Practice Test 15 - Algebra 1

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

Start practice test

1. In algebra, consider the literal equation $ax + by = c$, where $a$, $b$, and $c$ are constants. Solve for $y$ in terms of $x$, $a$, $b$, and $c$ using the same steps as solving a numeric equation.
2. What is the boundary line for the linear inequality $3x - y \le 6$?
3. What is the coefficient of $x$ in the expression $x^2 - 4x + 1$?
4. What is the vertex of $y=x^2+4x+9$? (Find it by completing the square.)
5. A student correctly calculates that $16^{3/4} = 8$. Using this result and the properties of exponents, what is the value of $16^{-3/4}$?
6. A population growth model $P(t) = 1200 \cdot 1.05^t$ represents the number of bacteria in a culture after $t$ hours. Laboratory observations show the culture dies after 48 hours due to resource depletion. Considering both the mathematical properties and biological constraints, how should the domain be defined?
7. What is $x$ in the equation $5x-8=2x+10$?
8. Given $f(x)=\sqrt{x}$ and $g(x)=x+7$, evaluate $f(g(9))$. Give your answer in simplest form.
9. What is the intersection point of the lines $y=x+1$ and $y=-x+5$?
10. A water tank contains 600 liters and is draining at a constant rate of 25 liters per minute. Express the remaining volume $V(t)$ (in liters) as a function of time $t$ (in minutes) after draining begins.
11. Convert $65\text{ mi/hr}$ to feet per second (ft/sec). Use $1\text{ mi}=5280\text{ ft}$ and $1\text{ hr}=3600\text{ sec}$.
12. Identify the error in the student work shown for solving $\frac{x}{3}+4=10$: 1) $\frac{x}{3}+4=10$ 2) $x+4=10$ 3) $x=6$ What is the error?​
13. Solve: $x^2 - 12x + 36 = 0$
14. Rewrite $27^{2/3}$ using radical notation and evaluate.​​
15. A school club is buying notebooks and pens for a fundraiser. Notebooks cost $3 each and pens cost $2 each. The club has at most $60 to spend and needs to buy at least 25 total items. Let $x$ = number of notebooks and $y$ = number of pens. Which system of inequalities models all constraints (including that you can't buy negative items)?
16. Two students solve $x^2-5x+6=0$. Student A: 1) $x^2-5x+6=0$ 2) $(x-2)(x-3)=0$ 3) $x-2=0$ or $x-3=0$ Student B: 1) $x^2-5x+6=0$ 2) $x(x-5)+6=0$ 3) $x=5$ or $6=0$ Which statement correctly explains why Student A's step 3 is valid?
17. If $r(x)=-(x-2)^2+5$, what is $r(1)$?
18. Complete the square to show that the function $f(x)=-x^2+10x-7$ has a maximum, and determine the $x$-value where the maximum occurs.
19. The function $p(x)=(x-5)(x+1)$ is in factored form. What does this reveal about the graph? Choose the correct zeros and axis of symmetry.
20. Let $f(x)=x^2+2$ and $g(x)=x-3$. Evaluate $f(g(0))$.​

Practice tests