Practice Test 33 - Algebra 1

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

How many terms are in the expression $2x^3 - 5x^2 + x - 9$ ?
Consider the expression $5x^2 - 3x + 8$ . What are the terms in $5x^2 - 3x + 8$ ?
If a customer pays $27 for shipping, and the statement "$ $C(w) = 27$ $" represents this situation, what does the expression "$ $C(w + 2)$ $" represent in this context?
Solve $x^2 + 4x + 8 = 0$ . Express complex solutions in $a \pm bi$ form.
A bacteria culture grows according to $N(t) = 300\cdot 2^t$ , where $t$ is hours and $N(t)$ is the number of bacteria. What does the parameter $300$ represent in this context?
Which direction should be shaded for the inequality $y<-3x+2$ ?
What is the sum of $(3x^3 - 2x^2 + x - 5)$ and $(x^3 + 4x^2 - 3x + 2)$ ?
Solve the system: $\begin{cases} x+y=7 \\ x-y=1 \end{cases}$ What is the solution $(x, y)$ ?
Verify whether the point $(2,3)$ is a solution to the linear-quadratic system (it must satisfy BOTH equations): $\begin{cases} y = x^2 - 1 \\ y = 2x - 1 \end{cases}$ Which statement is correct?
What are the factors of the expression $5(x-1)$ ?
How can the expression $4x^2(3x-5)$ be viewed to reveal its structure? (Treat $(3x-5)$ as one unit.)
A function $C(t) = 15t + 200$ represents the total cost in dollars to rent a venue for $t$ hours, where there is a base fee plus an hourly rate. The venue is available for rental from 9 AM to 11 PM on any given day. What is the most appropriate domain for this function in the given context?
A line is graphed on a coordinate plane and is represented by the equation $y = -2x + 5$ . For the function $y = -2x + 5$ , what is the slope?
Find the complex solutions to $x^2 + 4x + 8 = 0$ . Express solutions in $a \pm bi$ form and use $\sqrt{-1} = i$ (so $i^2 = -1$ ).
Factor $x^2 + 6x + 9$ and find its zeros.
Use the factored form $P(x)=x(x-3)^2(x+2)$ to identify the zeros (with multiplicities) and state at which zeros the graph of $y=P(x)$ touches the x-axis rather than crossing it.
A radioactive substance has a half-life of 6 hours. Starting with 320 grams, how much will remain after 18 hours, and what percent of the original amount is this?
A function $f$ is defined on the integers $n = 1, 2, 3, \dots$ by $f(1) = 2$ and $f(n+1) = 2\,f(n)$ . What is $f(4)$ ?
A sequence is defined recursively by $a_1=4$ and $a_{n+1}=a_n+3$ for $n=1,2,3,\dots$ . What is $a_5$ ?
The quadratic function $y = - (x - 3)^2 + 4$ is graphed on a coordinate plane. What is the maximum value of the function?

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