SUHSD 2016-2017 Math 1 Semester 2 Final Exam 1. Solve the following system of linear equations.

𝑦 = −2𝑥 + 2

𝑦 = −2𝑥 − 2

a. (0, 2) b. (−2, 0) c. 𝑁𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 d. 𝐼𝑛𝑓𝑖𝑛𝑖𝑡𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

2. Solve the following system of linear equations.

−3𝑥 − 4𝑦 = 2

3𝑥 + 3𝑦 = −3

a. (1, −2) b. (−2, 1) c. (−6,5) d. (−4, −5)

3. Select ALL the possible answers that contain a correct first step for solving this system of equations by elimination.

Equation A: −4𝑥 + 9𝑦 = 9

Equation B: 𝑥 − 3𝑦 = −6

a. Multiply Equation B by 3 b. Multiply Equation B by 4

c. Multiply Equation A by 3 d. Multiply Equation A by 4

4. Select ALL the possible answers that contain a correct first step for solving this system of equations by

substitution.

Equation A: 𝑦 = 3𝑥 + 2

Equation B: 𝑥 = 3𝑦 − 6

a. Substitute for y in Equation A, 3𝑦 − 6 = 3𝑥 + 2

b. Substitute for y in Equation B, 𝑥 = 3(3𝑥 + 2) − 6

c. Substitute for x in Equation A, 𝑦 = 3(3𝑦 − 6) + 2

d. Substitute for x in Equation B, 3𝑥 + 2 = 3𝑦 − 6

5. Select the graph that corresponds to the given inequality: 3𝑥 + 4𝑦 < 12 a. b.

c. d.

6. Select the corresponding graph for the system of inequalities:

𝑥 + 2𝑦 ≤ 8

−4𝑥 − 2𝑦 ≤ 4

a. b.

c. d.

7. Peter is investigating parallel lines. Peter draws lines r and s as two distinct parallel lines. Select ALL

statements that are true about lines r and s.

a. Lines r and s will never intersect.

b. Lines r and s have no point in common.

c. Lines r and s form at least one right angle.

d. Lines r and s have exactly one point in common.

8. Perpendicular lines are two distinct lines that intersect to form what type of angle?

a. an acute angle b. corresponding angle

c. an obtuse angle d. a right angle

9. What is the definition of an angle? a. An angle is a part of a line starting at a particular point and extending infinitely in one direction.

b. An angle is the set of all points that are a fixed distance from a given point.

c. An angle is all points between and including two given points.

d. An angle is formed by two rays sharing a common endpoint.

10. Two rectangles are shown on the coordinate plane below.

Fernando claims that the two rectangles are congruent. He has found four ways to prove that the rectangles

are congruent. Which ONE does not apply?

a. The rectangles are congruent since a translation of 6 units down and 7 units to the left carries

Rectangle 1 onto Rectangle 2.

b. The rectangles are congruent since a reflection over the x–axis followed by a translation of 7 units

to the right carries Rectangle 1 onto Rectangle 2.

c. The rectangles are congruent since a reflection over the y–axis followed by a translation of 1 unit to

the right and 6 units up carries Rectangle 1 onto Rectangle 2.

d. The rectangles are congruent since a rotation of 180° clockwise about the origin followed by a

translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2.

11. Select ALL the possible transformations that carry a square onto itself.

a. a reflection over one of the square's sides

b. a reflection over one of the square's diagonals

c. a rotation of 90° clockwise about the square's center

d. a rotation of 180° about one of the square's vertices

12. Use the regular polygon in the figure below to answer the following question.

Select the rotation or reflection that does NOT carry Figure 2 onto itself.

a. a rotation of 90° clockwise about the center

b. a rotation of 90° clockwise about one of the vertices

c. a reflection over a line connecting two opposite vertices

d. a reflection over a line connecting the midpoints of two opposite sides

13. A student claims that a rotation of 180° about the center of a regular polygon carries the polygon onto

itself.

Which statement best describes the student's claim?

a. The student's claim is true for all regular polygons.

b. The student's claim is not true for any regular polygon.

c. The student's claim is true for regular polygons with an odd number of sides.

d. The student's claim is true for regular polygons with an even number of sides.

14. A parallelogram is shown below. Which angles and sides must be congruent to each other? Select all that

apply.

a. 𝐴𝐵 ≅ 𝐵𝐶 b. 𝐴𝐵 ≅ 𝐶𝐷 c. 𝐴𝐶 ≅ 𝐵𝐷

d. ∠𝐴 ≅ ∠𝐵 e. ∠B ≅ ∠D f. ∠A ≅ ∠D

15. Anthony draws quadrilateral ABCD below and investigates the reflections and rotations that carry it onto

itself.

Anthony claims that a rotation of 360° is the only transformation that carries quadrilateral ABCD onto itself.

Which of the following transformations could be used to show Anthony's claim is incorrect?

a. A reflection over diagonal AC.

b. A reflection over diagonal BD.

c. A rotation of 90° clockwise about its center.

d. A rotation of 180° clockwise about its center.

16. A triangle with coordinates 𝐴(1, 1), 𝐵(4, 2), 𝐶(3, 5) is translated five units to the left and three units

down. What are the coordinates of the new triangle?

a. 𝐴′(– 2, – 4), 𝐵′(1, – 3), 𝐶′(0, 0) b. 𝐴′(– 4, – 2), 𝐵′(– 1, – 1), 𝐶′(– 2, 2)

c. 𝐴′(– 4, – 2), 𝐵′(– 7, – 3), 𝐶′(– 6, 0) d. 𝐴′(– 4, – 2), 𝐵′(– 1, – 3), 𝐶′(– 2, – 6)

17. Square 1 and Square 2 are shown in the coordinate plane below.

Audrey claims that Square 1 is congruent to Square 2. Which of the following transformations or

sequences of transformations can be used to support her claim? Select TWO that apply.

a. a rotation of 180° about the point (–1, –2)

b. a translation of 6 units right and 4 units up

c. a reflection over the line y = –2 followed by a translation of 10 units right

d. a reflection over the line y = –1 followed by a reflection over the line x = –2

e. a translation of 8 units up followed by a rotation of 180° about the point (–1, 0)

18. In the figure below, ∠𝐻𝐹𝐺 ≅ ∠𝐻𝐾𝐽 and 𝐻𝐹 ≅ 𝐻𝐾.

Select the triangle congruence criterion that can be used to prove that 𝛥𝐻𝐹𝐺 ≅ 𝛥𝐻𝐾𝐽.

a. angle – angle – side (AAS) b. angle – side – angle (ASA)

c. side – angle – side (SAS) d. side – side – side (SSS)

19. In the figure below, ∠𝑇𝑅𝑆 ≅ ∠𝑅𝑇𝑈 and 𝑆𝑅 ≅ 𝑈𝑇.

Which of the following triangle congruence criteria proves that 𝛥𝑇𝑅𝑆 ≅ 𝛥𝑅𝑇𝑈?

a. side – side – side (SSS) b. angle – angle – side (AAS)

c. angle – side – angle (ASA) d. side – angle – side (SAS)

20. The corresponding sides of triangles ABC and DEF are congruent. Which statements are always true for

triangles ABC and DEF? Select ALL that apply.

a. Triangles ABC and DEF are congruent by Side–Side–Side.

b. Triangles ABC and DEF are both equilateral triangles by Side–Side–Side.

c. There is a sequence of rigid motions transformations that carries triangle ABC to triangle DEF.

d. Triangles ABC and DEF are congruent by Angle-Angle-Angle

21. What is the slope of a line parallel to the line 𝑦 = −3

2𝑥 + 3?

a. −3

2 b. −

2

3 c.

3

2 d.

2

3

22. Find the slope of a line perpendicular to the line defined by the equation 3𝑥 – 5𝑦 = 12.

a. 5

3 b.

3

5 c. −

3

5 d. −

5

3

23. What is the distance between the points (−1, 2) and (4,1)?

a. 6 b. 5 c. √26 d. √40

24. Given triangle ABC in the coordinate grid below, what is the perimeter of this triangle?

a. 5 units

b. 6 units

c. 7 units

d. 12 units

25. Two functions, f(x) and g(x), are shown in the coordinate plane. The function g(x) is a transformation of

the function f(x).

What equation represents the relationship between f(x) and g(x)?

a. 𝑔(𝑥) = 𝑓(𝑥) – 3 b. 𝑔(𝑥) = 𝑓(𝑥) + 3

c. 𝑔(𝑥) = 𝑓(𝑥) d. 𝑔(𝑥) = 𝑓(𝑥) – 4

26. Select the histogram that represents the given weights of a group of dogs.

54, 24, 21, 56, 83, 42, 47, 65, 72, 86

Which of the following histograms correctly displays this data set?

a. b.

c. d.

27. Which of the following bar graphs corresponds to a data set with a median of 3? Select TWO that apply.

a. b.

c. d.

28. A student researches the number of miles in the U.S. highway system since 1990 and creates the scatter

plot below. The student draws a line to fit the data points on the scatter plot.

Which of the following statements is true?

a. The line is a good fit as the line passes through the first plotted data point.

b. The line is a good fit as the line shows the same linear trend as the data points.

c. The line is not a good fit as the line should be closer to more of the data points.

d. The line is not a good fit as the line should be below all of the data points, not above.

29. A car manufacturer collects data on the number of gallons of gasoline left in the gas tank after driving for

different numbers of miles. The manufacturer creates a scatter plot of the data and determines that the

correlation coefficient is –0.92.

Select EACH true statement based on this correlation coefficient.

a. There is no correlation between the number of miles driven and the gallons of gasoline left in the tank.

b. There is a weak correlation between the number of miles driven and the gallons of gasoline left in the tank.

c. There is a strong correlation between the number of miles driven and the gallons of gasoline left in the tank.

d. There is a positive correlation between the number of miles driven and the gallons of gasoline left in the tank.

e. There is a negative correlation between the number of miles driven and the gallons of gasoline left

in the tank.

30. A student researches the average cost of electricity, in cents per kilowatt–hour, in the United States since

2000 and creates the scatter plot below.

Which of the following best models a linear function fitted to the data in the scatter plot?

a. b.

c. d.