College Algebra Practice Questions - Part 1

Q1) If $\dfrac{( k + 1 ) ! \cdot ( k + 2 ) !}{ k ! \cdot ( k + 3 ) !} = \dfrac{3}{4} $, then $k =$ ?

A. $1$

B. $2$

C. $3$

D. $4$

E. $5$

Q2) Express as a single logarithm: $2\log_b x+3\log_b y - \dfrac{1}{2}\log_b z$

A. $\log_b (x^2y^3-\sqrt z)$

B. $\log_b (2 x + 3y-\dfrac{1}{2}z)$

C. $\log_b (\dfrac{x^2y^3}{\sqrt z})$

D. $\dfrac{9}{2}\log_b(x+y-z)$

E. $\dfrac{\log_b(x^2 y^3)}{\log_b(\sqrt z)}$

Q3) $f(x)$ and $g(x)$ are functions defined by the tables of values below. What is the value of $f(g(-4))$?

$x$ $f(x)$ $-10$ $0$ $0$ $3$ $2$ $6$ $3$ $7$ $6$ $21$

$x$ $g(x)$ $-10$ $-20$ $-8$ $-10$ $-5$ $0$ $-4$ $3$ $-3$ $5$

A. $5$

B. $7$

C. $0$

D. $-3$

E. $3$

Q4) The imaginary number $i$ is defined such that $i^2=−1$. What does $i−i^2+i^3−i^4+i^5−i^6...−i^{20}$ equal?

A. $0$

B. $-i$

C. $1-i$

D. $i$

E. $1+i$

Q5) What is the next term in the geometric sequence $1$,$-\dfrac{1}{2}$,$\dfrac{1}{4}$,$−\dfrac{1}{8}$,…?

A. $-\dfrac{1}{16}$

B. $-\dfrac{1}{32}$

C. $\dfrac{1}{32}$

D. $\dfrac{1}{16}$

E. $\dfrac{1}{2}$

Q6) A ball thrown from an initial height of $2$ feet at an initial velocity of $40$ feet per second has its height, as a function of time, given by the equation $h=−16 t^2+40 t+2$ , where $h$ is the height of the ball in feet and $t$ is the time in seconds after the ball was thrown. After how many seconds will the ball reach its maximum height?

A. $1.25$

B. $2.5$

C. $2.0$

D. $40.0$

E. $16.0$

Q7) If the fifth term of an arithmetic sequence is equal to $−12$ and its eleventh term is equal to $−24$, then what is the first term of this sequence?

A. $-4$

B. $-2$

C. $0$

D. $-6$

E. $-8$

Q8) If $e^{x+1}=e^{(x+1)^2}$, then $x=$?

A. $1$ or $2$

B. $3$ or $4$

C. $5$ or $6$

D. $7$ or $8$

E. $-1$ or $0$

A. $-2$ or $9$

B. $9$

C. $2$ or $-9$

D. $0$ or $1$

E. $-9$

Q10) For all $x \gt −1$, $\log_4 \dfrac{\sqrt{x+1}}{(x+2)^2}=$

A. $\log_4 \dfrac{1}{2}(x+1)-\log_4 2(x+2)$

B. $\log_4 (\sqrt{x+1}-(x+2)^2)$

C. $\dfrac{1}{2} \log_4 (x+1)-2 \log_4 (x+2)$

D. $\log_4 \sqrt{x+1}+\log_4 (x+2)^2$

E. $\dfrac{1}{2} \log_4 (x+1)+ 2 \log_4 (x+2)$