Algebra 1 – 300

Final Exam Review

Free Response Problems from the 2nd Semester - Preparation for the Final Exam

1.) Solve for x and then find the length of each side (Remember the Pythagorean Theorem 𝑎2 + 𝑏2 = 𝑐2

a.)

x + 3

x + 4

x - 4

2.) Graph the following quadratic. Then identify the following: a.) the coordinates of the vertex, b.) the

axis of symmetry, c.) the coordinates of the x-intercepts and d.) the coordinates of the y-intercept.

𝑦 = −𝑥2 + 4𝑥 + 5

a.) Vertex______________

b.) Axis of Symmetry________________

c.) x-intercept(s) _______________________

d.) y-intercept______________

3.) Solve each quadratic using the quadratic formula (round to 2 decimal places)

𝑥 =−𝑏 ± √𝑏2 − 4𝑎𝑐

2𝑎

a.) 𝑥2 − 11𝑥 + 15 = 0

b.) 2𝑥2 + 5𝑥 − 9 = 0

Solve each quadratic equation using factoring (split the middle term)

c.) 5𝑥2 + 6𝑥 + 1 = 0

d.) 2𝑥2 + 3𝑥 − 9 = 0

4.)

a.) Find the area of the rectangle below

b.) Find the perimeter of the rectangle above.

Simplify

c.) (−2𝑥6)3 ∙ (𝑥2)5

d.) −90𝑎2𝑏

−72𝑎3

13𝑥𝑦2

20𝑥2

5.)

a.) Multiply: (3𝑥 − 7)(𝑥2 + 𝑥 − 10)

b.) Simplify: 16√60 − √135

c.) Multiply: (5 − √14)(5 + √14)

d.) Solve for x: 3 + 7√𝑥 + 1 = 31

6.) Simplify the following rational expressions:

a.) 20𝑥2+35𝑥6

10𝑥2

b.) 𝑥2−9

𝑥2−𝑥−12

c.) 𝑥2+3𝑥−10

𝑥2−𝑥−6∙

𝑥2+2𝑥

𝑥2−2𝑥

d.) 12±√80

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