MATH Practice Midterm 2

Part I: No calculators allowed .

1. Write an equation in slope - intercept form for the line through the given points.

(a) (3,-5) and (-2, 4) (b) (-4,-3) and (0,-1)

2. Write an equation in slope -intercept form for the line graphed below:

3. Rewrite the following in slope-intercept form, and then graph it:

4. The gure below shows the graph of

(a) Using the graph, solve
(b) Using the graph, solve
(c) Using the graph, solve 

5. On the axes below, sketch the graph of

6. Using transformations, sketch a graph of f(x) = |x + 3| - 4. Explicitly state the
coordinates of at least 3 points.

7. Solve each of the following equations or inequalities algebraically .

8. Write each expression without negative exponents, and simplify .

9. Solve.

10. Solve by factoring or by completing the square . Solutions obtained via the quadratic
formula will not receive any credit.

11. Solve each quadratic inequality.

12. Solve algebraically :

y = -x² + 4x + 2
4y -3x = 24

13. Solve algebraically:

x + 5y = 11
2x + 3y = 8

14. Decide whether the following system is inconsistent , dependent, or independent:

2x - 3y = 4
6x - 9y = 12

15. Graph the following parabola, being sure to explicitly state the coordinates of the
vertex and all intercepts.
y = -3x² + 2x + 8

16. The amount of power, P, generated by a windmill varies directly with the cube of
the windspeed , w. A particular windmill produces 2000 kilowatts of power when the
windspeed is 10 miles per hour.

(a) Write a function expressing the power as a function of windspeed.

(b) How much power would the windmill produce in a gentle breeze of 4 miles per hour?

(c) If the windspeed doubles, by what factor does the power output increase?

17. Solve the quadratic equation 2x² +5x+4 = 0. Write your solutions in the form a+bi.

18. Find the zeros, along with their multiplicities, of the function f(x) = x⁴ - 9x². Then
make a rough sketch of the graph of f, being sure to show the correct long- term be -
havior and x-intercept behavior.

19. Multiply.

(a) (x² - 2x - 3)(2x² + x - 5)

(b) (x + 3)(2x - 1)(2x + 5)

(c) (x - 4)³

(d) (3 + 2i)(-5 - i)

20. Find the x⁴ term in the product (3 - 2x + 2x³)(5 + 3x - 2x² + 4x⁴).

21. Factor 8x³ - 27y³.

Part II: Calculator problems.

22. The following table shows the teenage birth rates in the US from 1991 to 2000 (mea-
sured in the number of births per 1000 women).

(a) Let t represent the number of years after 1990. Find the equation of the regression
line which gives B, the number of births, in terms of t.
(b) Estimate the teen birth rate in 1994.
(c) Predict the teen birth rate in 2010.

23. Solve the inequality 5x² + 39x + 27 ≥ 5.4