Download MATH 022 Exam I, Sample D - Solved Mathematical Equations and Inequalities and more Exams Analytical Geometry and Calculus in PDF only on Docsity!
- Solve the following equation for x : 2(x + 2) − 3 = −x.
a) (^13) b) 1 c) − 1 d) 3 e) − (^13)
- Solve the following equation for p: p^ − 6 4 − 23 p =^1 − 2 3 p.
a) (^76) b) (^43) c) − (^13) d) (^56) e) − (^52)
- Solve the following equation for x: 3x^2 − 5 x = 12.
a) x = − 3 , x =^43 b) x = 3, x = − (^34) c) x =^13 , x = − (^43) d) x = 3, x = − (^43) e) x = − 13 , x =^43
- Put the quadratic function f (x) = x^2 + 3x into the form (x − h)^2 + k by completing the square.
a) (x − 3)^2 + 9 b)
x +^32
c)
x − (^32)
+^94
d) (x + 3)^2 − 9 e)
x − (^32)
- Given the quadratic equation − 3 x^2 + √ 5 x − 1 = 0, find the dis- criminant and determine the number of real solutions.
a) Discriminant 7; 2 real solutions b) Discriminant 7; no real solutions c) Discriminant -7; 2 real solutions d) Discriminant -7; 1 real solution e) Discriminant -7; no real solutions
- Solve the following equation for x: (x + 2)^3 − 2(x + 2)^2 + (x + 2) = 0.
a) x = − 1 , x = − 2 b) All real numbers c) No solutions d) x = 1, x = − 2 e) x = − 1 , x = 2
- Solve the following equation for x: |x^2 − 3 x| = 2.
a) x = 2, x = 1, x = −3 +^
2 , x^ =^
b) x = − 2 , x = − 1 , x = 3 +^
2 , x^ =
c) x = 2, x = 1, x = 3 +^
2 , x^ =
d) x = − 2 , x = 1, x = −3 +^
2 , x^ =^
e) x = 2, x = − 1 , x = −3 +^
2 , x^ =^
- Solve the following inequality for x: (x − 2)(x + 1)(2x + 3) ≤ 0.
a)
[
]
∪ [2, ∞)
b) (− 1 , 2) c)
]
∪ [− 1 , 2]
d)
[
]
∪ [2, ∞)
e)
- Solve the following inequality for x: | 2 − 3 x| − 4 ≥ 3.
a)
]
∪ [3, ∞)
b) (−∞, −3] ∪
[ 5
3 ,^ ∞
c) (−∞, −3] d)
[
e)
]
∪ [3, ∞)
- Solve the following inequality for x: 2x − 1 > x − 2(3 + 2x).
a) (−∞, 1] b) (−∞, ∞) c) No solutions d) [− 1 , ∞) e) (− 1 , ∞)
- Solve the following inequality for x: (^1) x + x ≤ x
(^2) − x − 1 x. a) [0, 2) b) (0, 2] c) (− 2 , 0) d) [− 2 , 0] e) [− 2 , 0)
- Find the domain of f (x) = √x^3 − x^2 + x − 1.
a) (−∞, −1) ∪ (1, ∞) b) [1, ∞) c) (−∞, −1] ∪ [1, ∞) d) [− 1 , 1] e) (−∞, −1)
- The surface area of a sphere of radius r is given by S(r) = 4πr^2. Find S
( (^) r 2
a) 2 π b) πr^2 c) 2 πr^2 d) 12 πr^2 e) 2 πr
- If f (x) = x^2 + 1, find f^ (x^ +^ h h)^ −^ f^ (x).
a) h b) − 2 x − h c) − 2 x + h d) 2 x + h e) 2 x − h
- Determine if the following functions f and g are even, odd or neither: f (x) = x^3 − x, g(x) = √ 1 1 − x 2.
a) Both functions are odd. b) Both functions are even. c) f is even, g is odd. d) f is odd, g is even. e) Both functions are neither even nor odd.
- Which of the following statements is always true?
a) The graph of a function may have several y-intercepts. b) Every function’s graph must have at least one x-intercept. c) The graph of a function can have at most one x-intercept. d) The graph of a constant function has no y-intercepts. e) The graph of a function may have more than one x-intercept.
- Suppose g(x) =
2 x√^ ifx^ if 0−^2 ≤< x < x < 1;0; |x| if x ≥ 1. Find g
and g
a) g
= 0.2, g
b) g
= 0.2, g
c) g
= 0.2, g
d) g
= 100, g
e) g
= −100, g
