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MATH 041 EXAM I SAMPLE A
- Solve the equation x^2 − 4 x + 2 = 0 for x.
a) − 2 ± √ 2 b) 2 ± √ 2 c) 2 ± √ 6 d) − 2 ± √ 6
- A pasture is 2 feet longer that it is wide and encloses an area of 35 square feet. How wide is the pasture?
a) 7 feet b) 5 feet c) 3 feet d) 33 feet
- How many real solutions does the equation x^2 − 3(x − 1) = 0 have?
a) One b) Two c) None d) Cannot be determined from the given information.
- Write the complex number (^1 2) − i in the form a + bi where a and b are real numbers.
a) 2 − 2 i b) 1 +^12 i c) 1 − i d) 1 + i
- Find all solutions of the equation x^4 + x^3 + x^2 + x = 0.
a) x = 0 b) x = 0, − 1 c) x = 0, − 1 , ±i d) x = 0, ± 1 , ±i
- Solve the inequality 3 + 3 −^ xx ≥ 1.
a) [− 3 , 3) b) (−∞, 0] ∪ (3, ∞) c) (−∞, −3] ∪ (3, ∞) d) [0, 3)
- Solve the inequality 3 − | 2 x + 4| ≤ 1.
a) (−∞, −3] ∪ [− 1 , ∞) b) [− 1 , ∞) c) (−∞, −1] ∪ [3, ∞) d) [− 3 , ∞)
- Find the midpoint between the points (− 2 , 4) and (10, 0).
a) (8, 4) b) (4, 2) c) (7, 2) d) (2, 0)
- Find the center and radius of the circle x^2 + y^2 − 2 x + 4y + 1 = 0.
a) r = 2 at (1, −2) b) r = 4 at (1, −2) c) r = 2 at (− 1 , 2) d) r = 4 at (1, 2)
- Test the equation y = x^2 + |x| for symmetry.
a) No symmetry b) Symmetric about the origin c) Symmetric about the x axis d) Symmetric about the y axis
- Find the slope of the line perpendicular to the line 2x + 3y = 1.
a) m = − 32 b) m =^15 c) m = − 23 d) m =^32
- Find the domain of the function f (x) = x
2 √ 6 − x. a) (−∞, 6) b) (−∞, 6) and (6, ∞) c) (−∞, 0) and (0, ∞) d) (−∞, 0)
MATH 041 EXAM I SAMPLE A
- Find the x and y intercepts of the equation y^3 = 2x + 1.
a) x intercept 1, y intercept 0 b) x intercept 1, y intercept − 21 c) x intercept − 2 1 , y intercept 1 d) x intercept − 2 1 , y intercept 0
- Which one of the following equations does not describe y as a function of x?
a) 2 |x| + y = 0 b) 2 x + |y| = 0 c) y = x^4 d) 1 = √^4 x + y + 3x^2
- Explain how the graph of the function g(x) = 2(x−1)^2 −3 is obtained from the graph of the function f (x) = x^2.
a) Stretch vertically by a factor of 2 units, shift right by 1 unit, shift down by three units. b) Stretch horizontally by a factor of 2 units, shift left by 1 unit, shift down by three units. c) Stretch vertically by a factor of 2 units, shift left by 1 unit, shift up by three units. d) Stretch horizontally by a factor of 2 units, shift left by 1 unit, shift up by three units.
- Which one of the following functions is odd?
a) f (x) = −x^3 + x b) f (x) = x^2 + πx^3 c) f (x) = √x d) f (x) = (^1) −^1 x
- If f (x) = (^) x x+ 1 , g(x) = x^2 , and h(x) = x + 2 what is the value of (f ◦ g ◦ h)(1)?
a) (^254) b) (^12) c) (^94) d) 109
- Which one of the following functions is 1-1?
a) f (x) = 2(x − 1)^3 + 4 b) f (x) = x^2 + 4 c) f (x) = |x − 4 | d) f (x) = (^) x^12
- Find the inverse of the function f (x) = 4 + √^3 x.
a) f −^1 (x) = 4^3 − x 4 b) f −^1 (x) = (x − 4)^3 c) f −^1 (x) = x^3 − 4 d) f −^1 (x) = x^3 + 4
- Find the average rate of change for f (x) = 2x^2 + 1 from -1 to 1.
a) 3 b) 2 c) 1 d) 0
EXAM I- SAMPLE A
1. B 2. B 3. C 4. D 5. C 6. D 7. A 8. B 9. A 10. D 11. D 12. A
13. C 14. B 15. A 16. A 17. D 18. A 19. B 20. D
