Practice Test 47 - Algebra 1

20 questions. Answer them in any order, then submit to see your score and every explanation.

Identify the unit error in this calculation for distance: A car travels at $60\text{ mi/hr}$ for $30\text{ min}$ . A student writes $60\,\text{mi/hr}\times 30\,\text{min}=1800\,\text{mi}$ Which statement best describes the unit mistake?
For $P(x)=-x(x-3)(x+2)$ , identify the zeros and determine the correct end behavior to guide a rough sketch. Which option is correct?
Why is $\pi+\frac{1}{2}$ irrational? Choose the option that gives a correct contradiction argument.
A ball's height (in feet) after $t$ seconds is modeled by $H(t)=-t^2+10t+4$ . Complete the square to find the maximum height and the time when it occurs.
Write both the explicit formula and the recursive formula for the arithmetic sequence $4, 9, 14, 19, \dots$ .
Which statement about long-term growth is true? Compare $f(x)=1000x$ (linear), $g(x)=x^3$ (polynomial), and $h(x)=1.1^x$ (exponential).
Temperature conversion can be written as $C = \dfrac{5}{9}(F - 32)$ , where $C$ is degrees Celsius and $F$ is degrees Fahrenheit. Solve for $F$ in terms of $C$ .
Is the expression $\frac{1}{2}+\pi$ rational or irrational? Choose the option with correct reasoning.
A medicine amount in the bloodstream is modeled by $M(t)=60(0.95)^t$ , where $t$ is in hours. What percent rate of change does this function represent per hour?
If $p$ and $q$ are both irrational numbers, which of the following statements about $p \cdot q$ is most accurate?
A ball's height (in feet) after $t$ seconds is modeled by $h(t) = -t^2 + 4t - 3$ . The ball hits the ground when $h(t)=0$ . What are the zeros of $h(t)$ ?
On a coordinate plane, the quadratic function $y = x^2 - 9$ is graphed. What are the x-intercepts of $y = x^2 - 9$ ?
Factor $P(x)=x^4-5x^2+4$ and use the zeros to sketch a rough graph. Your sketch should show all x-intercepts and the correct end behavior.
Consider the quadratic expression $4x^2 - 4x - 8$ . After factoring completely to reveal the zeros, what is the sum of the squares of the zeros?
A gym charges a one-time sign-up fee plus a constant cost per month. The total cost $C$ (in dollars) after $m$ months is shown below. Does this table show a constant rate of change of $C$ with respect to $m$ ? If yes, what is the rate (in $\$/month$ )?
The volume of a rectangular prism is $V = lwh$ , where $V$ is volume, $l$ is length, $w$ is width, and $h$ is height. Solve for $h$ in terms of $V$ , $l$ , and $w$ .
For the piecewise function $f(x)=\begin{cases}2x+1, & x \geq 0 \\ -x+4, & x<0\end{cases}$ what is $f(-3)$ ?
A parabola is graphed on a coordinate plane for the function $f(x) = (x - 2)^2 - 9$ . Graph the function and identify the vertex.
Given $f(x)=5-x$ and $g(x)=2x+1$ , what is $f(g(x))$ ?
At what point does the graph of $y = \frac{1}{2}x - 3$ cross the y-axis?

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