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Back to Tutor Intake Assessment: Expressions and Equations

8.EE Tutor Intake -- Expressions and Equations

This short check helps your tutor see where to start. Work each problem
on your own, without a calculator or notes. If you are unsure, give your
best try — the goal is to find what to work on together, not to grade you.

Grade 8·15 problems·~14 min·Common Core Math - Grade 8·domain·ee
Work through problems with immediate feedback
A

Concepts

1

Simplify 34⋅3−63^4 \cdot 3^{-6} and write the result as a fraction
with a positive exponent. Which expression is correct?

2

Consider the two equations x2=49x^2 = 49 and x3=8x^3 = 8.
Which statement correctly describes their solutions?

3

A car travels at a constant speed. Its distance dd (in miles)
and time tt (in hours) are proportional, and the graph of dd
against tt 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.

4

A student solves a linear equation correctly and the equation
simplifies to 0=00 = 0. What does this tell you about the original
equation's solutions?

5

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

B

Procedures

1

Simplify (23)2⋅2425\dfrac{(2^3)^2 \cdot 2^4}{2^5} to a single power of 2,
then evaluate it. Enter the resulting whole number.

2

Write the number 0.000370.00037 in scientific notation, in the form
a×10na \times 10^{n} where 1≤a<101 \le a < 10 and nn is an integer.

3

Multiply (4×105)(3×106)(4 \times 10^5)(3 \times 10^6) and write the result in
proper scientific notation, in the form a×10na \times 10^{n} where
1≤a<101 \le a < 10.

4

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

5

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

6

Solve for xx: 5x−3=2x+125x - 3 = 2x + 12. Enter the value of xx.

7

Solve for xx: 12(x+6)=2x−3\dfrac{1}{2}(x + 6) = 2x - 3. Enter the value
of xx.

8

Solve the system for xx and yy:
y=2x+1y = 2x + 1 and 3x+y=113x + y = 11.
Enter the solution as an ordered pair (x,y)(x, y).

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