Question 1

Simplify the following expression and select the correct answer:

$$(-2x + 3y) + (5x + 8y)$$

Accepted Answer

$$3x + 11y$$

Question 2

A triangle has sides of lengths $$(4x - 5)$$, $$(3x - 6)$$, and $$(7x + 10). $$What is the perimeter of the triangle in terms of $$x$$?

Accepted Answer

$$14x - 1$$

Question 3

A hexagon has 3 sides of length $$(5x - 2)$$ and 3 sides of length $$(3x - 7). $$What is the perimeter of the hexagon in terms of $$x$$?

Accepted Answer

$$24x - 27$$

Question 4

What must you add to $$(5x^2 + 3x - 9$$)$$ to get (10x^2$ - 3x + 8)$$?

Accepted Answer

$$5x^2 - 6x + 17$

Question 5

Simplify the product: $$(c^5d^8$)(c^2d^6$)$

Accepted Answer

$$c^7d$$^{14}$

Question 6

Find the area of a rectangle with length $$5m^4$$ and width $$9x^2m^7$.

Accepted Answer

$$45x^2m$$^{11}$

Question 7

Find the volume of a cube whose side measures $$-3k^2x^5$.

Accepted Answer

$$-27k^6x$$^{15}$

Question 8

Simplify the following expression:

$$(b^2y^3$)^3$$

Accepted Answer

$$b^6y^9$

Question 9

A rectangular classroom has a length that is 5 less than four times the width. Let $$w$$ represent the width. Which expression represents the area of the classroom?

Accepted Answer

$$4w^2 - 5w$

Question 10

Find the product:

$$(3x + 2)(x^2$ - 2x - 7)$$

Accepted Answer

$$3x^3$$ - $$4x^2 - 25x - 14$

Question 11

A rectangular flag has a length of $$(2x + 7)$$ feet and a width of $$(x - 5)$$ feet. What is the area of the flag?

Accepted Answer

$$2x^2 - 3x - 35$

Question 12

Find the area of a square flower garden with side length $$(2x - 1)$$ meters.

Accepted Answer

$$4x^2 - 4x + 1$

Question 13

Simplify the following expression:

$$3w(w^2 - 2w - 4$$) + $$2w^2(2w + 10$$)$$

Accepted Answer

$$7w^3$$ + $$14w^2 - 12w$

Question 14

Find the perimeter of a rectangle with length $$(a^2 - 3$$)$$ and width (2a^2$ + 6).$$

Accepted Answer

$$6a^2 + 6$

Question 15

A rectangular prism has a base area of $$(3x^2 + 5x - 2$$)$$ and a height of (4x + 1$$)$$. What is the volume of the prism?

Accepted Answer

$$24x^3$$ + $$46x^2 - 6x - 4$

Question 16

Simplify the following product:

$$-3a y^2$ (a y - a b)$$

Accepted Answer

$$-3a^2$$ $$y^3$$ + $$3a^2$$ $$y^2 b$

Question 17

If the area of a rectangle is $$16x^9y$$^{10}$$ and the length is 2x^3$y^3$$, what is the width?

Accepted Answer

$$8x^6y^7$

Question 18

Simplify the following expression:

$$(-3s^3v^2$)(4sv^3)^2$

Accepted Answer

$$-48s^5v^8$

Question 19

A rectangle has a length of $$(2x^3y^6$)$$ and a width of $$(9xy + x^5$)$. What is the area of the rectangle?

Accepted Answer

$$18x^4y^7$ + 2x^8$y^6$$

Question 20

A real estate developer is designing a rectangular park. The length is $$3x - 6 cm $$and the width is $$2x + 8 cm. $$What is the area of the park?

Accepted Answer

$$6x^2 + 12x - 48$

Intermediate Algebra Exam Review: Step-by-Step Guidance

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