Title: FIRST PARTIAL EXAM
Course: 2025 Probabilidad y Estadística

Q: A city has streets that run north and south, and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure. The walking distance between points A and B is 7 blocks; that is, 4 blocks east and 3 blocks north. To find the straight-line distance d, we must use the Distance Formula.

[Image] | [Image]

Find the walking distance and the straight-line distance between the corner of 4th St. and 2nd Ave. and the corner of 19th St. and 38th Ave.
- The walking distance is 51 blocks and the straight-line distance is 40 blocks. (Incorrecta)
- The walking distance is 50 blocks and the straight-line distance is 39 blocks. (Incorrecta)
- The walking distance is 53 blocks and the straight-line distance is 41 blocks. (Incorrecta)
- The walking distance is 50 blocks and the straight-line distance is 40 blocks. (Incorrecta)
- The walking distance is 51 blocks and the straight-line distance is 39 blocks. (Correcta)
A: The walking distance is 51 blocks and the straight-line distance is 39 blocks.

Q: A rectangle has the vertices of A(4, 1), B(9, 1), C(4, –1), and D(9, –1) on a coordinate plane. Find the area of the rectangle.

​
- 9 (Incorrecta)
- 14 (Incorrecta)
- 10 (Correcta)
- 11 (Incorrecta)
- 6 (Incorrecta)
A: 10

Q: An equation and its graph are given. Find the x-intercepts.

​

[Image]

​ [Image]

​
- 0 (Incorrecta)
- 0, 2 (Incorrecta)
- 2 (Incorrecta)
- 0, 5 (Correcta)
- 5 (Incorrecta)
A: 0, 5

Q: Calculate the y-coordinates in the table below for the function [Image].

x | y
–4 | ?
–1 | ?
1 | ?
2 | ?
7 | ?

​

​

x | y
–4 | 249
–1 | 24
1 | 9
2 | 9
7 | 84
- ​​​ x | y –4 | 249 –1 | 24 1 | 9 2 | 9 7 | 84 ​ (Incorrecta)
- ​ x | y –4 | 84 –1 | 9 1 | 9 2 | 24 7 | 247 (Incorrecta)
- ​ x | y –4 | –84 –1 | –9 1 | –9 2 | –24 7 | –249 ​ (Incorrecta)
- ​ x | y –4 | 84 –1 | 8 1 | 9 2 | 24 7 | 249 ​​ (Incorrecta)
- ​​ x | y –4 | 84 –1 | 9 1 | 9 2 | 24 7 | 249 ​ (Correcta)
A: ​​ x | y –4 | 84 –1 | 9 1 | 9 2 | 24 7 | 249 ​

Q: Calculate the y-coordinates in the table below for the function [Image].

x | y
–5 | ?
–2 | ?
1 | ?
2 | ?
3 | ?

​

​

x | y
–5 | ?
–2 | ?
1 | ?
2 | ?
3 | ?

x | y
–5 | ?
–2 | ?
1 | ?
2 | ?
3 | ?
- ​​ x | y –5 | 19 –2 | 10 1 | 1 2 | –2 3 | –5 (Correcta)
- ​ x | y –5 | 20 –2 | 11 1 | 3 2 | 1 3 | –1 (Incorrecta)
- ​ x | y –5 | 17 –2 | 8 1 | 0 2 | –3 3 | –6 (Incorrecta)
- ​ x | y –5 | –5 –2 | –2 1 | 1 2 | 10 3 | 19 (Incorrecta)
- ​ x | y –5 | –19 –2 | –10 1 | –1 2 | 2 3 | 12 (Incorrecta)
A: ​​ x | y –5 | 19 –2 | 10 1 | 1 2 | –2 3 | –5

Q: Determine the graph of the equation [Image]

​
- [Image] (Incorrecta)
- ​ [Image] (Correcta)
- [Image] (Incorrecta)
- [Image] (Incorrecta)
- [Image] (Incorrecta)
A: ​ [Image]

Q: Determine what form the given equation represents.

​

[Image]

​
- The equation represents a single point. (Correcta)
- The equation represents an ellipse. (Incorrecta)
- The equation represents an empty set. (Incorrecta)
- The equation represents a circle. (Incorrecta)
- The equation represents a semi-circle with a curve approaching the positive x-axis. (Incorrecta)
A: The equation represents a single point.

Q: Determine which point A(5, 6) or B(4, 7) is closer to the origin?

​
- Point A(5, 6) is closer to the origin. (Correcta)
- Point B(4, 7) is closer to the origin. (Incorrecta)
A: Point A(5, 6) is closer to the origin.

Q: Draw the square with vertices A(1, 3) , B(3, 3) , C(3, 5) , and D(1, 5) on a coordinate plane. Find the area of the square.

​
- [Image] ​ The area is 4. (Incorrecta)
- [Image] ​The area is 2. (Incorrecta)
- [Image] The area is 4. (Correcta)
- [Image] The area is 2. (Incorrecta)
- [Image] The area is 8. (Incorrecta)
A: [Image] The area is 4.

Q: Fill in the table of values for the function [Image].

x | y
–2 | ?
–1 | ?
1 | ?
2 | ?
3 | ?
- ​ x | y –2 | 46 –1 | 33 1 | 29 2 | 15 3 | –23 ​ ​ (Incorrecta)
- ​ x | y –2 | –47 –1 | –33 1 | –29 2 | –15 3 | 23 ​ ​ (Incorrecta)
- ​ x | y –2 | –23 –1 | 15 1 | 29 2 | 33 3 | 47 ​ ​ (Incorrecta)
- ​ x | y –2 | 47 –1 | 33 1 | 29 2 | 13 3 | –23 ​ ​ (Incorrecta)
- ​ x | y –2 | 47 –1 | 33 1 | 29 2 | 15 3 | –23 ​ ​ (Correcta)
A: ​ x | y –2 | 47 –1 | 33 1 | 29 2 | 15 3 | –23 ​ ​

Q: Fill in the table of values for the function [Image].

x | y
–2 | ?
–1 | ?
1 | ?
2 | ?
3 | ?

​
- ​ x | y –2 | –10 –1 | 35 1 | 35 2 | –10 3 | –205 (Correcta)
- ​ x | y –2 | –205 –1 | –10 1 | 35 2 | 36 3 | –10 (Incorrecta)
- ​ x | y –2 | 10 –1 | –35 1 | –35 2 | 10 3 | 205 (Incorrecta)
- ​ x | y –2 | –10 –1 | 35 1 | 34 2 | –10 3 | –205 (Incorrecta)
- ​ x | y –2 | –9 –1 | 35 1 | 35 2 | –10 3 | –205 (Incorrecta)
A: ​ x | y –2 | –10 –1 | 35 1 | 35 2 | –10 3 | –205

Q: Fill in the table of values for the function y = | x- 8 | .

x | y
–3 | ?
–2 | ?
–1 | ?
4 | ?
7 | ?

​
- ​ x | y –3 | -11 –2 | -10 –1 | 9 4 | 4 7 | 1 ​ ​ (Incorrecta)
- ​ x | y –3 | 11 –2 | 10 –1 | -9 4 | -4 7 | -1 ​ ​ (Incorrecta)
- ​ x | y –3 | –11 –2 | –10 –1 | –9 4 | –4 7 | –4 ​ ​ (Incorrecta)
- ​ x | y –3 | 1 –2 | 4 –1 | 9 4 | 10 7 | 11 ​ ​ (Incorrecta)
- ​ x | y –3 | 11 –2 | 10 –1 | 9 4 | 4 7 | 1 ​ ​ ​ (Correcta)
A: ​ x | y –3 | 11 –2 | 10 –1 | 9 4 | 4 7 | 1 ​ ​ ​

Q: Fill the table of values for the function [Image].

x | y
–8 | ?
–4 | ?
1 | ?
4 | ?
8 | ?

​
- ​ x | y –8 | 1 –4 | 2 1 | 8 4 | –2 8 | –1 ​ (Incorrecta)
- ​ x | y –8 | 1 –4 | 2 1 | –8 4 | –2 8 | –1 ​ ​ (Incorrecta)
- ​ x | y –8 | –1 –4 | –2 1 | 8 4 | 2 8 | 1 ​ (Correcta)
- ​ x | y –8 | –1 –4 | –2 1 | 8 4 | –3 8 | –9 ​ (Incorrecta)
- ​ x | y –8 | –1 –4 | –2 1 | 8 4 | –8 8 | –4 ​ (Incorrecta)
A: ​ x | y –8 | –1 –4 | –2 1 | 8 4 | 2 8 | 1 ​

Q: Find the coordinates of the points shown in the figure.

​

[Image]

​
- (1, - 2), (4, 4) (Correcta)
- (- 1, 2), (4, - 4) (Incorrecta)
- (1, 2), (4, 4) (Incorrecta)
- (1, - 2), (- 4, 4) (Incorrecta)
- (1, - 2), (4, - 4) (Incorrecta)
A: (1, - 2), (4, 4)

Q: Find the x - and y-intercepts of the graph of the equation [Image].

​
- [Image] (Incorrecta)
- ​ [Image] (Incorrecta)
- [Image] (Incorrecta)
- [Image] (Correcta)
- [Image] (Incorrecta)
A: [Image]

Q: Find the x and y - intercepts of the graph of [Image].

​
- x - intercepts [Image], y - intercepts [Image] (Incorrecta)
- x - intercepts [Image], y - intercepts [Image] (Correcta)
- x - intercept [Image], y - intercepts [Image] (Incorrecta)
- x - intercept [Image], y - intercept [Image] (Incorrecta)
- x - intercepts [Image], y - intercepts [Image] (Incorrecta)
A: x - intercepts [Image], y - intercepts [Image]

Q: Find the x- and y-intercepts of the graph of the equation [Image].

​
- [Image] (Incorrecta)
- [Image] (Incorrecta)
- [Image] (Incorrecta)
- [Image] (Incorrecta)
- [Image] (Correcta)
A: [Image]

Q: If the points P(–7, –4), Q(1, –1), and R(5, 4) are plotted on a coordinate plane, where should the point S be located so that the figure PQRS is a parallelogram?

​
- (–2, 1) (Incorrecta)
- (–3, –1) (Incorrecta)
- (–3, 1) (Correcta)
- (1, –4) (Incorrecta)
- (–4, 2) (Incorrecta)
A: (–3, 1)

Q: If the points P(5, 4), Q(0, 9), and R(–5, 4) are drawn on a coordinate plane, where must the point S be located so that the figure PQRS is a square?

​
- (0, –1) (Correcta)
- (–3, 0) (Incorrecta)
- (0, 0) (Incorrecta)
- (–1, 0) (Incorrecta)
- (0, –2) (Incorrecta)
A: (0, –1)

Q: Test the equation [Image] for symmetry.

​
- The symmetry is around the x-axis. (Incorrecta)
- The symmetry is around the y-axis. (Incorrecta)
- The symmetry is around the point (4, 4). (Incorrecta)
- The symmetry is around the origin. (Correcta)
- There is no symmetry. (Incorrecta)
A: The symmetry is around the origin.

Q: Test the equation for symmetry to determine the correct graph.

​

[Image]

​
- origin- symmetry [Image] (Incorrecta)
- x-axis symmetry [Image] (Incorrecta)
- x-axis symmetry [Image] (Correcta)
- y-axis symmetry [Image] (Incorrecta)
- none (Incorrecta)
A: x-axis symmetry [Image]

Q: The parallelogram has the vertices of A(4, 3), B(8, 3), C(10, 6), and D(6, 6) on a coordinate plane. Find the area of the parallelogram.

​
- 11 (Incorrecta)
- 12 (Correcta)
- 14 (Incorrecta)
- 10 (Incorrecta)
- 13 (Incorrecta)
A: 12

Q: A rectangle has vertices of A(5, 8), B(11, 8), C(5, 2), and D(11, 2) on a coordinate plane. Find the area of the rectangle. Do not add units to your answer.
A: 36