A Few Practice Problems for Midterm 2
Notes: Be sure you write neatly using complete sentences and correct grammar. Diagrams should be included where appropriate. Neatness and organization are necessary for full credit. Consider every one of these questions as a possible test question. If you cannot figure out how to do the problem on your own come by for hints and help before the last minute.
1) Outline the various modifications to f(x) that will shift or stretch y = f(x).
Be able to solve any quadratic or linear equation plus a few radical equations.
2) Solve for x= -4b / 3) Solve for b
A = · h / 4) Solve for x / 5) Solve for y
y =
6) Solve for b
= 10a / 7) Solve for a
a·w + 1 = / 8) Solve for y
a·x2 + b·y2 = 1 / 9) Solve for a
1 =
10) Solve for b
D = / 11) Solve for z
− 1 = 0 / 12) Solve for R
V = / 13) Solve for y
14) Solve for W / 15) Solve for x
-2(3x – 1) + = / 16) Solve for x
(x + 1) – = / 17) Solve for x
+ 2 = |9 – 13|
18) Solve for x / 19) Solve for r
S = 2π r + r h / 20) Solve for x / 21) Solve for h
SA = π r h + 2 π r2
Be able to solve equations graphically:
22) Solve for k: (a) 3k2 + 5k + 6 = 18 (b) Solve for Q: 3x2 + = 7x3 + 2x − 5
23) Solve for x: (a) 6 − 4x(x + 2) + 1 = x3 + 12 (b) Solve for y: 2y · + 4y =
24) Be able to find roots, y-intercepts, maxima and minima.
25) Find the equation of the line through (a) (6, -7) and (-2, 3) (b) (-152, 78) and (-213, 93)
(c) (x0, y0) and (a, f(a)) (d) (a, b) with slope
26) Find the equation of the line through (5, -7) and parallel to 6x − 9y = 108
27) Find the equation of the line through (-8, 12) and perpendicular to y = -0.6 x + 20
28) Graph (a) y = -¾ x + 24 (b) y = -0.6 x + 20 (c) 6x − 9y = 108 (d) 5(x − 2y) + 3x − 4y = 2x + 7
29) Give the Domain for (a) y = + 1 (b) y = − 1 (c) y =
30) Graph the quadratic and adjust the viewing window to show all four critical points of y = -0.1x2 − 0.5x + 15. Then find them accurate to the hundredth's place.
31) Find all intersections of P = 4w2 − 5w − 8 and P = w3 − w
32) Graph parametrically in an appropriate window: a) (3t + 5, -2t + 8) b) x(t) = 4t2 − 5t − 8, y(t) = t3 − t
c) x = y2 d) xy2 + x = (y − 2) e) x = f) x = (y − a)(y − b)
33) Translate f(x) as indicated:
a) / / b) / / c) /y = f(x + 3) − 2 / y = 2 f(x) − 4 / y = f(2x − 3)
34) Give the following: a) Q(-5) b) Q(7) c) Q(0)
d) Solution to Q (x) = 9 e) Solution to Q (x) = 3 f) All roots
g) All extrema h) Apparent Domain & Range
i) A parametric form for y = Q(x)
35) Compute the difference quotient : a) f(x) = 8x2 − 5x + 3 b) f(x) = /
36) The cost of a laborer is $8.75/hr and a supervisor costs $20/hr. 3 laborers and a supervisor work from noon onward while 2 laborers only work from 3 pm onward. Give the total cost to the employer as a function of time in hrs.
37) The cost of a rectangular box with a square bottom is $0.75/in2 and the sides cost $0.40/in2. The top costs $1.25/in2. The box holds 650 in3. Give the cost of the box as a function of the base measurement, x.
38) A delivery truck travels 50 mph on the hi-way and 25 mph on the rural roads. If he drives for 3 hours more on the rural roads as the hi-way, give his total distance driven as a function of the time he has driven.
39) Starting at zero, a mosquito population increases for 10 days, reaches a maximum and then decreases for 5 days back to zero. Call this function P = f(t). Describe: a) f(t − 10) b) 3 f(t) c) f(t/2) d) 10f(t/10)
40) A 20 ft wide pool that is circular with a flat bottom holds 10,000 gal. The pool has sprung a leak which leaks at 100 gal/hr. The pool was initially full. 15 hrs after the leak started it was detected. Although it was not fixed, water was added at 250 gal/hr to compensate. Give the pool's volume as a function of time staring with the beginning of the leak as t = 0.