Math 9
Review for Exam 2 – Rational expressions, radicals, rational exponents, geometry topics
(04, 05, 06_08)
1
25𝑥 3 −3𝑥 5
2
−5𝑥 2
2
𝑥 −2𝑥−15
3
𝑥 2 −3𝑥 −10
4−𝑥 2
4
𝑥 2 +2𝑥−8
50𝑥
5
𝑥 2 −3𝑥−10 10𝑥
25−9𝑥 2
3𝑥−5
8𝑥 2
÷
7
3
7
8
3𝑥 2
4𝑥
𝑥 2 −2𝑥+4
10
11
12
13
14
15
16
17
18
19
20
21
22
7
+
2𝑥+5
𝑥+1
+
4𝑥
=
=
=
𝑥+2
1
𝑥 2 −𝑥
5
𝑎𝑏
𝑎 𝑏
+
𝑏 𝑎
3
4− 2
𝑥
1
2−
𝑥
3
𝑥−5
∙
𝑥
9
=
=
6
−
=
+
−
5
𝑥2
5
=
12𝑥
4+2𝑥−5𝑥 2
(2𝑥+5)
=
=
=
=
√−27 =
6
√𝑥 12 𝑦 30 =
5
Simplify: √𝑥 24
4
Simplify: √162 =
Simplify: √50𝑥 25 𝑦 3 =
3
Simplify: √128 =
3
3
5 √5 + √40 =
√320 − √45 =
(5√3)(2√3) =
√5𝑥 3 𝑦√5𝑥𝑦 5 =
(3 + 5√3)(2 − 3√3) =
23 √8𝑥 5 𝑦
√2𝑥𝑦
24
25
26
27
=
Rationalize the denominator:
Rationalize the denominator:
1
16 −4
( )
81
6
=
5√3
3+√2
2+3√2
=
=
2
3
(−27) =
2
28
(8𝑥 6 𝑦 30 )3 =
29
𝑥 1/5 𝑥 2/7 𝑥 3/5 =
30 If one leg of a right triangle is 5, and the other is 12, what is the length of the hypotenuse?
31 Find the second leg of a right triangle with hypotenuse 7 and leg 3.
32 Determine if 7,24,25 are the lengths of the sides of a right triangle.
33 Find the area and perimeter of a rectangle with length 5 and width 3.
34 Find the area of a triangle whose height is 4 and base is 7.
35 Find the area and circumference of a circle with radius 4.
Answers:
𝑥(25 − 3𝑥 2 )
−5
−5 − 3𝑥
5
2𝑥
2
9
𝑥 + 6𝑥 − 5
𝑥 2 (𝑥 − 1)
2
5
13 𝑥 𝑦
3
17
4√2
21
5𝑥 2 𝑦 3
1
25
√2
2
29
𝑥 35
𝐴 = 15, 𝑃 = 16
33
38
2
6
10
14
18
22
26
𝑥+3
𝑥+2
𝑥 2 + 2𝑥 − 21
3(𝑥 + 2)
5
2
𝑎 + 𝑏2
5
𝑥 4 √𝑥 4
3
7√5
−39 + √3
3
2
15
−2 − 𝑥
𝑥+4
7 + 2𝑥
3𝑥 2
4𝑥 2 − 3
2𝑥 2 − 𝑥
4
3√2
19
23
5√5
2𝑥 2
3
7
11
27 9
30 13
31
√40
34 14
35
𝐶 = 8𝜋, 𝐴 = 16𝜋
4
8
5
𝑥+2
(6𝑥 2 − 4𝑥)
2𝑥 + 5
12 -3
16
20 30
24
5𝑥 12 𝑦√2𝑥𝑦
28
2√3
5
4𝑥 4 𝑦 20
32
𝑦𝑒𝑠