PRE-CALCULUS
WS 926
NAME _____________________________________________
PERIOD __________ DATE _____________________________
THIS WORKSHEET IS OPTIONAL FOR ALL “MATHLETES”. TO EARN POINTS, PLEASE HAVE ADEQUATE WORK
SHOWN, AND PLACE IT IN THE TEACHER’S BASKET BEFORE THE START OF CLASS.
WRITE THE WORD TRUE OR FALSE IN EACH BLANK. IF IT IS FALSE, CORRECT THE STATEMENTS TO MAKE IT
A TRUE ONE.
__________________1)
ALL linear functions can be defined by a formula.
__________________2)
The coplanar lines 3x + 2y = 9 and 2y – 3x = 10 are perpendicular line.
__________________3)
The linear equation y – 2 = 3(x – 7) is equivalent to y = 3x – 9.
__________________4)
Given H = g(D), the variable H is the dependent variable.
__________________5)
A quadratic function can have different rates of change over different
intervals.
SHORT ANSWER.
6)
Write the general form for each of the types of equations of lines.
Slope-intercept Form:
Point-Slope Form:
Standard Form:
7)
Define the term regression line.
8)
Briefly describe the Least-Squares regression line.
9)
Define the term correlation coefficient.
10)
Compare and contrast the terms extrapolation and interpolation.
11)
Define a function.
12)
Define domain and range.
Page | 1
HODGE-PODGE.
13)
Given the following table, could J a function of K? Explain.
Page | 2
J
K
-3
-1
-1
-3
0
4
-1
0
14)
Evaluate: log 5 5 − log 6 1 + log 49 7
15)
Simplify:
16)
If the correlation coefficient is a -0.54 identify if the relationship is a strong/weak and
positive/negative linear relationship.
(−5𝑎𝑏 −5 )3
What’s the domain of the given
relation?
18)
Could the following table represent a linear function? Explain. Calculations must be shown.
t
p(t)
-5
10
0
14
5
16
10
17
4
2
19) Could the following table represent a linear function? Explain. Calculations must be shown.
h
w(h)
-24
36
-8
22
0
15
16
1
Page | 3
20)
If a car’s initial value is $31,415 and it depreciates each year by 13%, could a mathematician create a
linear formula to represent the relationship between years since the car’s purchase and the car’s
value? Explain.
21)
Is the relationship between Celsius and Fahrenheit a linear relationship? Explain.
22)
Rewrite 8x + 5y + 1 = 10 + 22x in slope-intercept form. All steps must be shown.
23)
The table below gives data from a linear function. Find a formula in point-slope form for the
function. Algebra must be shown! Watch the variables.
Time, t
0
3
6
9
Population, 50000 51200 52400 53600
P = f(t)
24)
Suppose the g(x) is linear, with an x-intercept of 8 and y-intercept of 15. Find a formula for f in
standard form. Algebra must be shown!
25)
A salesman earns W(n) = 85n + 314, where n is the number of products sold, and W(n) is the weekly
wage, in dollars. Identify the vertical intercept and the slope, and explain their meaning in practical
terms.
Page | 4
26)
At a price of $3.14 per gallon, the average weekly demand by consumers for gasoline is 42.7 gallons.
If the price rises to $3.59 per gallon, the weekly demand drops to 37.2 gallons. Find the formula for
Q, the weekly quantity of gasoline demanded, in terms of p, the price per gallon, assuming the
demand is linear. Write your answer in slope-intercept form. Algebra must be shown.
27)
Wilma has found that there is a linear relationship between the number of times she eats at
McDonald’s and her weight. When she eats at McDonalds eight times a week, she weighs 314
pounds. Morever, if she ate there three fewer times, she weighed 25 pounds lighter.
Let x be the number of times she eats at McDonalds. Find the formula for y, Wilma’s weight.
If necessary, round your answer to 4 decimal places. Algebra must be shown.
The wild rabbits of Australia weight seem to be related to the number of rabbits living in the area. The
table below gives the number(n) of rabbits (in thousands) and the average weight of the rabbits (w).
n
60
61
62
63
65
w
3.1
3.6
3.8
4
4.1
28)
Find the equation of the least squares regression line for this data. (Be sure to use n and w in the
equation). Round to the nearest hundredth.
29)
What is the correlation coefficient? (Round to the nearest hundredth)
30)
Describe the correlation. (Strong/weak, and positive/negative)
Bonus Hint: The bonus will cover either the 45° - 45° - 90° triangle or the 30° - 60° - 90° triangle.
Prepare and seize the day!