This test has nine questions worth 20 points in total and should take about 45 minutes. Show every step. Calculators are not needed. Questions cover equations of the forms px + q = r and p(x + q) = r with whole numbers, decimals, fractions and negative numbers.
Test information
- Grade: Grade 7
- Chapter: Two-Step Equations
- Common Core: 7.EE.B.3, 7.EE.B.4a
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 2 pts; Question 8: 3 pts; Question 9: 3 pts)
Question 1: Add, then multiply (2 points)
Solve \(6x+9=45\).
Question 2: Fraction of a variable (2 points)
Solve \(\frac{x}{3}-4=5\).
Question 3: Negative coefficient (2 points)
Solve \(-2x+7=-5\). Graph the solution on the number line.
Question 4: Parentheses (2 points)
Solve \(3(x-5)=21\).
Question 5: Decimal coefficients (2 points)
Solve \(1.5x+2.25=9.75\).
Question 6: Fraction coefficient (2 points)
Solve \(\frac{2}{3}x-4=6\).
Question 7: Find the error (2 points)
Liam solved \(4x+6=30\) and wrote: \(4x=30+6=36\), so \(x=9\). Explain his mistake and find the correct solution.
Question 8: School store receipt (3 points)
Noah buys 4 notebooks that cost \(n\) dollars each and one pen that costs \(\$3.50\). The total is \(\$17.50\).
- Write an equation. (1 point)
- Solve it to find the price of one notebook. (1 point)
- Check the answer. (1 point)
Question 9: Two ways to find a number (3 points)
Mei picks a number, adds 7, and multiplies the result by 4. She gets 52.
- Write an equation for the situation. (1 point)
- Solve the equation algebraically. (1 point)
- Solve the problem with arithmetic and explain how it matches the algebra. (1 point)
See every chapter on the Grade 7 math page.