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?

Accepted Answer

$$(-4, -6)$$

Question 2

A biker rides 60 miles into the wind in 6 hours, then returns the same distance with the wind in 5 hours. What is the speed of the wind?

Accepted Answer

$$1$$ mile per hour

Question 3

A nursery mixes rye seed at $$4.75 per pound with bluegrass seed at 2.50 $$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

$$50$$ lbs

Question 4

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

Accepted Answer

$$xy^2 + 2xy + 9$

Question 5

Simplify the expression:

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

What is the result?

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 + 15x + 36$

Accepted Answer

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

Question 8

Simplify the following expression and write with positive exponents:

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

Accepted Answer

$$4a^7b^2$

Question 9

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

Accepted Answer

$$28$$ feet

Question 10

Factor the following completely:

$$4x^2 - 25$

Accepted Answer

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

Question 11

Solve for $$x$$ using the zero-product property:

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

Accepted Answer

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

Question 12

Factor by grouping:

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

Accepted Answer

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

Question 13

Simplify the expression:

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

Accepted Answer

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

Question 14

Factor the trinomial:

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

Accepted Answer

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

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

Which of the following is the correct factorization of $$81x^2 + 36x + 4$?

Accepted Answer

$$(9x + 2)^2$

Question 17

Simplify using the quotient to a power rule:

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

Accepted Answer

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

Question 18

Factor the following by first factoring out the GCF, then factoring the trinomial:

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Which of the following is the correct solution set for $$c^2 + 9c + 20 = 0$?

Accepted Answer

$$\{-4, -5\}$$

Step-by-Step Guidance for Intermediate Algebra Practice Exam (Unit 2, Sections 4.2–6.7)

Study Guide - Practice Questions

Study Guide - Flashcards