height 2, and width 1?

• A.

2

• B.

3

• C.

4

• D.

5

• E.

6

B. 3
Explanation
Draw a diagram. One corner is two units below, two units to the left of, and one unit beside the other. Using the distance formula: sqrt(2^2+2^2+1) = sqrt(9) = 3

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• 22.

### How many cubes with a side length of 3 could fit evenly into the cylinder of radius 3 and height 21?

• A.

7

• B.

11

• C.

15

• D.

18

• E.

21*pi

A. 7
Explanation
The cylinder has a radius of 3 and a height of 21. The cubes have a side length of 3. To determine how many cubes can fit evenly into the cylinder, we need to find the volume of the cylinder and divide it by the volume of one cube. The volume of the cylinder is calculated using the formula V = πr^2h, where r is the radius and h is the height. Plugging in the values, we get V = π(3^2)(21) = 189π. The volume of one cube is calculated by cubing the side length, so V_cube = 3^3 = 27. Dividing the volume of the cylinder by the volume of one cube, we get 189π/27 = 7. Therefore, 7 cubes with a side length of 3 can fit evenly into the cylinder.

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• 23.

### A circle is divided into eight sectors that are separated such that the first section is x degrees, the second is 2x degrees, and so forth. What is the angular measure of the second-largest sector?

• A.

40

• B.

60

• C.

70

• D.

90

• E.

120

C. 70
Explanation
The circle is divided into eight sectors, and each sector is separated by an increasing number of degrees. The first sector is x degrees, the second is 2x degrees, and so on. To find the angular measure of the second-largest sector, we need to determine the value of x. Since the sectors are separated by an increasing number of degrees, we can deduce that the value of x must be smaller than the value of 70 degrees. Therefore, the angular measure of the second-largest sector is 70 degrees.

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• 24.

### If two different circles are concentric, at how many points will they intersect?

• A.

0

• B.

1

• C.

2

• D.

3

• E.

More than 3

A. 0
Explanation
When two circles are concentric, it means that they share the same center point. Since the center point is the only point common to both circles, they do not intersect at any other point. Therefore, the correct answer is 0.

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• 25.

### The area of a circle 6 meters in diameter exceeds the combined areas of a circle 4 meters in diameter and a circle 2 meters in diameter by how many square meters?

• A.

0

• B.

3 pi

• C.

4 pi

• D.

5 pi

C. 4 pi
Explanation
The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle. In this question, the diameter of the first circle is given as 6 meters, so the radius is 6/2 = 3 meters. The area of this circle is therefore A1 = π(3^2) = 9π square meters. The combined areas of the second and third circles can be calculated in the same way. The diameter of the second circle is 4 meters, so the radius is 4/2 = 2 meters, and its area is A2 = π(2^2) = 4π square meters. The diameter of the third circle is 2 meters, so the radius is 2/2 = 1 meter, and its area is A3 = π(1^2) = π square meters. The combined areas of the second and third circles is A2 + A3 = 4π + π = 5π square meters. Therefore, the difference in area is A1 - (A2 + A3) = 9π - 5π = 4π square meters.

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• Current Version
• Oct 13, 2023
Quiz Edited by
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• Mar 09, 2007
Quiz Created by
Vaibhav Agarwal

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