Math 253 Exam 1 Review

1. The singer James Taylor holds a concert at a small theater. He wants to know whether

the majority of his fans are adults or children, but doesn’t want to count all the ticket stubs. During his last show 5200 tickets were sold and receipts totaled $20, 335. The adult admission is $4.75 and a child’s admission is $2.50. How many adult and children saw his last concert?

2. A coin bank has twenty four coins in nickels, dimes and quarters. Their value is $2.40. There are twice as many dimes as quarters. How many nickels are in the bank?

3. When you take your car to a mechanic, he charges you for parts and labor. If the repair bill on your car was $316.55 and the charge for parts was $148.55 and the mechanic worked on your car for 4 hours. What was the charge per hour for labor?

4. A hiking instructor is preparing a trail mix for a group of young hikers. She mixes nuts that costs $3.99 a pound with pretzels that costs $1.29 a pound to make a 20 pound mixture that costs $2.37 a pound. Find the number of pounds of nuts used.

5. How many pounds of a 12% aluminum alloy must be mixed with 400 pounds of a 25% aluminum alloy to make a 17% aluminum alloy?

6. Solve the compound inequality and write answer with interval notation.

2x -7 > -1 and 3x + 1

7. Solve the inequality and write answer in interval notation.

8. Solve the inequality and write answer in interval notation.

9. Find the distance between the points ( -2, 5) and ( 6, -7). Approximate the answer using two places after the decimal.

10. Create solutions to the equation y = x² - 1 using x = - 2, -1, 0, 1, 2. Plot these solutions on a Cartesian coordinate system.

11. Determine which of the following represents a function.

a) ( 2, 9), ( 3, 11), ( 4, 5), ( 1, 9), ( 33, 19)

b) ( 1, 8), ( 5, 88), ( 3, 22), ( 2, 5), ( 5, 23)

c) The points represented by the equation y = 3.

12. Find the domain and range of the function.

13. Find the domain of each function

a) b) c) d) f(x) = 4x - 5

14. If f(x) = x² - 3, find

a) f(-4) b) f(7) c) f( s ) d) f( t - 2)

15. Graph the equation y = -2x + 4. Explain how the points on the graph are related to the equation.

16. Find the x and y intercepts for -2x + y = 4. Write intercepts as ordered pairs. Now graph the line using these intercepts.

17. Draw any three lines that have a slope of – 2/3.

18. Find the equation of a line that goes through the points ( 2, -4) and ( 3, -5).

19. Find the equation of the line that contains the point ( 3, 4) and has an undefined slope.

20. Are the lines 3x + 5y = 7 and – 5x + 3y = 42 parallel, perpendicular or neither. Justify your answers.

21. Find the equation of the line that contains the point ( 3, -4) and is parallel to the line 2x – 5y = 9. Put the final answer in slope intercept form.

22. Do the following represent functions?

23. Solve the equation

24. Find the slope of each line given by the equations:

a) 3x – 2y = 5 b) x = 3 c) y = -6

25. At sea level, the boiling point of water is 100 degrees Celsius. At an altitude of 2 km, the Boiling point is 93 degrees Celsius. Write a linear equation for the boiling point of water in terms of the altitude above sea level. Use your equation to predict the boiling point of water on top of Mount Everest which is 8.85 km above sea level. Round to the nearest degree.

26. Solve the compound inequality and write the answer in interval notation.

3x + 2 > 4 or 2x > -4

12) D={ 2,-1, 9, 3}

R= { 5, 3, 10, 11}

d) t²- 4t +1

13) a and d) All Reals

b)

c)

c) Yes

24. a) 3/2 b) undefined c) 0

25. y = -3.5x +100, 69 degrees.

26.