Introduction to algebra

Advanced Math 7 · Unit 3 · algebra-foundations-7 · Teacher edition

algebra-foundations-7

Name ______________________________Date ______________

1.
In the expression $5x^2 - 3x + 7$ , what is the coefficient of $x$ ?
Answer: ______________
2.
Write an expression for “seven less than twice a number $n$ .”
Answer: ______________
3.
Here are four algebraic sentences.

(i) $3x + 2 = 11$ (ii) $A = \pi r^2$ (iii) $2(x + 3) = 2x + 6$ (iv) $4x - 7$

Which one is an identity — true for every value of $x$ ?
1. (A)
  (i)
2. (B)
  (ii)
3. (C)
  (iii)
4. (D)
  (iv)
4.
Which of these is an expression (not an equation)?
1. (A)
  $x = 5$
2. (B)
  $\dfrac{1}{2}x - 4$
3. (C)
  $2x + 3 = 9$
4. (D)
  $y = 3x$
5.
What is the value of $x^3 - 2x^2 + 3x - 4$ when $x = -2$ ?
Answer: ______________

Answer key — Introduction to algebra

1.
-3algebra-foundations-7-01
The $x$ -term is $-3x$ , so the coefficient is $\mathbf{-3}$ . ( $5$ is the coefficient of $x^2$ ; $7$ is the constant term.)
2.
$2n-7$ algebra-foundations-7-02
Twice $n$ is $2n$ ; seven less than that is $\mathbf{2n - 7}$ . ( $7 - 2n$ reads the words in order and gets the subtraction backwards.)
3.
(C)
(iii)
algebra-foundations-7-03
(iii): $2(x + 3) = 2x + 6$ is true for every $x$ (expand the left side), so it is an identity. (i) is true only at $x = 3$ — an equation to solve. (ii) is a formula. (iv) is an expression. Answer: (iii).
4.
(B)
$\dfrac{1}{2}x - 4$
algebra-foundations-7-04
$\mathbf{\tfrac{1}{2}x - 4}$ has no equals sign, so it is an expression. $x = 5$ is an equation (its solution is $5$ ), and so are $2x + 3 = 9$ and $y = 3x$ .
5.
-26algebra-foundations-7-05
$(-2)^3 - 2(-2)^2 + 3(-2) - 4 = -8 - 8 - 6 - 4 = \mathbf{-26}$ . (Reading $-2x^2$ as $(-2x)^2 = 16$ gives $-8 + 16 - 6 - 4 = -2$ , the classic sign error.)