Q: Which of the following systems of equations has no solution?

$\begin{cases} x - y = 2 \\ 2x - 2y = 5 \end{cases}$

Q: Which of the following is the correct result of applying one step of Gauss-Jordan elimination to the augmented matrix $\begin{bmatrix} 1 & 2 & | & 5 \\ 2 & 4 & | & 10 \end{bmatrix}$?

$\begin{bmatrix} 1 & 2 & | & 5 \\ 0 & 0 & | & 0 \end{bmatrix}$

Question 1

Which of the following systems of equations has no solution?

Accepted Answer

$\begin{cases} x - y = 2 \ 2x - 2y = 5 \end{cases}$

Question 2

Solve the following system using the substitution method: $\begin{cases} x + 2y = 7 \ 3x - y = 5 \end{cases}$

Accepted Answer

$x = 3,\ y = 2$

Question 3

Which of the following is the correct result of applying one step of Gauss-Jordan elimination to the augmented matrix $\begin{bmatrix} 1 & 2 & | & 5 \ 2 & 4 & | & 10 \end{bmatrix}$?

Accepted Answer

$\begin{bmatrix} 1 & 2 & | & 5 \ 0 & 0 & | & 0 \end{bmatrix}$

Question 4

What is the sum of the complex numbers $3 + 4i$ and $2 - 5i$?

Accepted Answer

$5 - i$

Question 5

Which of the following is a solution to the quadratic equation $x^2 - 6x + 13 = 0$?

Accepted Answer

$x = 3 + 2i$

Question 6

A ball is thrown upward from the ground with an initial velocity of $32$ ft/s. Its height $h$ (in feet) after $t$ seconds is given by $h = -16t^2 + 32t$. After how many seconds does the ball hit the ground again?

Accepted Answer

$2$ seconds

Question 7

Solve for $x$: $\sqrt{x + 5} = 3$

Accepted Answer

$x = 4$

Question 8

Which of the following equations is quadratic in form?

Accepted Answer

$x^4 - 5x^2 + 6 = 0$

Question 9

Solve the rational equation: $\frac{2}{x} + 1 = 3$

Accepted Answer

$x = 1$

Question 10

Which of the following is the solution set for $|2x - 5| = 7$?

Accepted Answer

$\left\{ 6, -1 \right\}$

Question 11

Find the distance between the points $A(2, 3)$ and $B(8, 7)$.

Accepted Answer

$2\sqrt{10}$

Question 12

What is the equation of a circle with center at $(3, -2)$ and radius $5$?

Accepted Answer

$(x - 3)^2 + (y + 2)^2 = 25$

Question 13

Given the function $f(x) = \frac{1}{x-2}$, what is the domain of $f$?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 14

If $f(x) = 2x + 1$ and $g(x) = x^2$, what is $(f \circ g)(3)$?

Accepted Answer

$19$

Question 15

Which of the following describes a function that is decreasing on its entire domain?

Accepted Answer

$f(x) = -2x$

Question 16

A quadratic equation models the height $h$ (in meters) of a projectile: $h = -4.9t^2 + 19.6t + 2$. What is the maximum height reached by the projectile?

Accepted Answer

$21.6$ meters

Question 17

Which of the following relations is NOT a function?

Accepted Answer

$\{ (1,2), (2,3), (1,4) \}$

Question 18

Solve for $x$: $x^{2/3} = 16$

Accepted Answer

$x = 64$

Question 19

Which of the following best describes the range of the function $f(x) = |x|$?

Accepted Answer

$[0, \infty)$

Question 20

Given the points $A(-1, 4)$ and $B(3, -2)$, what is the midpoint of $AB$?

Accepted Answer

$(1, 1)$

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