Practice Test 49 - Algebra 1

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

Start practice test

1. A car's value after $t$ years is modeled by $V(t)=25000(0.90)^t$. Is this exponential growth, decay, or neither?
2. Solve and check for extraneous solutions: $\frac{x}{x-2}=3$
3. A population starts at 500 and decreases by 10% each year. Let $t$ be the number of years. Write the function $P(t)$ that models the population.
4. Function $f$ is given by the equation $f(x)=-(x-1)^2+6$. Function $g$ is described as: "A parabola that opens downward with vertex at $(3,4)$." Which function has the larger maximum value?
5. A bacteria culture is modeled by $N(t)=500\cdot b^t$. If it grows by 8% each hour, what is the value of the growth factor $b$?
6. Multiply: $(2x - 1)(x + 5)$
7. Let $p(x) = 3x - 1$ and $q(x) = \frac{x + 1}{3}$. A student evaluates $(p \circ q)(5)$ by first computing $p(5) = 14$, then computing $q(14) = 5$, and concludes that $(p \circ q)(5) = 5$. What error did the student make?
8. Suppose we want the rule $(b^a)^c=b^{ac}$ to remain true when $a=\tfrac{1}{2}$. What property requires $b^{1/2}$ to mean $\sqrt{b}$ (for $b>0$)?
9. Factor $P(x)=x^2+3x-10$ and use the zeros to determine the x-intercepts of the graph of $y=P(x)$.
10. Function $h$ is described verbally as: "A linear function with y-intercept 6 and slope −2." Function $k$ is given by $k(x)=x+1$. Which function has the greater rate of change (slope)?
11. A nutritionist plans a meal with chicken and rice. Each serving of chicken provides 25g protein and 200 calories. Each serving of rice provides 5g protein and 150 calories. The meal must have at least 40g protein but no more than 650 calories. If $c$ represents servings of chicken and $r$ represents servings of rice, which system represents these nutritional constraints?
12. A movie theater charges $9 per ticket plus a one-time online fee of $2. The total cost is $T(x) = 9x + 2$. What is $T(3)$?
13. What is the coefficient of $y^3$ in $-2y^3+y-1$?
14. Convert $65\ \text{mi/hr}$ to feet per second (ft/sec). Use $1\ \text{mi}=5280\ \text{ft}$ and $1\ \text{hr}=3600\ \text{sec}$.
15. A ball's height (in meters) after $t$ seconds is modeled by $h(t) = -t^2 + 4t$. At what times is the height zero (when the ball is on the ground)?
16. A material's stretch factor is modeled by multiplying a constant calibration factor and an exponential response. Let $f(x)=3$ and $g(x)=2^x$. Find $(f\cdot g)(x)$.
17. The equation $x^2 - 6x + k = 0$ has exactly one real solution. If this equation is solved by completing the square, what is the value of the perfect square trinomial that results?
18. A bakery uses the function $C(n)=2.50n+15$ to model the cost (in dollars) to make $n$ cupcakes, where $n$ is the number of cupcakes. The bakery can make at most 120 cupcakes in one batch. What domain makes sense for $n$?
19. What is the maximum value of the function $h(t) = -t^2 + 4t + 1$?​
20. A student claims: "If $a$ and $b$ are rational numbers, then $a+b$ must be an integer." Which option correctly refutes the claim using correct reasoning about rational numbers?​​​

Practice tests