Jr. Mathematics
Test I
Name
October 4, 2019
Parents’ signature
Problem 1. Consider the two points A: (2, 6) and B: (−3, −6), answer the following.
[12 points]
a. Find the distance between the two points.
b. Find the slope of the line through the two points.
c. Find the midpoint of the segment having the two points as endpoints.
d. Give an equation for the line through points A and B.
[3]
e. Give an equation for the circle centered at A and passing through B.
[3]
Problem 2. Give the quadratic formula used to solve equations of the form ax2 +bx+c = 0.
[3 points]
Problem 3. Express the roots of the equation 5x2 + 7x − 4 = 0 in radical form. [3 points]
Problem 4. The function f (x) is graphed below.
[15 points]
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−8 −7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
8
a. What is the domain of f (x)?
b. What is the range of f (x)?
c. Find f (3).
d. For what values of x is f (x) = 3?
e. Does f (x) have an inverse function?
[1]
f. Find the relative maximum of f (x).
g. On the axes above, graph y = f (x + 1) − 2.
[4]
Problem 5. The function g(x) is graphed below.
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
[12 points]
−8−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7 8
a. Evaluate g(g(2)).
b. On what interval(s) is g(x) decreasing?
c. What are the x-intercepts of g(x)?
d. What is the y-intercept?
e. Does g(x) have a relative minimum at x = 3?
f. Does g(x) have a relative maximum at x = −2?
Problem 6. Factor completely.
a. x2 − 4x − 12
b. 4x2 − 12x + 9
c. x2 − 81
[9 points]
Problem 7. consider f (x) = x2 + 2 and g(x) =
√
x − 2.
[12 points]
a. Find f (3).
b. Find g(6).
c. Find f (g(6)).
d. Find g(f (−3)).
e. Is g the inverse function of f ?
f. Find an expression for f (x + h)
Problem 8. Find the center and radius of the following circle.
[3 points]
a. (x − 3)2 + (y + 2)2 = 12
Problem 9. Solve the following equations:
a.
3
2
1
− 2
=
x − 3 x − 8x + 15
x−5
[5 points]
Problem 10. Identify the six functions graphed below. You may identify them either by
name or by formula. For example you might identify one function as “the error function”
and another function as “f (x) = x3 − x2 − x + 1.”
[12 points]
2
2
1
1
0
0
−1
−1
−2
−4 −3 −2 −1 0
1
2
3
4
2
1
2
3
4
1
2
3
4
1
2
3
4
2
0
1
−1
0
−4 −3 −2 −1 0
1
2
3
4
−4 −3 −2 −1 0
2
2
1
1
0
0
−1
−1
−2
−4 −3 −2 −1 0
3
1
−2
−2
−2 −1 0
1
2
3
4
5
−2
−4 −3 −2 −1 0
Problem 11. For the six functions above...
[9 points]
a. Identify which have inverses.
[3]
b. Classify each as an odd function, an even function, or neither.
[6]
Choose any two of the following word problems.
Problem 12. A woman earns 15% more than her husband. Together they earn $69,875
per year. How much money does she make?
[6 points]
Problem 13. A movie star, unwilling to give his age, posed the following riddle to a
gossip columnist. “Seven years ago, I was eleven times as old as my daughter. Now I am
four times as old as she.” How old is the star?
[6 points]
Problem 14. A plumber and his assistant work together to replace the pipes in an old
house. The plumber charges $45 per hour for his own labor and $25 per hour for his
assistant’s labor. The plumber works twice as long as the assistant on this job, and the
labor charge on the bill is $4025. How long did the plumber work on this job? [6 points]
Problem 15. The length of a rectangular garden is 2 feet more that twice its width. If
22 feet of fencing is needed to enclose the garden, what are its dimensions?
[6 points]