Download Practice Problems for Sunday

Sunday’s Problems
1. Show the entire expansion of (5x4 – 2i)3
2. Graph f(x) = log3(x + 2) – 1, state the equation of the asymptote and state the value of f(79).
3. Graph y = (½) x – 3 + 2 over the interval 1 ≤ x ≤ 5.
Graph y = 2x+1 – 3 over the interval -3 ≤ x ≤ 1
State the equation of the asymptote.
State the equation of the asymptote.
4. Simplify completely.
a.
3
 8x y
10
18
b.
 25 x y
16
39
c.
48 x 5 y 8  5 xy 108 x 3 y 6
2x 2 y 3
5. You have two options to choose from for an investment.
Option 1: Interest in compounded continuously with a deposit of $10,000 at a rate of 2.12%
for 15 years.
Option2: Interest is compounded weekly with a minimum investment of $12,000 at a rate of
2.43% for 15 years.
Assuming the minimum balance required is not a problem, which option should you chose? To
the nearest ten dollars, how much would you have at the conclusion of the investment? Show
all work to support your decision.
6. Given the quadratic equation, state the sum and the product of the roots and then find the
roots, in simplest a +bi form.
3x2 + 2x + 10 = 0
7. Given
x 1  1
, simplify completely.
x 1
8. The following are the results of a test given in a science class containing 12 students.
52, 63, 71, 74, 75, 78, 80, 83, 85, 86, 90, 94
Find the mean and the standard deviation, to the nearest thousandth.
How many data points lie within one standard deviation of the mean? What percentage of
scores falls within one standard deviation from the mean?
How many data points lie within two standard deviations of the mean? What percentage of
scores falls within two standard deviations from the mean?
Using your answers above, does this data set represent a normal distribution? Explain.
9. There are two classes of statistics at high school A.
The following is a partial list of the scores on a recent test for
Class 1: 42, 53, 91, 97, 98, 99, 100, 100.
The following is a partial list of the scores on a recent test for
Class 2: 73, 84, 84, 86, 87, 88, 88, 89
State the 5-number summary for each. State the mean, variance, and the standard deviation
for each.
Which class had the most consistent results? What statistical measure supports your answer?
Explain.
10. Describe the transformations from the parent function for the following equation, the axis
of symmetry , the vertex and the appropriate table of x-values that would be used to reflect
the symmetry of the graph.
y = (x + 7)2 + 3
11. Find the maximum value of k that would result in the quadratic equation kx2 + 9x + 3 = 0
having real roots.
Find the minimum integer value of a that would result in the quadratic equation
4x2 – 7x + a = 0 having imaginary roots.
12. The temperature, T, of a given cup of hot chocolate after it has been cooling for t minutes
can best be modeled by the function below, where
is the temperature of the room and k is
a constant.
A cup of hot chocolate is placed in a room that has a temperature of 68°. After 3 minutes, the
temperature of the hot chocolate is 150°. Compute the value of k to the nearest thousandth.
[Only an algebraic solution can receive full credit.] Using this value of k, find the temperature,
T, of this cup of hot chocolate if it has been sitting in this room for a total of 10 minutes.
Express your answer to the nearest degree. [Only an algebraic solution can receive full credit.
13. Given g(x) = 8.2 + 3ln(5x + 7)
a. Find g(2)
b. Find the value of x, to the nearest tenth, when g(x) = 18