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MATH 121
Review Sheet

The numbers (italics) indicate the section in Bittinger, Beecher, Ellenbogen, Penna 4th edition where more problems of the same type can be found.

R.21.Simplify:
R.62.Simplify:
R.73.Simplify:    Write answer in radical form.
R.74.Simplify:
R.75.Rationalize the denominator and simplify: a) b)
Simplifying Rational Expressions handout.
R.4-R.66.Simplify: x-4(x + 5) - x(x + 5)-1
R.67.Simplify:
R.68.Simplify:
R.69.Simplify:
R.510.Solve: 6(2x + 3) - 3(x - 5) = 7
3.411.Solve:
1.512.Solve for w: S = 2(lw + hw + hl)
2.3-127
R.5
13.Solve by factoring: 6x2 - x = 15
3.214.Solve by quadratic formula and give exact answer: 5x2 - 7x - 3 = 0
3.215.Solve by graphing and give answers to nearest .01: 3x2 - 5x - 4 = 0
3.216.Solve algebraically: 10x4 - 17x2 + 3 = 0
1.617.Solve and give answer in interval form: x(x - 1) < (x + 3)(x - 2)
1.618.Solve and give answer in interval form:
3.519.Solve and give answer in interval form: |2x - 5| > 3
4.620.Solve and give answer in interval form:
4.621.Solve and give answer in interval form: 3x3 - 8x2 - 9x + 4 ≤ 0  (round endpoints in interval to the nearest hundredth.)
3.2 and 3.422.
Find the x- and y- intercepts of: a) 4x2 - 3y2 = 16 and b)
1.123.Write the equation of a circle if (1, 3) and (-5, 7) are endpoints of a diameter.
1.1 and 3.224.Given x2 - 14x + y2 + 4y = -18, find the center and the radius of the circle.
2.425.Given the graph below, state whether graph has x-axis, y-axis, or origin symmetry.
2.426.Use tests for symmetry to determine if x + 2 = 3y2 has x-axis, y-axis, or origin symmetry.
1.227.
Given f(x) = -x2 - 2x + 3 find ; f(a + 1)
1.228.Given the graph of y = f(x), estimate: a) f(x) when x = 1; b) x when f(x) = 1
1.229.Is the given graph a function?
1.230.Use the graph to find the domain and range of the function:
Domain ___________________

Range ____________________
1.231.Find the domain of: f(x) =
1.432.Write the equation of the line through the points (3, -7) and (-5, -2).
2.133.Draw the graph of f(x): f(x) =
1.434.Write the equation of the line through A (3, 2) and perpendicular to 4x - 5y = 22.
1.435.Write the equation of the perpendicular bisector of segment given A (3, 5) and B (7, 6).
2.436.State the transformations necessary to graph f(x) = 3(x - 2)2 + 1 from f(x) = x2, then draw the graph.
3.237.f(x) = 2x2 - 7x + 3
  1. Complete the square to find the vertex...use any way, just show work.
  2. Find the line of symmetry.
  3. Find the range of the function.
  4. Does the function have a maximum or minimum?
3.338.If a quadratic function has vertex (2, 3) and passes through point (4, 7), find the equation of the function.
 39.If f(x) = and g(x) = x2 + 2, find:
2.3  
  1. (f+g)(x)
  2. (fg)(5)
  3. fg (5)
  4. fg (x)
2.440.Given the graph of y = f(x) draw the graph of y = 2 + 3f(x - 1).
2.441.If f(x) = x2 write the equation of the quadratic if the following geometric transformations are applied: Vertical stretch by a factor of 2, reflect through the x- axis, horizontal shift 3 left and vertical shift 5 down.
5.142.Is the given graph one to one?
5.143.Find the domain and range for the inverse of f if f(x) =
5.144.Find the rule for the inverse of f if f(x) =
5.145.Draw the graph of f and its inverse on the same set of axes: f(x) = x2 + 5 (x ≥ 0)
3.346.a) Draw a complete graph of f(x) = 2x3 - 7x2 - 5x + 4.
b) State coordinates of all local maximum and minimum points.
c) State intervals where graph is increasing; decreasing.

(for parts b & c, round each coordinate/interval endpoint to 2 decimal places.)

2.447.State whether the function f(x) = is odd, even, or neither.
4.348.Use synthetic division to divide 4x3 - 7x2 + 2 by (x - 3) and state the quotient and the remainder.
3.349.Find the remainder if f(x) is divided by (x + 1): f(x) = 3x75 - 4x + 6
4.350.Find the quotient Q(x) and remainder R(x) if P(x) = x3 + 2x2 + 5 is divided by d(x) = x2 - 4.
3.351.Determine if (x - 3) is a factor of 2x3 - 13x2 + 23x - 6.
4.352.Given that f(x) = x2 + (k - 1)x - 3k - 17 has x + 2 as a factor, find k.
4.453.Write a polynomial of degree 4 with real coefficients and zeroes of -2, 3, and 4 + i (DO NOT MULTIPLY OUT). Write the polynomial as a product of linear factors.
4.454.
Write a 2nd degree polynomial f with real coefficients if the graph of
y = f(x) is as given:
3.155.Simplify: 2(3 + 5i) - 4(3 - 2i)
3.156.Simplify:
4.457.Find all complex zeros of f: f(x) = x4 + 6x3 - 3x2 + 24x - 28
4.458.Find to the nearest 0.01 all real zeros of f: f(x) = 3x3 - 2x2 - 7x + 3
4.559.Given the rational function: f(x) =
   a) List all vertical asymptotes.
b) List all horizontal asymptotes.
c) Find the domain of f.
3.460.Solve:
4.561.Draw a complete graph of y = f(x) showing (a) all zeroes, (b) y- intercept, (c) vertical asymptotes, (d) horizontal asymptotes, (e) oblique asymptotes.
f(x) =

(parts c, d, & e should be written as EQUATIONS of asymptotes.)

4.462.
Given the graph of y = f(x), write a polynomial function f of least degree:

detail of y = f(x) on [2.5, 4.5]

y = f(x)
4.663.Solve and give answer in interval form to the nearest 0.01:
3.464.Solve algebraically:
3.465.Solve algebraically:
2.466.Draw the graph of f(x) = by applying geometric transformations to the graph of . State the domain and the range of f.
5.267.Sketch a graph of y = 3(x + 1) - 2 by applying geometric transformations to the graph of y = 3x. State domain, range and any asymptotes.
5.568.Solve: without a calculator.
5.569.Graph f on the interval [-3, 3]; find all maxima and minima. f(x) =
5.470.Evaluate: a) log4(-2)   b) log3(81)   c)
5.371.Sketch the graph of f(x) = log5(x + 1) - 2. State the domain, range and asymptotes.
5.572.Solve without a calculator: log3(7x + 3) = log3(x - 4) + 2
5.473.a) Change log3X = P to exponential form;
b) Change 3Q = R to logarithmic form.
5.474.Express in terms of sums and differences of logarithms: log
5.475.Write the expression as one logarithm: 5 log4x - 1/2 log4(3x - 4) - 3 log4(5x + 1)
5.576.Solve exactly: 5(42x - 1) = 21
5.577.Solve graphically: a) 42x + 3 = 5x - 2   b) ln x + ln(x - 2) = 5
5.478.Evaluate: log517
1.479.The table below lists the height of a person and the person's sleeve length.
a) Fit a linear regression line to the data, use inches for height.
b) Predict a sleeve length if the person is 510 tall.
c) What is the correlation coefficient? How well does the regression line fit the data?
HeightSleeve length (inches)
5′5″ 28
5′6″29
5′8″30
6′33
2.180.A long rectangular sheet of metal 10 inches wide is to be made into a gutter by turning up sides equally so they are perpendicular to the sheet. Find the height of the turned-up sides so a maximum cross-sectional area is provided.
2.181.From a rectangular piece of cardboard having dimensions 25 inches by 33 inches, an open box is to be made by removing squares of area x2 from each corner and turning up the sides. Find the value of x so the volume is a) 1400 cubic inches b) maximal.
2.182.An aquarium of height 2 feet is to have a volume of 10 ft3. Let x denote the length of the base and y the width.
a) Express y as a function of x;
b) Express the total number S of square feet of glass needed as a function of x (4 sides & bottom are glass -- no top).
3.283.When a CD player is priced at $300 per unit, a store sells 15 units per week. Each time the price is reduced by $10, however, the sales increase by 2 per week. What selling price will result in revenue of $7000/week?
3.284.A rectangular plot of ground having dimensions 30 feet by 36 feet is surrounded by a walk of uniform width. If the area of the walk is 1000 sq. ft., what is its width?
4.685.The braking distance d (in feet) of a certain car traveling v (mi/hr) is given by: d = v + Determine the velocities that result in braking distance of less than 80 feet.
3.386.If a ball is thrown up from the roof of a 100 foot building at an initial velocity of 25 ft/sec:
a) What is its maximum height?
b) How long does it take to hit the ground? (S(t) = -16t2 + V0t + S0)

(round all answers to the nearest hundredth)

3.387.A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 2000 yards of fencing, what dimensions will give the maximum rectangular area?
5.688.The amount of bacteria in a certain culture triples every 2 hours. Assuming growth is exponential and there are 500 bacteria to start, how many will be present after 6 hours?
5.689.A certain radioactive substance decays according to a formula , where q0 is the initial amount of the substance and t is the time in days. Approximate the half-life of the substance.
1.590.My bowling average is 156. So far tonight, I have bowled lines of 140 and 162. What score must I have on the third line to bowl at least my average for the game? A game is 3 lines.
5.291.Find the interest rate so that $2000 grows to $3000 in 5 years if interest is compounded quarterly.

(find the interest rate to the nearest hundredth of a %)

1.392.A small business purchases a piece of equipment for $25,000. After 10 years, it will have to be replaced. Its value then is expected to be $2,000. Use a linear equation to find when its value will be $13,000.
5.693.Consider the scatterplot. Determine which (if any), of these functions could be used as a model for the data.
  
i) Linear
ii) Quadratic
iii) Polynomial but not linear or quadratic.
iv) Exponential
a) b)
5.694.The table below gives the real estate taxes (in millions) collected for the Columbus, Ohio Public Schools.
School Tax Data

Year

Real Estate taxes

1988

130.8

1989

136.8

1990

139.4

1991

142.6

1992

188.2

1993

193.3

a) Graph a scatter plot of the real estate tax data.
b) Compute and graph an exponential regression equation for the real estate tax data. (Let x = 0 represent 1988, x = 1 represent 1989, and so forth.) (round each factor of the exact linear regression equation to the nearest hundredth.)
c) Use the regression equation to estimate the real estate taxes the schools will receive in 1998. (DON'T use rounded equation from part b. Use the exact linear regression equation and then round final answer to the nearest tenth.)
4.195.The time t required to empty a tank varies inversely as the rate r of pumping. If a pump can empty a tank in 35 minutes at the rate of 200 gal/min, how long will it take to empty the same tank at the rate of 500 gal/min?

See a separate solutions page for answers.