Algebra 1 Semester 1 exam review - My CCSD

Algebra 1 Semester 1 exam review 1. Solve for x. −10𝑥 = 5(3 + 𝑥) (A) x = –1 (B) x = –4 (C) x = 1 (D) x = 4

Algebra 1 Semester 1 exam review 2. Units of measurement

Algebra 1 Semester 1 exam review 3. The population N of students in a school can be modeled with the function N = 1500 – 30y, where y is the number of years since 2000. Which statement is true? (A) The student population is increasing by 30 students/year. (B) The student population is decreasing by 30 students/year. (C) The student population is decreasing by 1500 students/year. (D) The student population is increasing by 1500 students/year.

Algebra 1 Semester 1 exam review

4. Safety goggles function best at room temperature, or 70°F. A pair of special safety goggles can function at temperatures that differ from this value by at most 30°F. Write an absolute-value inequality to find the range of acceptable temperatures.

𝑡 − 70 ≤ 30

Algebra 1 Semester 1 exam review 5. Which graph represents the linear inequality –3x + 4y ≤ 12?

Algebra 1 Semester 1 exam review 6. What is the solution set of 3 𝑥 − 5 = 18

(A) (B) (C) (D)

14, −14 −4, 14 14 −4

Algebra 1 Semester 1 exam review 7. Which is the graph of −6𝑚 − 8𝑛 = −24?

Algebra 1 Semester 1 exam review 8. The base salary for a job is $1,800 per month. For each full year a person holds the job, the salary increases by $150 per month. Which gives the monthly salary S as a function of years worked, y? 𝐴 𝐵 𝐶 𝐷

𝑆 𝑦 𝑆 𝑦 𝑆 𝑦 𝑆 𝑦

= 1800 + 150𝑦 = 1800𝑦 + 150𝑦 = 𝑦 + 150 = 1950𝑦

Algebra 1 Semester 1 exam review 9. Supply and demand Show example on board

Algebra 1 Semester 1 exam review 10. Which best describes the exponential function 𝑓 𝑥 = 1.034 𝑥

(A) (B) (C) (D)

f(x) is a growth function with a rate of 34%. f(x) is a growth function with a rate of 3.4%. f(x) is a decay function with a rate of 34%. f(x) is a decay function with a rate of 96.6%.

Algebra 1 Semester 1 exam review 11. A sequence is defined as 𝑓 𝑛 = 4𝑛 + 3. Which graph shows the first 5 terms of the sequence f?

Algebra 1 Semester 1 exam review 12. What is the x-coordinate of the point of intersection of these two lines? 𝑦 = 3𝑥 − 4 −2𝑥 + 𝑦 = −1

(A) 3 (B) 5 (C) -3 (D) The lines do not intersect.

Algebra 1 Semester 1 exam review For questions 13–16, use this scenario. A group of 4 people equally share the cost of a meal, including tax and tip. The price of the meal equals m. Tax is 6% of the meal’s price and the tip will be 10% of the meal’s price. For each expression below, choose (A) True if the expression correctly represents each person’s share of the total cost of the meal. Choose (B) False if it does not.

Algebra 1 Semester 1 exam review 17. Which sequence is equivalent to t(n) = 5 + 3n, where n ≥ 1? (A) t(1) = 5; t(n + 1) = t(n) + 3 (B) t(1) = 5; t(n + 1) = 3t(n) (C) t(1) = 8; t(n + 1) = 3t(n) (D) t(1) = 8; t(n + 1) = t(n) + 3

Algebra 1 Semester 1 exam review For questions 18–21, consider the point (-1, 4) which lies on the line 𝑙 in the coordinate plane.

18. x = 4 could represent line 𝑙. (A) True (B) False


19. y = 4 could represent line 𝑙. (A) True (B) False


20. −𝑥 + 4𝑦 = 0 could represent line 𝑙. (A) True (B) False


21. 𝑦 = −4𝑥 could represent line 𝑙. (A) True (B) False

Algebra 1 Semester 1 exam review

22. The maximum height reached by a bouncing ball is given by ℎ 𝑥 = 10(0.9)𝑥 where h is measured in feet and x is the bounce number. Describe the domain of this function and what it means when x = 0 .

Algebra 1 Semester 1 exam review 23. The graph shows a system of inequalities. Write the systems of inequalities 2 𝑦 ≤ 𝑥+4 3 𝑦 > −2𝑥 − 1

Algebra 1 Semester 1 exam review 24. A system of two linear equations has no solution. Which statement is true about the lines’ slopes and y-intercepts?

Algebra 1 Semester 1 exam review 25. The number of bacteria in a dish is initially measured to be N. The population grows by 8.2% per hour. Which expression represents the number of bacteria after h hours?

(A) (B) (C) (D)

𝑁 1+

0.082 ℎ ℎ ℎ

𝑁(0.82) N 1 + ℎ 8.2 𝑁(1.082)ℎ

Algebra 1 Semester 1 exam review 26. A club has two membership levels: gold and silver. Gold members pay $20 per year and silver members pay $10 per year. The club made $500 on memberships this year. Let g = the number of gold members this year and let s = the number of silver members this year. Which graph models the relationship between the number of gold and silver members?

Algebra 1 Semester 1 exam review 27. Which shows the inequality 𝑚𝑚 + 𝑛 ≤ 𝑝 solved for x, where 𝑚 is a negative number, and n and m are positive numbers?

-𝑚𝑚 + 𝑛 ≤ 𝑝 −𝑛 −𝑛 -𝑚𝑚 ≤ 𝑝 − 𝑛 −𝑚 − 𝑚 𝑝−𝑛 𝑥 ≥ −𝑚

𝑛−𝑝 𝑥 ≥ 𝑚

Algebra 1 Semester 1 exam review For questions 28–29, use the linear functions described below. 𝒙

𝑔(𝑥)

-3

0

3

6

0

5

10

15

ℎ 𝑥 = 2𝑥 − 4

28. The slope of function g is less than the slope of function h. (A) True (B) False

Algebra 1 Semester 1 exam review For questions 28–29, use the linear functions described below. 𝒙

𝑔(𝑥)

-3

0

3

6

0

5

10

15

ℎ 𝑥 = 2𝑥 − 4

29. The y-intercept of function g is less than the y-intercept of function h. (A) True (B) False

Algebra 1 Semester 1 exam review 30. This graph shows a model of food energy production, per person, in the United States from the year 1960 to the year 2010. Example from board

Algebra 1 Semester 1 exam review For questions 31–32, consider this scenario. Sam is working with the function s(x). He found that s(5) = 6. Tina is working with the function t(x). She found that t(5) = 6. 31. The functions s(x) and t(x) must be the same function. (A) True (B) False

Algebra 1 Semester 1 exam review For questions 31–32, consider this scenario. Sam is working with the function s(x). He found that s(5) = 6. Tina is working with the function t(x). She found that t(5) = 6. 32. The point (6, 5) lies on both of the graphs 𝑦 = 𝑠(𝑥) and 𝑦 = 𝑡 𝑥 . (A) True (B) False

Algebra 1 Semester 1 exam review 33. Which graph models 20% growth?

Algebra 1 Semester 1 exam review 34. A sports league has 20 teams. Each team must send at least one player to the league’s annual meeting, but may send as many as 2. Holding the meeting costs the league $500 for the facility, plus $40 per player for food and materials. The league cannot spend more than $1,700 on the meeting. Which inequality shows the number of players, n, who could be at the meeting?

(A) 0 ≤ n ≤ 30 (C) 20 ≤ n ≤ 40

(B) 0 ≤ n ≤ 20 (D) 20 ≤ n ≤ 30

Algebra 1 Semester 1 exam review 35. The first five terms of a sequence are given. 128 512 50, 40, 32, , 5 25 Which equation describes the nth term of the sequence? 𝐴

𝐵

4 𝑡 𝑛 = 62.5 5 𝑛 4 𝑡 𝑛 = 5

𝑛

𝐶

𝐷

5 𝑡 𝑛 = 62.5 4

𝑛

𝑡 𝑛 = 62.5(5)𝑛

Algebra 1 Semester 1 exam review For questions 36–37, use this graph showing the line y = f(x) where the domain is x ≥ 0. 36. The y-intercept of y = f(x) + 3 equals 9. (A) True (B) False 37. The slope of y = f(x) + 3 equals 4. (A) True (B) False

Algebra 1 Semester 1 exam review 38. Use the table below. 𝒙

𝑓(𝑥) ℎ(𝑥)

𝑔(𝑥)

0

1

2

3

250

300

350

400

250

500

1000

2000

250

25

2.5

0.25

+50

×2 ÷ 10

Which functions are linear? Which functions are exponential?

Linear: 𝑓(𝑥)

exponentional: h 𝑥 , 𝑔(𝑥)

Algebra 1 Semester 1 exam review 39. The solution to the system of equations 3𝑥 + 5𝑦 = 𝑎 −2𝑥 + 2𝑦 = 𝑏

is the ordered pair (3, k). Which is equal to a + b?

7𝑘 + 3