1. Coordinate Algebra Practice EOCT Answers Unit 1

2. #1 Unit 1 A rectangle has a length of 12 m and a width of 400 cm. What is the perimeter of the rectangle? Step 1: Change 12 meters to centimeters × 100 cm 1 m = 1200 cm 12 m 1 Step 2: Find perimeter using formula P = 2L + 2W 400 cm 1200 cm P = 2(1200 cm) + 2(400 cm) P = 2400 cm + 800 cm P = 3200 cm A. 824 cm B. 1600 cm C. 2000 cm D. 3200 cm

3. #2 Unit 1 The tension caused by a wave moving along a string is found using the formula T =. If m is the mass of the string in grams, L is the length of the string in centimeters, and v is the velocity of the wave in centimeters per second, what is the unit of the tension of the string, T ?

4. #2 Unit 1 (cm) 1 A. gram-centimeters per second squared B. centimeters per second squared C. grams per centimeter-second squared D. centimeters squared per second

5. #3 Unit 1 The distance a car travels can be found using the formula d = rt, where d is the distance, r is the rate of speed, and t is time. How many miles does the car travel, if it drives at a speed of 70 miles per hour for ½ hour? d = r  t = 35 miles A. 35 miles B. 70 miles C. 105 miles D. 140 miles

6. #4 Unit 1 A certain population of bacteria has an average growth rate of 0.02 bacteria per hour. The formula for the growth of the bacteria’s population is A= P (2.71828) 0.02t, where P 0 is the original population, and t is the time in hours. If you begin with 200 bacteria, about how many bacteria will there be after 100 hours? A= 200(2.71828) 0.02  100 A= 200(2.71828) 2 A= 200(7.389046) A= P(2.71828) 0.02t = 1477.81 Answer 1478

7. #5 Unit 1 The sum of the angle measures in a triangle is 180°. Two angles of a triangle measure 20° and 50°. What is the measure of the third angle? Third Angle = x x + 20° + 50° = 180° x + 70° = 180° –70° x = 110° A. 30° B. 70° C. 110° D. 160°

8. #6 Unit 1 Which equation shows P = 2l + 2w when solved for w ? –2l P = 2l + 2w P – 2l = 2w P – 2l 2w 22 P – 2l 2 = = w A. B. C. D.

9. #7 Bruce owns a business that produces widgets. He must bring in more in revenue than he pays out in costs in order to turn a profit.  It costs $10 in labor and materials to make each of his widgets.  His rent each month for his factory is $4000.  He sells each widget for $25. How many widgets does Bruce need to sell monthly to make a profit? A. 160 B. 260 C. 267 D. 400 C = 10x + 4000 R = 25x Cost to make x widgets Revenue (in dollars) from selling x widgets Unit 1 Note: A profit occurs when enough widgets are made and sold to break even. (i.e. R = C) R = C 25x = 10x + 4000 (Set up equation)

10. #7 Bruce owns a business that produces widgets. He must bring in more in revenue than he pays out in costs in order to turn a profit.  It costs $10 in labor and materials to make each of his widgets.  His rent each month for his factory is $4000.  He sells each widget for $25. How many widgets does Bruce need to sell monthly to make a profit? A. 160 B. 260 C. 267 D. 400 Unit 1 25x = 10x + 4000 (Set up equation) –10x 15x = 4000 15x 4000 15 = x = 267 Note: A minimum of 267 widgets must be sold in order to make a profit.

11. Coordinate Algebra Practice EOCT Answers Unit 2

12. #1 Unit 2 Which equation shows ax – w = 3 solved for w ? –ax ax – w = 3 –w = 3 – ax –ax = –1 –w 3 – ax –1 w = –3 + ax w = ax – 3 A. w = ax – 3 B. w = ax + 3 C. w = 3 – ax D. w = 3 + ax

13. #2 Unit 2 Which equation is equivalent to ? A. 17x = 88 B. 11x = 88 C. 4x = 44 D. 2x = 44 Least Common Denominator 8 14x – 3x = 88 11x = 88

14. #3 Unit 2 Which equation shows 4n = 2(t – 3) solved for t ? 4n = 2(t – 3) 2n = t – 3 2 4n 2(t – 3) 2 = +3 2n + 3 = t 4n = 2(t – 3) 4n = 2t – 6 +6 4n + 6 = 2t 2n + 3 = t Method #1Method #2 4n + 6 2t 22 =

15. #4 Unit 2 Which equation shows 6(x + 4) = 2(y + 5) solved for y ? 6(x + 4) = 2(y + 5) –10 6x + 24 = 2y + 10 –10 6x + 14 = 2y 3x + 7 = y 6x + 14 2y 22 = A. y = x + 3 B. y = x + 5 C. y = 3x + 7 D. y = 3x + 17

16. #5 Unit 2 This equation can be used to find h, the number of hours it takes Flo and Bryan to mow their lawn. How many hours will it take them to mow their lawn? A. 6 B. 3 C. 2 D. 1 Least Common Denominator 6 2h + h = 6 3h = 6 h = 2 3h 6 33 =

17. #6 Unit 2 This equation can be used to determine how many miles apart the two communities are. What is m, the distance between the two communities? A. 0.5 miles B. 5 miles C. 10 miles D. 15 miles Least Common Denominator 20 2m = m + 10 –m–m–m–m m = 10

18. #7 Unit 2 For what values of x is the inequality true? A. x < 1 B. x > 1 C. x < 5 D. x > 5 Least Common Denominator 3 2 + x > 3 –2 x > 1

19. #8 Unit 2 A manager is comparing the cost of buying ball caps with the company emblem from two different companies. A. 10 caps B. 20 caps C. 40 caps D. 100 caps Company X charges a $50 fee plus $7 per cap. Company Y charges a $30 fee plus $9 per cap. For what number of ball caps (b) will the manager’s cost be the same for both companies? Cost Formula: Company X C X = 7b + 50 Cost Formula: Company Y C Y = 9b + 30 C X = C Y 7b + 50 = 9b + 30 (Subtract 7b on both sides) 50 = 2b + 30 (Subtract 30 on both sides) 20 = 2b (Divide 2 on both sides) 10 = b

20. #9 Unit 2 A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased? Let x = # of one-pound bags Let y = # of three-pound bags Method #1 Substitution (Total number of bags) x + y = 9 Equation #1: (Total value of bags) 2x + 5y = 36 Equation #2: Solve Equation #1 for x x + y = 9 –y x = 9 – y Substitute x = 9 – y into Equation #2 2(9 – y) + 5y = 36 18 – 2y + 5y = 36 18 + 3y = 36 3y = 18 y = 6 6 three-pound bags

21. #9 Unit 2 A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased? Let x = # of one-pound bags Let y = # of three-pound bags Method #2 Elimination (Total number of bags) x + y = 9 Equation #1: (Total value of bags) 2x + 5y = 36 Equation #2: Multiply Equation #1 by –2 –2(x + y) = –2(9) Add New Equation #1 and Equation #2 3y = 18 y = 6 6 three-pound bags –2x – 2y = –18 2x + 5y = 36 (New Equation #1)

22. #10 Unit 2 Which graph represents a system of linear equations that has multiple common coordinate pairs? A. C. D. Has one common coordinate pair  Has one common coordinate pair  Has no common coordinate pairs Multiple common coordinate pairs (Two lines overlap) B.

23. #11 Unit 2 Which graph represents x > 3 ? A. B. C. D. x > 3 x < 3

24. #12 Unit 2 Which pair of inequalities is shown in the graph? A. y > –x + 1 and y > x – 5 B. y > x + 1 and y > x – 5 Line 1 Line 2 Both given inequalities have slopes equal to positive one. This is a contradiction to the slope of Line 1 being negative. Note Line 1 graph has a negative slope. Line 2 graph has a positive slope.

25. #12 Unit 2 Which pair of inequalities is shown in the graph? C. y > –x + 1 and y > –x – 5 D. y > x + 1 and y > –x – 5 Line 1 Line 2 Note Line 1 graph has a negative slope. Line 2 graph has a positive slope. Both given inequalities have slopes equal to negative one. This is a contradiction to the slope of Line 2 being positive. Line 2 has a positive slope with a negative y-intercept. However, the line y > x + 1 has a positive slope, but the y-intercept is positive.

26. #12 Unit 2 Which pair of inequalities is shown in the graph? A. y > –x + 1 and y > x – 5 B. y > x + 1 and y > x – 5 Line 1 Line 2 Both given inequalities have slopes equal to positive one. This is a contradiction to the slope of Line 1 being negative. Note Line 1 graph has a negative slope. Line 2 graph has a positive slope.