Practice Test 64 - Algebra 2

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

When a divisor is $(x-c)$ , synthetic division is a streamlined alternative to long division: list coefficients (use $0$ if needed), then bring down, multiply by $c$ , and add. Use synthetic division to divide $P(x)=x^4-2x^3+0x^2+5x-1$ by $(x+1)=(x-(-1))$ (so $c=-1$ ). What are the quotient and remainder (remainder $=P(-1)$ )?
Graph $f(x)=x(x-4)(x+1)^2$ showing all zeros, whether the graph crosses or touches at each zero, and the end behavior.
A medication dose starts at 120 mg in the bloodstream. Each hour, $25\%$ of the medication is eliminated. Create an exponential decay model for the amount $M(t)$ after $t$ hours, then solve for when the amount drops to 30 mg. Round to the nearest tenth of an hour and interpret your result.
A ball is dropped from $10$ ft and each bounce reaches $80\%$ of the previous height. What is the total vertical distance traveled during the first 5 bounces (up and down), not including the initial drop? Distance for bounce $k$ is $2(10)(0.8^k)$ for $k=1,2,3,4,5$ .
Multiply and write the result in standard form (polynomials are closed under multiplication): $(x^2 - 3x + 2)(x + 4)$
A roller coaster's height above ground (in meters) is modeled on the interval $0\le x\le 6$ by the function $H(x)=-x^2+6x+1$ , where $x$ is horizontal distance (in tens of meters). What is the absolute maximum of $H$ on $[0,6]$ (give the point)?
A physics student is studying the relationship between the height $h$ of a pendulum's release point and its period $T$ . The data suggests the relationship $T = k\sqrt{h}$ where $k$ is a constant. If $T = 2$ seconds when $h = 16$ feet, which statement about graphing this relationship is correct?
Predict the solution type using the discriminant, then solve in $a\pm bi$ form: $x^2 - 6x + 10 = 0$ .
Determine whether the data are best modeled by a linear or exponential function, and write a function that models the data. Table: $x: 0,\ 1,\ 2,\ 3$ and $f(x): 18,\ 15,\ 12,\ 9$
A rectangular garden has a perimeter of 48 feet. Let $l$ be the length (ft) and $w$ be the width (ft). Write an equation relating $l$ and $w$ , and choose appropriate axes labels and a reasonable scale to graph the relationship in the first quadrant.
A number and its reciprocal have a sum of $\frac{10}{3}$ . Write and solve an equation to find the number. Let $x$ = the number (assume $x\ne 0$ ).
A ride-sharing company models driver earnings (in dollars) after $x$ hours by $E(x)=|x-5|-2$ . Identify the x-intercept(s) of $E$ (as points).
What is the horizontal asymptote of the exponential function $p(x)=2e^{x}+4$ ?
In chemistry, the ideal gas law is $PV = nRT$ , where $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is a constant, and $T$ is temperature. Solve $PV = nRT$ for $T$ .
Solve $x^2 - 7x + 10 = 0$ by factoring or by the quadratic formula. Which pair of solutions is correct?
Solve the equation $8\cdot e^{t/3}=90$ for $t$ . Give the exact answer as a logarithm and then approximate using technology.
For the sequence $14,\ 10,\ 6,\ 2,\ \dots$ , write both a recursive formula and an explicit formula for $a_n$ (with $n\ge 1$ ).
Show by composition that $f(x)=x^3+2$ and $g(x)=\sqrt[3]{x-2}$ are inverse functions. Compute $f(g(x))$ and $g(f(x))$ and check whether both simplify to $x$ .
Rewrite the exponential equation $10^3 = 1000$ in logarithmic form.
The function $f(x)=(x+1)^2-5$ is not one-to-one on all real numbers because it fails the horizontal line test. What is a suitable domain restriction that makes $f$ invertible?

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