Practice Test 27 - Algebra 1

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

Start practice test

1. A sequence is defined recursively on $n=1,2,3,\dots$ by $a_1=10$ and $a_{n+1}=a_n-2$. What are the first four terms $a_1, a_2, a_3, a_4$?
2. A recipe uses 250 mL of water measured with a cup marked in 10 mL increments (so measurements are to the nearest 10 mL). Which reporting shows appropriate precision for the measured amount?
3. Is $\left(\frac{2}{3}\right)+\left(-\frac{5}{6}\right)$ rational or irrational? Choose the best justification.
4. Is point $(0,0)$ in the solution region of the system $\begin{cases} y>2x-3 \\ y\le x+1 \end{cases}$ ?
5. Transform and solve by completing the square: $x^2 - 6x + 2 = 0$. First write it in the form $(x-p)^2=q$, then find the solutions.
6. A student solving $x^2 - 9 = 0$ factors to get $(x-3)(x+3) = 0$ and then writes $x = 3$ or $x = -3$. What property allows the conclusion that at least one factor must equal zero?
7. Use completing the square to find solutions to $x^2-6x+2=0$. Express it as $(x-p)^2=q$ and solve.
8. Factor $f(x)=x^2-6x+8$ to find the zeros and the axis of symmetry of the parabola.
9. Which describes the structure of $5\big(2x-1\big)^3?$ View $(2x-1)$ as a single unit.
10. The sequence $a_n$ is a function with domain $n=1,2,3,\dots$ and starts $6, 3, 0, -3, \dots$. Which recursive rule generates this sequence?
11. Solve for $x$: $3x + 7 = 22$
12. Verify whether $ (2,3) $ is a solution to the linear-quadratic system (i.e., an intersection point). Choose the correct statement. $\begin{cases} y = x^2 - 1 \\ y = 2x - 1 \end{cases}$
13. Factor $P(x)=x^2-5x+6$ and use the zeros to sketch a rough parabola. Your sketch should show the x-intercepts and whether the parabola opens up or down.
14. Graph the quadratic function $y=(x+1)^2+2$ on a coordinate plane. What is the vertex?
15. An amount decays by 20% per year, so after $t$ years it is multiplied by $(0.80)^t$. Rewrite $(0.80)^t$ to reveal the equivalent monthly decay factor.​​
16. Function $f$ is given by $f(x)=5-2x$. Function $g$ is given in the table. At $x=3$, which function has the greater output? Table for $g(x)$: - $g(1)=2$ - $g(2)=1$ - $g(3)=0$ - $g(4)=-1$
17. Solve using elimination: $\begin{cases} 3x-y=11\\ x+y=5 \end{cases}$ Find the solution $(x, y)$.
18. Perform the indicated operation and simplify. (Rational expressions are closed under multiplication, so the result is a rational expression.) $\frac{3}{x} \cdot \frac{x^2}{x+2}$
19. Rewrite $9x^2-24x+16$ using its structure as a perfect square trinomial.
20. What is the coefficient of $a$ in the expression $-5a+2a^2-1$?

Practice tests