8.EE Tutor Intake — Expressions and Equations

Simplify $3^4 \cdot 3^{-6}$ and write the result as a fraction
with a positive exponent. Which expression is correct?

Consider the two equations $x^2 = 49$ and $x^3 = 8$.
Which statement correctly describes their solutions?

A car travels at a constant speed. Its distance $d$ (in miles)
and time $t$ (in hours) are proportional, and the graph of $d$
against $t$ is a straight line through the origin. The car goes
120 miles in 2 hours. What is the slope of the graph, in miles
per hour? Enter a number.

A student solves a linear equation correctly and the equation
simplifies to $0 = 0$. What does this tell you about the original
equation's solutions?

Two lines are graphed on the same coordinate plane and cross at
the point $(3, 5)$. The lines are the graphs of a system of two
linear equations. What is the solution to the system?

Simplify $\dfrac{(2^3)^2 \cdot 2^4}{2^5}$ to a single power of 2,
then evaluate it. Enter the resulting whole number.

Write the number $0.00037$ in scientific notation, in the form
$a \times 10^{n}$ where $1 \le a < 10$ and $n$ is an integer.

Multiply $(4 \times 10^5)(3 \times 10^6)$ and write the result in
proper scientific notation, in the form $a \times 10^{n}$ where
$1 \le a < 10$.

A line passes through the points $(2, 3)$ and $(6, 15)$.
Calculate the slope of the line. Enter a number.

A line has slope $m = 2$ and crosses the $y$-axis at the point
$(0, -3)$. Which equation represents this line in the form
$y = mx + b$?

Solve for $x$: $5x - 3 = 2x + 12$. Enter the value of $x$.

Solve for $x$: $\dfrac{1}{2}(x + 6) = 2x - 3$. Enter the value
of $x$.

Solve the system for $x$ and $y$:
$y = 2x + 1$ and $3x + y = 11$.
Enter the solution as an ordered pair $(x, y)$.