Writing and Evaluating Algebraic Expressions: Grade 6 Math Test – PDF Download

Question 1: Parts of an Expression (2 points)

Consider the expression \(6x + 11y + 4\).

1. Name the coefficient of \(y\). (1 point)
2. State the number of terms. (1 point)

Question 2: Translating Phrases (2 points)

Write an algebraic expression for each phrase.

1. the sum of 12 and \(k\) (1 point)
2. \(w\) divided by 5 (1 point)

Question 3: Translating Longer Phrases (2 points)

Write an algebraic expression for each phrase.

1. 3 less than twice \(n\) (1 point)
2. 4 times the sum of \(x\) and 9 (1 point)

Question 4: Evaluating with One Variable (2 points)

Evaluate each expression when \(n = 8\).

1. \(5n – 12\) (1 point)
2. \(\frac{64}{n} + n^2\) (1 point)

Question 5: Evaluating with Two Variables (2 points)

Evaluate each expression when \(x = 3\) and \(y = 4\).

1. \(2x^2 + y\) (1 point)
2. \((x + y)^2 – 10\) (1 point)

Question 6: Cube Formulas (3 points)

A cube with edge length \(s\) has volume \(V = s^3\) and surface area \(A = 6s^2\).

1. Find the volume of a cube with \(s = 5\text{ in}\). (1 point)
2. Find the surface area of that cube. (1 point)
3. Find the volume of a cube with \(s = \frac{1}{2}\text{ in}\). (1 point)

Question 7: Equivalent Expressions (3 points)

1. Use the distributive property to expand \(7(3x + 2)\). (1 point)
2. Write \(12y + 18\) as the product of \(6\) and a sum. (1 point)
3. Simplify \(5a + 2 + 3a + 9\). (1 point)

Question 8: Testing Equivalence (2 points)

Maya says that \(4(x + 2)\) and \(4x + 2\) are equivalent expressions. Decide whether she is correct and justify your answer with numbers.

Question 9: Movie Night (2 points)

Jamal buys 3 movie tickets at $9 each and \(b\) buckets of popcorn at $6 each.

1. Write an expression for the total cost in dollars. (1 point)
2. Find the total cost when \(b = 2\). (1 point)

See every chapter on the Grade 6 math page.