Targeted Review Solutions

Note

Problems 1–2
While you can refer to the Formula Sheet at any time, it will be helpful to begin to recall the area formulas and exponent rules without it.

Find the area of the figure.

$A = b h A = (\frac{3}{2} w^{4} x) (\frac{2}{5} w x^{4})$

$A = \frac{3}{5} w^{5} x^{5}$

Determine the missing side length.

$A = \frac{1}{2} b h 6 x^{6} y^{3} = \frac{1}{2} (4 x^{3} y) h \frac{12 x^{6} y^{3}}{4 x^{3} y} = \frac{(4 x^{3} y) h}{4 x^{3} y}$

$h = 3 x^{3} y^{2}$

Note

Problems 3–4
Long division of numbers without a calculator is a critical step to be successful when doing polynomial long division in a later lesson.

Divide. Show ALL work. Write any remainders as a simplified fraction.

$25 13572$

$2500542 13572 - 0 13 - 0 135 - 125 107 - 100 72 - 50 22$

$542 \frac{22}{25}$

$14 3128$

$140223 3128 - 0 31 - 28 32 - 28 48 - 42 6$

$223 \frac{3}{7}$

Graph the system of inequalities. Label the intersection points.
$y \geq 0 x \geq 0 y \leq - \frac{1}{10} x + 30 y \geq \frac{1}{20} x + 15$

Use the objective function to find the minimum and maximum values.
$f (x, y) = - x + 3 y$

$f (0, 15) = - (0) + 3 (15)$

$f (0, 15) = 45$

$f (0, 30) = - (0) + 3 (30)$

$f (0, 30) = 90 maximum$

$f (100, 20) = - (100) + 3 (20)$

$f (100, 20) = - 40 minimum$

Braun’s Bakery uses three types of flour for their bakery. Three times the number of bags of triple-zero flour purchased is equal to the sum of all-purpose and wheat flour. Sixty-four total bags of flour are purchased weekly. Five times more all-purpose flour is purchased than wheat flour. Write a system of equations.

z: triple-zero flour, a: all-purpose flour, w: wheat flour

$3 z = a + w a + w + z = 64 5 a = w$

Note

Remember to define variables before writing the system of equations.

Solve the system you wrote in problem 7.

$P : 3 z = a + w Q : a + w + z = 64 R : 5 a = w$

Substitute R into Q
$\begin{array}{rcl} a + (5 a) + z & = & 64 \\ 6 a + z & = & 64 \end{array}$

Substitute R into P
$\begin{array}{rcl} 3 z & = & a + 5 a \\ 3 z & = & 6 a \\ z & = & 2 a \end{array}$

Use step 1 and 2 equations
$\begin{array}{rcl} 6 a + (2 a) & = & 64 \\ 8 a & = & 64 \\ a & = & 8 \end{array}$

$w = 5 (8) w = 40$

$\begin{array}{rcl} a + w + z & = & 64 \\ 8 + 40 + z & = & 64 \\ z & = & 16 \end{array}$

Braun’s Bakery purchased 8 bags of all-purpose flour, 40 bags of wheat flour, and 16 bags of triple-zero flour.

Multiple Choice

Determine the ordered triple that is the solution to the system of equations.
$4 x + 5 y - 6 z = 2 3 x + 2 y - 7 y = 15 - x + 4 y + 2 z = - 13$

(3, 2, 4)
(−3, −2, −4)
(−48, 18, −18)
No Solution

Note

This ordered triple has the opposite signs for all values.

This is the solution if the 3rd equation is written as $(x + 4 y + 2 z = - 13)$
Substitution was not used correctly in one or more equations.

$4 (- 3) + 5 (- 2) - 6 (- 4) = 2 ✓ 3 (- 3) + 2 (- 2) - 7 (- 4) = 15 ✓ - (- 3) + 4 (- 2) + 2 (- 4) = - 13 ✓$

The answer when one term is divided by another.

dividend
divisor
quotient
remainder

Note

A, B, and D words do not match the definition.

Use the graph to determine the equation in slope-intercept form.

$y = - \frac{6}{5} x - 3$
$y = - \frac{6}{5} x - 2.5$
$y = \frac{6}{5} x - 2.5$
$y = \frac{6}{5} x - 3$

The y-intercept is (0, −3) and the slope from the graph is $- \frac{6}{5}$

Note

B and C: The constant represents the x-intercept rather than the y-intercept.

C and D: The slope is positive when the given graph has a negative slope.

Solve the quadratic equation:
$(2 x - 5) (3 x + 2) = 0$

$x = - 2, 5$
$x = - \frac{3}{2}, \frac{2}{5}$
$x = - \frac{2}{3}, \frac{5}{2}$
$x = - \frac{5}{2}, \frac{2}{3}$

Note

This ignores the coefficients in the given equation.
This inverts both fractions (the reciprocal).

This switches the signs of the solutions.

$\begin{matrix} \begin{array}{rcl} 2 x - 5 & = & 0 \\ 2 x & = & 5 \\ x & = & \frac{5}{2} \end{array} & \begin{array}{rcl} 3 x + 2 & = & 0 \\ 3 x & = & - 2 \\ x & = & - \frac{2}{3} \end{array} \end{matrix}$

Problem	1	2	3	4	5	6	7	8	9	10	11	12
Origin	A1	A1	D	D	L1	L1	L2	L2	L2	FD	A1	A1

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