Algebraic expressions (Math 1)

High School Math 1 · Unit 2 · algebraic-expressions-m1 · Teacher edition

algebraic-expressions-m1

Name ______________________________Date ______________

1.
In the expression $7x^{2} - 4x + 9$ , what is the coefficient of $x$ ?
Answer: ______________
2.
Simplify $2(3x - 4) - 5x$ .
Answer: ______________
3.
Evaluate $4x^{2} - 6x + 1$ when $x = \dfrac{1}{2}$ .
Answer: ______________
4.
Which expression means “twice the sum of a number $x$ and $3$ , decreased by $5$ ”?
1. (A)
  $2x + 3 - 5$
2. (B)
  $2(x - 5) + 3$
3. (C)
  $2(x + 3) - 5$
4. (D)
  $5 - 2(x + 3)$
5.
A rectangular garden has width $w$ feet. Its length is $4$ feet more than three times its width. Which expression gives the perimeter of the garden, in feet?
1. (A)
  $4w + 4$
2. (B)
  $8w + 8$
3. (C)
  $6w + 8$
4. (D)
  $3w^{2} + 4w$

Answer key — Algebraic expressions (Math 1)

1.
-4algebraic-expressions-m1-01
The $x$ term is $-4x$ , so the coefficient of $x$ is $\mathbf{-4}$ . ( $7$ is the coefficient of $x^2$ ; $9$ is the constant term.)
2.
$x-8$ algebraic-expressions-m1-02
$2(3x - 4) - 5x = 6x - 8 - 5x = \mathbf{x - 8}$ .
3.
-1algebraic-expressions-m1-03
$4 \cdot \frac{1}{4} - 6 \cdot \frac{1}{2} + 1 = 1 - 3 + 1 = \mathbf{-1}$ .
4.
(C)
$2(x + 3) - 5$
algebraic-expressions-m1-04
Sum: $x + 3$ . Twice the sum: $2(x + 3)$ . Decreased by $5$ : $\mathbf{2(x + 3) - 5}$ . ( $2x + 3 - 5$ doubles only $x$ ; $5 - 2(x+3)$ subtracts in the wrong direction; $2(x - 5) + 3$ groups the wrong pair.)
5.
(B)
$8w + 8$
algebraic-expressions-m1-05
Length $= 3w + 4$ . Perimeter $= 2(3w + 4) + 2w = 6w + 8 + 2w = \mathbf{8w + 8}$ . ( $4w + 4$ adds one length and one width; $6w + 8$ forgets the two widths; $3w^2 + 4w$ is the area.)