Targeted Review Solutions

Sample:
The objective function is the function that is used to determine the minimum and maximum for a linear programming problem.

$LCM (7, 14, 2) = 14 LCM (x^{2}, x y, z) = x^{2} y z$

Simplify.

Note

Problems 3–4
Recall that a fraction bar represents division. The terms can be stacked vertically (problem 3) or written horizontally (problem 4).

$(\frac{5}{3} - \frac{1}{2}) \div 2 (\frac{10}{6} - \frac{3}{6}) \cdot \frac{1}{2} = \frac{7}{6} \cdot \frac{1}{2}$

$\frac{7}{12}$

$(2 \frac{3}{5}) \div (3 \frac{1}{2}) \frac{13}{5} \div \frac{7}{2} = \frac{13}{5} \cdot \frac{2}{7}$

$\frac{26}{35}$

$4 (x^{2} - 1) - z^{2} (x^{2} - 1) (x^{2} - 1) (4 - z^{2}) (4 - z^{2}) (x^{2} - 1) - (z^{2} - 4) (x^{2} - 1)$

$- (z + 2) (z - 2) (x + 1) (x - 1)$

$x^{2} - 8 x + 15 - x^{2} + 2 x + 3$

Bixby’s Bead Shop placed three orders for black, white, and purple beads.
In September, 30 black, 50 white, and 80 purple beads were purchased for $460.
In October, 80 black and 20 white beads were purchased for $260.
In November, $166 was spent on 22 white and 36 purple beads. Write a system with three variables. Do not solve.

$b : black, w : white, p : purple 30 b + 50 w + 80 p = 460 80 b + 20 w = 260 22 w + 36 p = 166$

Determine the value of Q that will make the equation a polynomial identity.
${(Q x - 3)}^{2} = {(2 x - 1)}^{2} - 8 (x - 1)$

${(Q x - 3)}^{2} Q^{2} x^{2} - 3 Q x - 3 Q x + 9 Q^{2} x^{2} - 6 Q x + 9$

${(2 x - 1)}^{2} - 8 (x - 1) 4 x^{2} - 2 x - 2 x + 1 - 8 x + 8 4 x^{2} - 12 x + 9$

$\begin{array}{rcl} - 6 Q x & = & - 12 x \\ 6 Q & = & 12 \\ Q & = & 2 \end{array}$

Multiple Choice

all real numbers
y ≤ 1
y ≥ 0
y ≥ 1

The range represents the y-values. The graph approaches the horizontal asymptote, y = 1, and is above this line. This makes the range ≥ 1.

Note

Determine the value of (y + z) for the system:
$2 x - 3 y - 3 z = 22 2 x + y + z = 14$

16
8
2
–2

$\begin{array}{rcl} (3) (2 x + y + z & = & 14) \Rightarrow \begin{array}{l} 2 x - 3 y - 3 z = 20 \\ + 6 x + 3 y + 3 z = 42 \\ 8 x = 64 \\ x = 8 \end{array} \\ 2 (8) + y + z & = & 14 \\ 16 + y + z & = & 14 \\ y + z & = & - 2 \end{array}$

Note

Your student should solve for x to find the sum of y and z.

Determine the expression that when set equal to
${(a x)}^{3} - {(b y)}^{3}$ would form a polynomial identity.

$(a x - b y) ({(a x)}^{2} - a b x y - {(b y)}^{2})$
$(a x - b y) ({(a x)}^{2} + a b x y + {(b y)}^{2})$

This is the polynomial identity for the difference of cubes.
$(a x - b y) (a x^{2} + a b x y + b y^{2})$
$(a x - b y) ({(a x)}^{2} + 2 a b x y + {(b y)}^{2})$

Note

Select the word that best represents the polynomial.
An expression with three terms with 2 as the highest degree

Note

A–B) A linear expression has the highest degree of 1

Problem	1	2	3	4	5	6	7	8	9	10	11	12
Origin	L01	FD	FD	FD	L03	L03	L02	L04	A1	L02	L04	A1

L = Lesson in this level, A1 = Algebra 1: Principles of Secondary Mathematics, FD = Foundational Knowledge