Practice Test 31 - Algebra 1

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

For $m(x)=\frac{1}{2}x+3$ , calculate the average rate of change over the interval $[4,10]$ .
A teacher wants to describe the relationship between homework time and quiz performance in their class over the last unit (not predict future scores). Which set of variable definitions is most appropriate?
A parabola is graphed on a coordinate plane and is represented by $y = x^2 + 6x + 8$ . What is the vertex of the quadratic function $y = x^2 + 6x + 8$ ?
A bike rental shop charges $12 to rent a bike plus $4 per hour. Let $h$ be the number of hours and $T$ be the total cost in dollars. Which equation models the relationship between $h$ and $T$ ?
The number of members in a chess club can be represented by $\frac{180}{n + 5}$ , where $n$ is the number of years since the club started. Which inequality represents when the club will have fewer than 12 members?
In the expression $-x^2 + 3x - 4$ , what is the leading coefficient?
The value of a machine decreases over time according to $V(t)=200-15t$ , where $V$ is in dollars and $t$ is in years. What is the average rate of change of $V(t)$ from $t=2$ to $t=8$ ? Include units.
Use factoring to analyze $s(x)=-(x^2-4x-12)$ . Which statement correctly describes the zeros and axis of symmetry?
A student is solving $\frac{3x}{x-1} - \frac{2x}{x+1} = \frac{x^2 + 5}{x^2 - 1}$ and multiplies everything by the LCD $(x^2 - 1)$ . After simplification, the student gets $3x(x+1) - 2x(x-1) = x^2 + 5$ . What equation results after expanding and collecting like terms?
A spring scale measures force in newtons (N). When a mass is attached, the spring stretches according to the formula $F = k \times d$ , where $F$ is force in newtons, $d$ is displacement in centimeters, and $k$ is the spring constant. If $k = 15$ , what are the units of the spring constant?
The graphs of $y=x+1$ and $y=-x+5$ intersect at what point?
Which situation involves a constant percent rate of change (exponential), not a constant additive change (linear)?
Solve the linear-quadratic system algebraically (by substitution). The solutions correspond to the intersection points of the line and the parabola: $\begin{cases} y = 2x + 1 \\ y = x^2 + 1 \end{cases}$
Given $h(x) = x^2 + 1$ , what is $h(x + 2)$ ?
A water tank's volume (in gallons) after $t$ minutes is $V(t)=120-6t$ . What is the average rate of change of $V(t)$ from $t=5$ to $t=15$ ? (Compare $(5,V(5))$ and $(15,V(15))$ .)
Why must $5+\sqrt{3}$ be irrational? Choose the reasoning that correctly justifies the conclusion.
The function $p$ is defined by $p(x)=-(x-1)^2+4$ . What is the range of $p$ ? (Give your answer in interval notation.)
A student is solving the equation $3(x-4)=2x+5$ and writes: 1) $3(x-4)=2x+5$ 2) $3x-12=2x+5$ 3) $x-12=5$ Which statement correctly justifies the step from line 2 to line 3?
How many terms are in the expression $x^2+0x-6$ ?
A cyclist rides at a constant speed of 18 km/hr for 45 min. Find the distance traveled in kilometers. Show unit tracking (convert minutes to hours).

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