Algebraic Expressions and Properties of Real Numbers: math test, Grade 9 – download the PDF

1 Order of operations and evaluating / 4 pts

1. Compute \(7+2\cdot(9-4)^2\div 5\). (2 pts)
2. Evaluate \(2x^2-3xy+y\) for \(x=-3\) and \(y=4\). (2 pts)

2 Properties of real numbers / 3 pts

Name the property used in each statement.

1. \(9+(-9)=0\)
2. \((2\cdot 7)\cdot 5=2\cdot(7\cdot 5)\)
3. \(6(m-2)=6m-12\)

3 Simplifying / 4 pts

Simplify each expression.

1. \(8p-3+2p+11-p\) (2 pts)
2. \(5(2y+1)-3(y-4)\) (2 pts)

4 Classifying real numbers / 3 pts

For each number, list every set it belongs to among natural, whole, integer, rational, and irrational.

1. \(\sqrt{36}\)
2. \(-4.5\)
3. \(\sqrt{30}\)

5 Translating and evaluating / 3 pts

1. Write an expression for “three more than the quotient of a number \(n\) and 5”. (1 pt)
2. Write an expression for “twice the difference of a number \(n\) and 8”. (1 pt)
3. A taxi charges $4 plus $2.50 per mile. Write an expression for a ride of \(m\) miles and evaluate it for 8 miles. (1 pt)

6 The garden / 3 pts

A rectangular garden has length \((2x+3)\) feet and width \(x\) feet.

1. Write a simplified expression for the perimeter. (1 pt)
2. Write a simplified expression for the area. (1 pt)
3. Find both when \(x=5\). (1 pt)