Practice Test 16 - Algebra 1

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

Solve algebraically (using substitution) and identify the intersection point(s) of the line and parabola: $\begin{cases}\n y = 2x + 1 \\ \n y = x^2 + 1\n\end{cases}$
An investment changes from $800 to $840 in one year and then to $882 in the next year. Does this represent constant percent growth, and if so, what is the percent rate per year?
Which set represents the domain of the function $f(x)=\dfrac{x+1}{x^2-9}$ ? Give your answer in interval notation.
Factor $q(x)=x^2+2x-15$ to find the zeros and the axis of symmetry.
A recursive formula for a sequence is given as $a_1 = 7$ and $a_n = a_{n-1} + 4$ for $n \geq 2$ . Which explicit formula represents the same sequence and what is the value of $a_{15}$ ?
What is the common difference $d$ of the arithmetic sequence $15, 11, 7, 3, \dots$ ?
A car's distance from home (in miles) after $t$ hours is $d(t)=50t+20$ . What is the average rate of change of $d(t)$ from $t=1$ to $t=4$ , and what are the units?
A student solving $\frac{x}{2} + \frac{x}{3} = 5$ decides to multiply the entire equation by 6. When asked to justify this choice, which explanation demonstrates the best mathematical reasoning?
The function $f(x)=3(x-1)(x+3)$ is in factored form. What does this reveal about the graph?
A balance is modeled by $(1.20)^t$ for $t$ years (20% annual growth). Which is an equivalent form that highlights the approximate monthly growth factor?
A school fundraiser sells bracelets for $5 each and charges a one-time $10 setup fee for the order. Let $b$ be the number of bracelets and let $C$ be the total cost (in dollars). What equation represents the relationship between $C$ and $b$ ?
How many solutions does the system have? $\begin{cases} 2x+4y=10 \\ x+2y=5 \end{cases}$
A medication amount in the bloodstream decreases by 20% every hour. Which function represents the amount $A(t)$ after $t$ hours if $A(0)=80$ mg?
A rational expression $\frac{P(x)}{x^2 + 4}$ is rewritten as $x^2 - 4 + \frac{3x + 12}{x^2 + 4}$ . What is $P(2)$ ?
The cost (in dollars) to rent a bike is given by $C=3h+8$ , where $h$ is the number of hours. What is the constant term in $3h+8$ ?
A pet shelter is buying bags of dog food and cat food. Let $x$ be the number of dog-food bags and $y$ be the number of cat-food bags. - Dog food costs $18 per bag and cat food costs $12 per bag. Budget is at most $240: $18x+12y\le 240$ . - Storage space allows at most 20 bags total: $x+y\le 20$ . - They need at least 6 dog-food bags: $x\ge 6$ . - $x\ge 0$ and $y\ge 0$ . Check whether $(x,y)=(6,12)$ satisfies all constraints.
On a coordinate plane, graph $y=x^2+4x+3$ . What are the $x$ -intercepts (as points)?
Verify that the definition $8^{2/3}=(8^{1/3})^2$ is consistent with exponent properties. Which explanation uses exponent rules correctly (not just computation)?
Given $g(x) = x - (2x - 1)$ , evaluate $g(4)$ .
Determine whether the function $g(x) = x^2 + 2x$ has a constant rate of change.

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