Equation Showdown Test
EQUATION SHOWDOWN
Algebra 1 • Unit 1 Assessment
Name:
Date:
Period:
Directions: Read each question carefully. For full credit, show all algebraic steps neatly in the spaces provided. Simplify your final answers completely.
Q1 LITERAL EQUATIONS
Solve the formula for the area of a triangle for the height, h:
\(A = \frac{1}{2}bh\)
Show Your Work:
Answer: h =
Q2 VARIABLES ON BOTH SIDES
Solve the linear equation for x:
\(8x - 3 = 5x + 9\)
Show Your Work:
Answer: x =
Q3 DISTRIBUTIVE PROPERTY
Solve the linear equation for x:
\(3(2x - 4) = 4(x + 2)\)
Show Your Work:
Answer: x =
Algebra 1 • Equation Showdown Page 1 of 3
EQUATION SHOWDOWN • Part I Continued
SECTION B: SIGN & VARIABLE COGNITION
Q4 DISTRIBUTIVE & NEGATIVES
Solve the equation for x. Watch your signs carefully:
\(2(3x - 1) = -2(x + 5)\)
Show Your Work:
Answer: x =
Q5 LITERAL PERIMETER
Solve the perimeter formula for the rectangle's width, w:
\(P = 2l + 2w\)
Show Your Work:
Answer: w =
Q6 MULTI-STEP VARIABLE
Solve the equation for x. Simplify all terms first:
\(6(x + 2) - 4 = 2(2x + 8)\)
Show Your Work:
Answer: x =
Q7 LITERAL LINEAR
Solve the slope-intercept equation of a line for x:
\(y = mx + b\)
Show Your Work:
Answer: x =
Algebra 1 • Equation Showdown Page 2 of 3
EQUATION SHOWDOWN • Part II: High Level Concepts
SECTION C: REAL WORLD & STANDARD FORM
Q8 LITERAL TEMPERATURE
Solve the Celsius conversion formula for Fahrenheit, F:
\(C = \frac{5}{9}(F - 32)\)
Show Your Work:
Answer: F =
Q9 GEOMETRIC CONTEXT
Two rectangles have the same area. Rectangle A has a width of \(3\) and a length of \(2x + 5\). Rectangle B has a width of \(5\) and a length of \(x + 7\). Write and solve an equation to find the value of x.
Rectangle A Area = \(3(2x + 5)\)
Rectangle B Area = \(5(x + 7)\)
Show Your Work:
Eq: x =
Q10 STANDARD TO SLOPE-INTERCEPT
Solve the linear equation in standard form for y (where \(B \neq 0\)):
\(Ax + By = C\)
Show Your Work:
Answer: y =
Confidence Level:
1 2 3 4 5
Page 3 of 3
Equation Showdown Answer Key
EQUATION SHOWDOWN KEY
Teacher Grading Guide • 10 Points Total
STATUS: COMPLETE WORKED SOLUTIONS
Grading Rubric (per question): 1.0 Point total. 0.5 points for correct steps and clear algebraic properties used; 0.5 points for the correct simplified final answer.
Q1 KEY 1.0 Point
Solve \(A = \frac{1}{2}bh\) for h:
Worked Steps:
1. Multiply both sides by 2 to clear the fraction:
\(2A = bh\)
2. Divide both sides by \(b\) to isolate \(h\):
\(h = \frac{2A}{b}\)
FINAL ANSWER: h = \(\frac{2A}{b}\)
Common Error: Students may divide by 2 instead of multiplying, leading to \(h = \frac{A}{2b}\).
Q2 KEY 1.0 Point
Solve \(8x - 3 = 5x + 9\) for x:
Worked Steps:
1. Subtract \(5x\) from both sides:
\(3x - 3 = 9\)
2. Add \(3\) to both sides:
\(3x = 12\)
3. Divide by 3: \(x = 4\)
FINAL ANSWER: x = 4
Common Error: Mixing up signs when shifting constants, e.g., \(9 - 3 = 6\) instead of \(9 + 3 = 12\).
Q3 KEY 1.0 Point
Solve \(3(2x - 4) = 4(x + 2)\) for x:
Worked Steps:
1. Distribute on both sides:
\(6x - 12 = 4x + 8\)
2. Subtract \(4x\) from both sides:
\(2x - 12 = 8\)
3. Add 12 & divide by 2: \(x = 10\)
FINAL ANSWER: x = 10
Common Error: Forgetting to distribute to the second term inside parentheses (e.g. \(6x - 4\)).
Algebra 1 • Equation Showdown Key Page 1 of 3
EQUATION SHOWDOWN KEY • Part I Continued
SECTION B: SOLUTION BREAKDOWNS
Q4 KEY 1.0 Point
Solve \(2(3x - 1) = -2(x + 5)\) for \(x\):
1. Distribute negative correctly:
\(6x - 2 = -2x - 10\)
2. Add \(2x\) to both sides:
\(8x - 2 = -10\)
3. Add 2 to both sides: \(8x = -8\)
4. Divide by 8: \(x = -1\)
FINAL ANSWER: x = -1
Q5 KEY 1.0 Point
Solve \(P = 2l + 2w\) for \(w\):
1. Subtract \(2l\) to isolate width term:
\(P - 2l = 2w\)
2. Divide both sides by 2:
\(w = \frac{P - 2l}{2}\) or \(w = \frac{P}{2} - l\)
Either form is mathematically correct and earns full credit.
FINAL ANSWER: w = \(\frac{P - 2l}{2}\) or \(\frac{P}{2} - l\)
Equation Showdown Remediation Exit Ticket
EQUATION SHOWDOWN: REMEDIATION
Unit 1 Exit Ticket • Mastery Check
Name:
Date:
Period:
Goal: Demonstrate your growth on these target Algebra 1 equation-solving standards. Show every algebraic property you use to isolate the variable.
SKILL A DISTRIBUTIVE PROPERTY
Solve the equation for x:
\(2(2x - 3) = 3(x + 1)\)
Show Your Work:
Answer: x =
SKILL B LITERAL EQUATIONS
Solve the volume of a rectangular prism formula for the height, h:
\(V = lwh\)
Show Your Work:
Answer: h =
SKILL C NEGATIVES & COEFFICIENTS
Solve the equation for x. Watch your signs:
\(4(x - 2) = -2(x - 8)\)
Show Your Work:
Answer: x =
My Strategy Goal:
Distribute first Show inverse steps Double-check signs
Mini-Quiz
