Covers Precalculus

Sample Quiz Number 0, Math 1251, Scot Adams, Fall 1998

No calculators. 50 minutes. Every problem is worth one point.

Answers: ACD*CAGA DDTE**FCE ETFEBDFFE EEAA

%*****************

1. What is the slope of the line through (2,8) and (5,2)?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
(F) -1/2
(G) 1
(H) 1/2
(I) none of these
%section precalc

%*****************

2. What is the equation of the line through (-1,4) with slope -2?
(A) x+1=-2(y-4)
(B) y+1=-2(x-4)
(C) y-4=-2(x+1)
(D) x-4=-2(y+1)
%section precalc

%*****************

3. What is the function which corresponds to the expression 3x^3-5x?
(Note: \cdot means a centered dot.)
(A) 3t^3-5t
(B) 3(\cdot)^3-5
(C) 3(8^3)-5(8)
(D) 3(\cdot)^3-5(\cdot)
(E) none of these
%section precalc

%*****************

4. Compute (d/dx)(3x^8-7x+4).
%section 2.2 Differentiation formulas

%*****************

5. Which of the following expressions of x is a polynomial in x?
(A) 5x^2+3x-1  \over  3x+3
(B) x^2\sin x+4
(C) (\sin 7)x^3+8x^2-1
(D) e^{x^2+x+1}
(E) none of a,b,c,d are right
(F) all of a,b,c,d are right
%section precalc

%*****************

6. If I have not done so already, please remind me to put a graph of
a function f on the board. Using this graph, compute f(2).
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
%section precalc

%*****************

7. Find the x-intercept of the line through (2,5) with slope 1.
(A) 4
(B) -4
(C) 2
(D) -2
(E) 5
(F) -5
(G) none of these
%section precalc

%*****************

8. Which of the following is a closed interval?
(A) [0,1]
(B) [-1,2)
(C) (2,4)
(D) (5,15)
(E) none of these
%section precalc

%*****************

9. What is the degree of x^3+x^4+10x^5?
(A) 3
(B) 4
(C) 1
(D) 5
(E) 10
(F) none of these
%section precalc

%*****************

10. Which of the following is a transcendental function?
(A) 3x^4+5x-5
(B) \sin 15
(C) 2x+4  \over  5x-1
(D) none of these
%section precalc

%*****************

11. True or False: Every constant is a rational function.
(T) True
(F) False
%section precalc

%*****************

12. A rod is growing in length. At time t seconds, its length is
t^3 meters. Find the average rate of growth (in meters per second)
between time t=1 and time t=3.
(A) 3^3-1
(B) 3-1
(C) (3-1)/(3^3-1^3)
(D) (3^3-3)/(1^3-1)
(E) (3^3-1^3)/(3-1)
(F) (1^3-1)/(3^3-3)
%section precalc

%*****************

13. Compute (d/dx)(\tan(8x^2)).
%section 2.2 Differentiation formulas

%*****************

14. Compute (d/dx)((\tan x)\sqrt{x}).
%section 2.2 Differentiation formulas

%*****************

15. True or False: Any polynomial function is a constant function.
(T) True
(F) False
%section precalc

%*****************

16. What is the slope of the line y-15=4(x-3)
(A) 0
(B) 3
(C) 4
(D) 15
(E) none of these
%section precalc

%*****************

17. What is the slope of the line y=5x-4
(A) -4
(B) 0
(C) 3
(D) 4
(E) none of these
%section precalc

%*****************

18. Which of the following is a compact interval?
(A) [2,\infty)
(B) (-\infty,\infty)
(C) [1,4)
(D) (1,8)
(E) [1,8]
(F) all of the above
(G) none of these
%section precalc

%*****************

19. True or False: The domain of any polynomial is (-\infty,\infty).
(T) True
(F) False
%section precalc

%*****************

20. True or False: The domain of any rational function is (-\infty,\infty).
(T) True
(F) False
%section precalc

%*****************

21. What is the range of f(x)=x^2?
(A) (-\infty,\infty)
(B) (-\infty,0)
(C) (0,\infty)
(D) (-\infty,0]
(E) [0,\infty)
(F) (-\infty,\infty)\backslash\{0\}
(G) none of these
%section precalc

%*****************

22. Which of the following is a linear combination of \sin t and
\cos t?
(A) t\sin t+8\cos t
(B) (\sin 4)(\sin t)-\pi(\cos t)
(C) 1+t+t^2
(D) none of these
%section precalc

%*****************

23. Which of these is the equation of the line through (2,4) with
slope -6?
(A) y-2=6(x-4)
(B) y-6=2(x-4)
(C) y-4=2(x-6)
(D) none of these
%section precalc

%*****************

24. What is the domain of f(x)=\sqrt{x-3}?
(A) (-\infty,\infty)
(B) [0,\infty)
(C) (0,\infty)
(D) (-\infty,0]
(E) (-\infty,0)
(F) [3,\infty)
(G) (3,\infty)
(H) (-\infty,3]
(I) (-\infty,3)
(J) [-3,\infty)
(K) (-3,\infty)
(L) (-\infty,-3]
(M) (-\infty,-3)
(N) none of these
%section precalc

%*****************

25. True or False: For all a,b\in(-\infty,\infty), we have (a+b)^2=a^2+b^2.
(T) True
(F) False
%section precalc

%*****************

26. Which of these is equal to a^{-1/5}?
(A) a^5\qquad
(B) 1/a^5\qquad
(C) 1/\sqrt{a}\qquad
(D) 1/a^{-5}\qquad
(E) none of these
%section precalc

%*****************

27. Rationalize the denominator in the expression
3-x  \over  \sqrt{2+x}-\sqrt{x}}.
(A) 3-x  \over  \sqrt{(2+x)-x}
(B) 3-x  \over  (2+x)-x
(C) (3-x)[(2+x)-x]  \over  (2+x)-x
(D) (3-x)(\sqrt{2+x}-\sqrt{x})  \over  (2+x)-x
(E) (3-x)(\sqrt{2+x}+\sqrt{x})  \over  (2+x)-x
(F) none of these
%section precalc

%*****************

28. Which of these is equal to \sqrt{a+b}
(A) \sqrt{a}+\sqrt{b}
(B) (a+b)^2
(C) 1  \over  (a+b)^2
(D) (a+b)^{-1/2}
(E) (a+b)^{1/2}
(F) none of these
%section precalc

%*****************

29. Which if these is equal to \csc x?
(A) 1  \over  \sin x
(B) 1  \over  \cos x
(C) \sin x  \over  \cos x
(D) \cos x  \over  \sin x
(E) \sin^2x+\cos^2x
(F) \tan^2x+\cot^2x
(G) \sec^2x+\csc^2x
(H) none of these
%section precalc

%*****************

30. Find the intervals of negativity of
f(x)={(x+1)^2(x-2)(x-3)  \over  (x+3)(x+4)^3}.
(A) (-4,-3) and (2,3)
(B) (-\infty,-4) and (-3,2) and (3,\infty)
(C) (-\infty,-4) and (-3,-1) and (-1,2) and (3,\infty)
(D) (-\infty,-1) and (2,3)
(E) (-3,2)
(F) (-3,-1) and (-1,2)
(G) (-\infty,\infty)
(H) none of these

%section precalc

END OF TEST