Question 1

Solve the following system of equations using substitution:

$$
\begin{cases}
y = \frac{1}{2}x - 4 \
y = -\frac{3}{4}x - 9
\end{cases}
$$

What is the solution to the system?

Accepted Answer

$$(-4, -6)$$

Question 2

A biker travels 60 miles into the wind in 6 hours, then returns the same distance with the wind in 5 hours. What is the biker's speed in still air?

Accepted Answer

$$11$$ miles per hour

Question 3

A nursery mixes rye seed costing $$4.75 per pound with bluegrass seed costing 2.50 $$per pound to make 120 pounds of a blend selling for $3.81 per pound. How many pounds of bluegrass seed are used?

Accepted Answer

$$50$$ pounds

Question 4

Which of the following is the correct graphing region for the system of inequalities:

$$
x \u003e 0 \
y \leq \frac{3}{5}x - 3
$$

?

Accepted Answer

The region to the right of $$x=0$$ and below the line $$y=\frac{3}{5}x-3.$$

Question 5

Simplify the expression:

$$
\$$left(-3p^6$$q^5$$\$$right)^6$$
$

Accepted Answer

$$729p^{36}q$$^{30}$

Question 6

Use the FOIL method to find the product:

$$(3x + 5)(3x - 1)$$

Accepted Answer

$$9x^2 + 12x - 5$

Question 7

Factor the trinomial completely:

$$x^2 + 9x - 36$

Accepted Answer

$$(x + 12)(x - 3)$$

Question 8

A ball is dropped from a $$77-$$foot building. Its height after $$t$$ seconds is given by $$h = -16t^2$ + 77. $$What is the height after $$\frac{7}{4}$$ seconds?

Accepted Answer

$$28$$ feet

Question 9

Simplify the following expression using the laws of exponents. Write your answer with positive exponents:

$$
\frac{8a^4$b^{-9}$$}{$$2a^{-3}b$$^{-7}$$}
$$

Accepted Answer

$$4a^7b^2$

Question 10

Factor the following completely by factoring out the GCF first:

$$z^3$$ + $$9z^2 - 36z$

Accepted Answer

$$z(z + 9)(z - 4)$$

Question 11

Solve the equation using the zero-product property:

$$(x - 1)(3x + 2) = 0$$

Accepted Answer

$$x = 1 or$$ $$x = -\frac{2}{3}$$

Question 12

Which of the following expressions is a trinomial of degree 3, written in standard form?

Accepted Answer

$$xy^2 + 2xy + 9$

Question 13

Factor the difference of two squares:

$$4x^2 - 25$

Accepted Answer

$$(2x - 5)(2x + 5)$$

Question 14

Simplify the following expression:

$$\frac{-10b^4$}{6b^2$}$$

Accepted Answer

$$-\frac{5b^2$}{3}$$

Question 15

A rocket's height is given by $$h = -16t^2$ + 144t. $$When will the rocket hit the ground?

Accepted Answer

$$9$$ seconds

Question 16

Factor the trinomial:

$$35b^2 - 39b - 14$

Accepted Answer

$$(5b - 7)(7b + 2)$$

Question 17

Which of the following is the correct product of $$(5n - 4p)(5n + 4p)$$?

Accepted Answer

$$25n^2$$ - $$16p^2$$

Question 18

Which of the following is the correct simplification of:

$$\left(\frac{5b^2$d^6$$}{$$a^6$$}\$$right)^3$

Accepted Answer

$$\frac{125b^6$d^{18}$$}{$$a^{18}$$}$

Question 19

Factor by grouping:

$$x^3$$ - $$4x^2 + 3x - 12$

Accepted Answer

$$(x^2 + 3)(x - 4$$)$$

Question 20

Find all solutions by factoring:

$$c^2 + 9c + 20 = 0$

Accepted Answer

$$c = -4, -5$$

Step-by-Step Guidance for Intermediate Algebra Practice Exam (Unit 2)

Study Guide - Practice Questions

Study Guide - Flashcards