Gateway Quiz DiagnosticTest

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Problem 1.

(1 point)

$\sqrt{48u^{10}v^{12}y^5} =$
A. $7 u^5 v^6 y^{9/2}$
B. $2\sqrt{12}\, u^{19/2} v^{23/2} y^{9/2}$
C. $\sqrt{48}\, u^{19/2} v^{23/2} y^{9/2}$
D. $2\sqrt{12}\, u^{9/2} v^{11/2} y^{5/2}$
E. $4\sqrt{3}\, u^5 v^6 y^{5/2}$

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Problem 2.

(1 point)

$e^{kt}\cdot e^3\cdot e =$
A. $e^{3kt+1}$
B. $e^{4kt}$
C. $e^{(k+4)t}$
D. $e^{k}e^{t}\cdot e^{4}$
E. $e^{kt+4}$

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Problem 3.

(1 point)

$3x^{-1}(x^2 - 1) =$
A. $3x + {3\over x}$
B. $3x - 1$
C. $3x^{-2} - {3\over x}$
D. $3x^{-2} - 1$
E. $3x - {3\over x}$

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Problem 4.

(1 point)

$5z^{-2}(3z^{-1}+2z^2) =$
A. $15z^2 + 10z^{-4}$
B. $15z^2$
C. $15z^{-3} + 10$
D. $15z^{-3}$
E. $15z^{-3} + 2z^2$

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Problem 5.

(1 point)

The expression $3r^2-11r-4$ factors as:
A. $(3r+4)(r-1)$
B. $(3r+1)(r-4)$
C. $(r+1)(3r-4)$
D. $(3r+2)(r-2)$
E. none of the above

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Problem 6.

(1 point)

Factor the expression $(1+r)^2+(1+r)^2r$

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Note: grading the test grades all problems, not just those on this page.

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