Download MATH 20 TEST 1

MATH 20
TEST 1
Write your number in the box above.
(SHOW SOME WORK.)
(1)
(2)
Name
Give one number according to the requirements:
(a) Give a number that is a whole number but not a natural number:
(1a)
(b) Give a number that is an integer but not a whole number:
(1b)
(c) Give a number that is a real number but not an integer:
(1c)
Express the number set that contains all the real numbers that are less than −1.5 and greater
than or equal to −5,
• in set-builder notation:
• on the number line:
r
r
r
r
r
r
r
r
r
-3
-2
-1
0
1
2
3
r
r
-
• in interval notation:
(3)
True (T)? False (F)?
(Number sets:
N —natural numbers set, W —whole number set, Z—interger set,
Q—rational number set, I—irrational number set, and R—real number set.)
(a) 0.5 ∈ Q
(d) − 39
3 ∈ Z
(g) N
(4)
S
Solve:
(b) 0 ∈ Z
(e)
W =W
4 − 5(2x + 1) = 10 + x
√
(c) −5 ∈ W
5∈
/ Q
(h) Q
T
I=Ø
(f) π ∈ I
(i) Q
S
(4)
I=R
3x−2
5 − 1 = 9 − 2x
(5)
Solve:
(6)
1
Solve the literal equation V = 2 ar + 2πr
(7)
Find 3 solutions of the equation
x
(5)
for a
(6)
4 + 3x = 2y, then graph it.
y
0
y6
6
5
4
-2
3
2
x
1
-5
−6−5−4−3−2−1 0 1 2 3 4 5 6
−1
−2
−3
−4
−5
−6
(8)
Find the (a) x-intercept and (b) y-intercept of the line whose equation is:
3x − 2y = 8
(8a)
(8b)
(9)
A line is passing through (7, −3) and its slope is − 12 , write its equation in
(a) Point-Slope form:
(9a)
then rewrite it to (b) Slope-Intercept form:
(9b)
(10)
A line is passing through (−2, 1) and (7, −2),
(a)
what is its slope?
(10a)
(b)
what is its equation in slope-intercept form?
(10b)
(11) Line l1 is perpendicular to Line l2 . The equation of Line l1 is x − 3y = −2. If Line l2 passes
through the point (1, −5),
(a) Find the slope of l1 first,
(11a)
(b) What is the slope of l2 ?
(11b)
(c) Write the equation of l2 in Slope-intercept form,
(11c)
(12)
5
Let f (x) = 4−x
and g(x) = 3 − 2x
(a)
f (5) =
(12a)
(b)
g(0) =
(12b)
(c)
f (g(2)) =
(12c)
(d)
g(f (2)) =
(12d)
(e)
g(−3a) =
(12e)
(13)
Solve for x:
| 5 − 3(2x − 1) |= 2
(14)
Solve for x:
(13)
| 4 − 3x |=| 6 + 5x |
(14)
Solve the following inequalities and graph the solution set on the given number line:
(15)
|1−
x
2
|≥ 3
(15)
q
(16)
(17)
5−x≥
q
q
q
q
q
q
q
q
q
q
q
2x−5
3
q
q
-
(16)
q
q
q
q
q
q
q
q
q
q
q
-5
-4
-3
-2
-1
0
1
2
3
4
5
−7 ≤ 2 − 3(x + 1) < 2
-
(17)
q
q
q
q
q
q
q
q
q
q
q
-5
-4
-3
-2
-1
0
1
2
3
4
5
-
Math20
Test 1,
100 points