algebra i – midterm exam review
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8th – Midterm Exam Review
Circle the correct answer. 1. Which is an algebraic expression for “the quotient of r + 5 and b”?
a. !!!! b.
!!!!
c. !
!! ! d.
!! + 5
2. Simplify 8 ∙ (5 − 3)! + 9.
a. 41 b. 57 c. 40 d. 22
3. Evaluate (r – s)2 for r = 9 and s = 6.5
a. 2.5 b. 3.5 c. 6.25 d. 12.25
4. Which of the following is NOT true of equations and inequalities?
a. Equations and inequalities are both mathematical sentences. b. Equations have one solution, whereas an inequality may have multiple
solutions. c. Equations are like a balanced scale, and inequalities are like an unbalanced
scale. d. Equations and inequalities are both mathematical phrases.
5. Which of the following represents an irrational number? a. 5 b. !
! c. 𝜋 d. 0.333333….
6. The variable a is an integer. Which of the following could NOT equal a3?
a. -‐27 b. -‐16 c. 8 d. 64
7. In which quadrant on the coordinate plane is (-‐3, -‐1)? a. Quadrant I b. Quadrant II c. Quadrant III d. Quadrant IV
8. Suppose you take a survey of all the schools in your state. What would you expect the relationship between the number of students and the number of teachers in each school to be?
a. positive correlation b. negative correlation c. no correlation d. cannot be determined
9. Evaluate -‐2xy for x = 3 and y = 4. a. -‐234 b. -‐68 c. -‐24 d. 24 10. Which compound inequality has the same meaning as 𝑥 + 4 < 8?
a. −12< 𝑥 < 4 b. −12 > 𝑥 > 4 c. 𝑥 < −12 𝑜𝑟 𝑥 > 4 d. 𝑥 > −12 𝑜𝑟 𝑥 < 4
Answer the following. Be sure to SHOW ALL WORK! 11. The sum of three consecutive integers is 216. Find the integers. 12. A 3.5 ft. child casts a 60-‐in. shadow. She is standing next to a telephone pole
that casts a 50-‐ft. shadow. How tall is the telephone pole?
13. Find the median, mode and range of the following data:
42, 18, 55, 37, 57, 37, 49, 47, 37 Median – Mode – Range –
14. What percentage of 56 is 14? 15. What is 30% of 130? 16. A cell phone costs $50. It is on sale for 30% off. How much money would you save? 17. A restaurant bill is $20. If you leave a 15% tip, what is the total cost of your meal (including tip)?
18. Find the hypotenuse of a right triangle with legs of 6 cm and 8 cm. 19. Do the following side lengths form a right triangle? a. 5, 8, 10 b. 3, 4, 5 Solve the following equations/inequalities. 20. −7𝑦 = 84 21. 5𝑡 − 4 ≥ 16 22. −8y – 4 > 28 23.
!! + 4 = 16
24. 7 𝑤 – 3 + 14 = 28 25.
!! (4y – 16) = 40
26. −9𝑘 = 81 27. !!!!
!= 4𝑥
Solve each equation. If the equation is an identity or if it has no solution, write identity or no solution. ***Remember that it is possible to get one solution for the equations below! 30. 14 – (2𝑞 + 5) = −2𝑞 + 9 31. 6𝑥 = 4 (𝑥 + 5) 32. 6 (𝑥 − 3) = 6𝑥 – 8 33. −8𝑥 + 14 = −2 (4𝑥 – 7) Evaluate each function rule for 𝒙 = 𝟒. 34. 𝑓 𝑥 = 14− 2𝑥 35. 𝑔 𝑥 = 𝑥! + 30
36. ℎ 𝑥 = !!!!!!
Find the range of each function for the given domain. 37. 𝑓 𝑥 = 9𝑥 + 1; −3, 0, 6 38. 𝑔 𝑥 = 𝑥! − 4; {−4, 1, 2, 4, 6} 39. ℎ 𝑥 = !!!
!; {−10, 0, 10, 20}
Simplify. Write each answer in standard form. 40. 7𝑥! − 3𝑥 + 1 − (𝑥! + 𝑥! − 2)
Simplify the product. Write in standard form. 41. (𝑥 + 3)(𝑥 – 2) 42. (𝑤 – 9)(𝑤 + 9) 43. 4𝑥 – 7 2𝑥 – 5 44. ℎ + 3 3ℎ − 6
45. Find the slope of the following linear function:
Calculate the slope of the line that passes through the following points. 47. (7, 2), (9, 0) 48. (3, 4), (9, 4) Identify the slope and y-‐intercept in the following linear equations: 49. 𝑦 = 8𝑥 − 3 slope: ____________________ y-‐intercept: _____________________ 50. 𝑦 = − !
!𝑥 slope: ____________________ y-‐intercept: _____________________
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