Algebra 1 Quarter 3 Exam

Systems & Exponentials • 50 Questions

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Date:

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Instructions: Select the best answer for each question. For equations and sequences, ensure your final choice matches your calculations. You may use the margins for scratch work. This exam contains 50 multiple-choice questions across two sections.

Part I Systems of Equations

1. What is the solution to a system of linear equations?

A) The sum of the x-intercepts of both lines.

B) Any point located on at least one of the lines.

C) The point \((x, y)\) where the two lines intersect.

D) The distance between the lines at the origin.

2. Solve the system by graphing: \(y = x - 2\) and \(y = -3x + 2\)

A) \((1, 1)\)

B) \((1, -1)\)

C) \((-1, 1)\)

D) \((2, 0)\)

3. Solve the system by graphing: \(y = -3x + 1\) and \(y = x - 7\)

A) \((2, -5)\)

B) \((-5, 2)\)

C) \((1, -6)\)

D) \((0, 1)\)

4. Which of these is the first step when graphing \(4x - 2y = 6\)?

A) Multiply the entire equation by 2.

B) Rewrite the equation in slope-intercept form.

C) Substitute 0 for \(x\) only to find the slope.

D) Add \(2y\) to both sides then divide by \(x\).

5. Solve by graphing: \(5x + 5y = 15\) and \(2x - 2y = 10\)

A) \((3, 0)\)

B) \((4, -1)\)

C) \((1, 2)\)

D) \((2, -1)\)

6. If two lines have different slopes, how many solutions does the system have?

A) Exactly one

B) Exactly two

C) None

D) Infinitely many

7. Which system is represented by lines that are parallel?

A) Same slope, same y-intercept

B) Same slope, different y-intercept

C) Different slope, same y-intercept

D) Different slope, different y-intercept

8. Solve the system: \(y = \frac{1}{2}x + 2\) and \(y = -x - 1\)

A) \((-2, 1)\)

B) \((1, -2)\)

C) \((-1, 0)\)

D) \((0, 2)\)

9. Solve by substitution: \(-2x + y = -8\) and \(7x + y = 10\)

A) \((2, 4)\)

B) \((2, -4)\)

C) \((-2, -4)\)

D) \((4, 0)\)

10. Solve by substitution: \(3x + y = -9\) and \(y = 5x + 7\)

A) \((-2, -3)\)

B) \((-2, 3)\)

C) \((2, -1)\)

D) \((0, -9)\)

11. Solve: \(x + 4y = 6\) and \(x - y = 1\)

A) \((2, 1)\)

B) \((1, 0)\)

C) \((3, 2)\)

D) \((2, 2)\)

12. Solve: \(2x + 3y = 4\) and \(y + 3x = 6\)

A) \((2, 0)\)

B) \((0, 2)\)

C) \((1, 3)\)

D) \((2, -1)\)

Algebra 1 Quarter 3 Exam • Page 2

13. In substitution, if you solve for \(x\) in the first equation, what is the next step?

A) Graph both on the same plane.

B) Substitute the expression for \(x\) into the second equation.

C) Substitute the expression for \(x\) back into the first equation.

D) Multiply both equations by a common factor.

14. Solve the system: \(y = 2x - 5\) and \(4x - y = 7\)

A) \((1, -3)\)

B) \((3, 1)\)

C) \((2, -1)\)

D) \((4, 3)\)

15. Solve: \(x = y + 3\) and \(2x + y = 12\)

A) \((5, 2)\)

B) \((3, 0)\)

C) \((6, 3)\)

D) \((4, 1)\)

16. Solve: \(y = -4x\) and \(x + y = 6\)

A) \((2, -8)\)

B) \((-2, 8)\)

C) \((-1, 4)\)

D) \((1, -4)\)

17. Solve: \(x = 2y - 4\) and \(7x + y = 17\)

A) \((2, 3)\)

B) \((1, 2.5)\)

C) \((0, 2)\)

D) \((3, 3)\)

18. Solve by elimination: \(x + y = 10\) and \(x - y = 4\)

A) \((7, 3)\)

B) \((6, 4)\)

C) \((5, 5)\)

D) \((8, 2)\)

19. Solve by elimination: \(2x + y = 7\) and \(x - y = 2\)

A) \((3, 1)\)

B) \((1, 3)\)

C) \((3, 2)\)

D) \((2, 0)\)

20. Solve: \(4x + 6y = -8\) and \(x - 2y = -2\)

A) \((2, 0)\)

B) \((-2, 0)\)

C) \((0, -2)\)

D) \((-1, -1)\)

21. Solve: \(9x - 2y = 34\) and \(5x + 2y = -6\)

A) \((2, -8)\)

B) \((4, 1)\)

C) \((2, 8)\)

D) \((-2, -8)\)

22. Solve: \(x + 6y = 28\) and \(2x - 3y = -19\)

A) \((2, 5)\)

B) \((5, 2)\)

C) \((-2, 5)\)

D) \((4, 4)\)

23. Solve: \(8x - 7y = -3\) and \(6x - 5y = -1\)

A) \((4, 5)\)

B) \((5, 4)\)

C) \((2, 3)\)

D) \((-1, -1)\)

24. Which multiplier should be used to eliminate \(y\) in: \(3x + 2y = 12\) and \(x - y = 4\)?

A) Multiply first eq. by 2.

B) Multiply second eq. by 2.

C) Multiply first eq. by 3.

D) Multiply second eq. by 3.

25. Solve the special system: \(4x + 2y = -14\) and \(y = -2x - 6\)

A) \((0, -6)\)

B) No solution

C) Infinitely many solutions

D) \((-2, -2)\)

Algebra 1 Quarter 3 Exam • Page 3

26. Solve: \(x = y + 2\) and \(-3x + 3y = 6\)

A) No solution

B) Infinitely many solutions

C) \((2, 0)\)

D) \((0, -2)\)

27. If a system of equations yields the statement \(0 = 0\) after substitution, what does this indicate?

A) The solution is the origin \((0, 0)\).

B) The system has no solution.

C) The system has infinitely many solutions.

D) An error was made; equations cannot equal zero.

28. You spend $20 on paint (\(x\)) and brushes (\(y\)). Paint is $4 each, brushes are $0.50 each. You buy twice as many brushes as paint. Which system represents this?

A) \(4x + 0.5y = 20\) and \(y = 2x\)

B) \(4x + 0.5y = 20\) and \(x = 2y\)

C) \(0.5x + 4y = 20\) and \(y = 2x\)

D) \(4x + 2y = 20\) and \(x + y = 2\)

29. In the paint/brush problem (Q28), how many tubes of paint and brushes did you purchase?

A) 2 paint, 4 brushes

B) 4 paint, 8 brushes

C) 5 paint, 10 brushes

D) 10 paint, 20 brushes

30. A movie theater sold 150 tickets and made $1,560. Adults are $12, children are $8. How many child tickets were sold?

A) 60

B) 90

C) 75

D) 50

Part II Exponential Essentials

31. Rewrite \(y = 10(0.65)^{t/8}\) to identify percent rate of change. What is the approximate rate of decay?

A) 35%

B) 5%

C) 65%

D) 95%

32. Identify growth/decay and rate for: \(f(t) = 4(1.25)^{t+3}\)

A) Decay; 25%

B) Growth; 1.25%

C) Growth; 25%

D) Decay; 75%

33. Which type of function does the table represent? (x: 0,1,2,3; y: 3,6,12,24)

A) Linear growth

B) Exponential growth

C) Exponential decay

D) Neither

34. A TV is $1500 and decreases by 14% each year. Which function represents value \(y\) after \(t\) years?

A) \(y = 1500(1.14)^t\)

B) \(y = 1500(0.14)^t\)

C) \(y = 1500(0.86)^t\)

D) \(y = 14(1500)^t\)

35. You earn 5% interest compounded quarterly. How many times per year is interest calculated?

A) 1

B) 2

C) 4

D) 12

36. Solve the equation: \(5^x = 5^{3x-2}\)

A) \(x = 1\)

B) \(x = -1\)

C) \(x = 2\)

D) \(x = 0\)

37. Solve the equation: \(\frac{1}{9} = 3^{x+6}\)

A) \(x = -4\)

B) \(x = -8\)

C) \(x = -3\)

D) \(x = 2\)

38. Solve the equation: \(2^x = \frac{1}{128}\)

A) \(x = -7\)

B) \(x = -6\)

C) \(x = 7\)

D) \(x = 64\)

Algebra 1 Quarter 3 Exam • Page 4

39. Solve the equation: \(256^{x+2} = 16^{3x-1}\)

A) \(x = 3\)

B) \(x = 5\)

C) \(x = -5\)

D) \(x = 2.5\)

40. Solve the equation: \(27^{2x+2} = 81^{x+4}\)

A) \(x = 2\)

B) \(x = 5\)

C) \(x = 4\)

D) \(x = 10\)

41. Find the common difference for: \((n=1, a_n=-6), (2, 8), (3, 22), (4, 36)\)

A) \(d = 14\)

B) \(d = -14\)

C) \(d = 2\)

D) \(d = 6\)

42. Identify the explicit rule for: \(400, 100, 25, 6.25, ...\)

A) \(a_n = 400(4)^{n-1}\)

B) \(a_n = 400(0.25)^{n-1}\)

C) \(a_n = 100(4)^{n-1}\)

D) \(a_n = 400 - 300(n-1)\)

43. Find the recursive rule for arithmetic: \(a_1 = -6, d = 14\)

A) \(a_n = a_{n-1} + 14\)

B) \(a_n = 14a_{n-1}\)

C) \(a_n = a_{n-1} - 6\)

D) \(a_n = -6(14)^{n-1}\)

44. A geometric sequence has \(a_1 = 3\) and \(a_2 = -12\). What is the third term, \(a_3\)?

A) -27

B) 36

C) 48

D) -48

45. Modeling \(P = (0.99988)^a\). Identify the decay factor.

A) 1

B) 0.00012

C) 0.99988

D) -0.99988

46. You run 20% farther each day. Day 1: 1km. Which rule represents distance on Day \(n\)?

A) \(a_n = 1(0.20)^{n-1}\)

B) \(a_n = 1(1.20)^{n-1}\)

C) \(a_n = 20(1)^{n-1}\)

D) \(a_n = 1 + 0.20(n-1)\)

47. Solve the equation: \(3^{x-2} = 1\)

A) \(x = 0\)

B) \(x = 2\)

C) \(x = -2\)

D) \(x = 1\)

48. Solve the equation: \((\frac{1}{16})^{3x} = 64^{2(x+8)}\)

A) \(x = -2\)

B) \(x = -4\)

C) \(x = 4\)

D) \(x = -2.67\)

49. Annual growth rate for \(y = (1.06)^{8t}\) as \(y \approx a(1+r)^t\)? (Round to whole %)

A) 6%

B) 48%

C) 59%

D) 159%

50. What is the next term in the sequence: \(2, 6, 18, 54, ...\)?

A) 108

B) 72

C) 162

D) 216

Algebra 1 Quarter 3 Exam Document

Algebra 1 Quarter 3 Exam Document

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