Practice Test 41 - Algebra 1

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

A student is assembling gift bags. Let $x$ be the number of sticker sheets and $y$ be the number of keychains. Constraints: - Sticker sheets cost $2 each and keychains cost $5 each. - The student has at most $40 to spend. - The student wants at least 10 total items. - $x$ and $y$ must be whole numbers and cannot be negative. Is the point $(x,y)=(5,6)$ a viable solution? Explain by checking the constraints.
Function $A$ is described as: "An exponential function with initial value $40$ that grows by $20\%$ each time $t$ increases by 1." Function $B$ is given by $B(t)=30(1.3)^t$ . Which function has the higher initial value (value when $t=0$ )?
A gym charges $25 to sign up and then $15 per month. Let $m$ be the number of months and let $C$ be the total cost (in dollars). How should the coordinate plane be set up to graph this relationship?
Does the function $f(x)=3x^2-1$ have a constant rate of change? (A constant rate means $\Delta y/\Delta x$ is the same for all equal intervals.)
If $a$ and $b$ are rational numbers with $a \neq 0$ , and $x$ is irrational, which statement about $\frac{ax + b}{a}$ is always true?
Simplify: $(2x^2 + 3x - 4) - (x^2 - 5x + 6)$
Which form of a quadratic function best shows the vertex immediately?
Two students are debating whether the point $(-2, 7)$ lies on the graph of $y = x^2 + 3$ . Student A says it does, Student B says it doesn't. How should they resolve this disagreement?
Order the following functions by growth rate for large $x$ (from slowest to fastest): $\quad f(x)=7x$ (linear), $g(x)=5x^2$ (quadratic), $p(x)=x^5$ (polynomial), $h(x)=1.2^x$ (exponential).
Solve the system: $\begin{cases} x+2y=10\\ x-y=1 \end{cases}$ What is the solution $(x,y)$ ?
The function $h$ is defined by $h(x)=x^2-9$ . What is the range of $h$ ? (Give your answer in interval notation.)
Solve using the method of completing the square: $x^2 - 8x + 12 = 0$ .
Graph the inequality $x < -2$ . Which description is correct?
A video game store sells used games for $12 each. Let $n$ be the number of games and $C$ be the total cost (in dollars). When graphing this relationship, what should the axes be labeled?
A quantity increases by 5% per year, so after $t$ years it is multiplied by $(1.05)^t$ . Rewrite $(1.05)^t$ to show the equivalent quarterly growth factor (4 quarters per year).
Use polynomial division to rewrite the rational expression $\frac{x^2+5x+7}{x+2}$ in the form $q(x)+\frac{r(x)}{x+2}$ , where $\deg(r)<\deg(x+2)$ .
Derive the finite geometric series sum formula starting from $S_n=a+ar+ar^2+\cdots+ar^{n-1}$ by multiplying by $r$ and subtracting to cancel the middle terms. Which expression correctly gives $S_n$ for $r \ne 1$ ?
An amount of medicine in the bloodstream is modeled by $M(t)=1000(0.80)^t$ , where $t$ is in hours. What percent rate of change does this function represent per hour?
To keep the power-of-a-power property $(b^a)^c=b^{ac}$ valid when $a=\tfrac{m}{n}$ (with integers $m$ and $n\ge 2$ ), we define rational exponents using radicals. Which statement correctly explains why $b^{m/n}=\sqrt[n]{b^m}=(\sqrt[n]{b})^m$ (for $b>0$ )?
Evaluate $16^{3/4}$ .

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