Numerical and Algebraic Expressions: math test, Grade 6 – download the PDF

1 Exponents and order of operations / 4 pts

Calculators are not allowed. Find the value of each expression.

1. \(5^3\)
2. \(40 - 2^4\)
3. \(3 \cdot (10 - 4)^2\)
4. \(100 \div 5^2 + 9\)

2 Writing expressions / 4 pts

Write an algebraic expression for each phrase.

1. 12 less than \(x\)
2. the product of 6 and the sum of \(y\) and 2
3. tickets cost 9 dollars each (\(t\) tickets) plus a 5-dollar fee
4. the quotient of \(n\) and 4, increased by 1

3 Evaluating expressions / 3 pts

Evaluate each expression when \(x = 4\) and \(y = 2\).

1. \(5x - y\)
2. \(x^2 + 3y\)
3. \(2(x + y)\)

4 Parts of an expression / 2 pts

Consider \(8m + 5n + 11\).

1. List its terms.
2. Give the coefficient of \(n\) and the constant term.

5 Distributive property and equivalence / 4 pts

1. Expand \(5(2x + 3)\).
2. Rewrite \(16y + 20\) as a product using the GCF.
3. Are \(3(x + 4)\) and \(3x + 4\) equivalent? Test \(x = 2\) and explain.

6 Simplifying and a rectangle / 3 pts

1. Simplify \(9a + 4 + 2a - 3\).
2. A rectangle has width 4 inches and length \(x + 6\) inches. Write its perimeter as an expression and simplify it.