Exam 1

1.1 & 1.2 linear equations

100

Solve: 

2x – 3(2x + 2) = 1 – 5(4x + 3) 

x = -1/2 

200

Solve the equation. Simplify if possible. 

–5(b – 5) – 1 = 13 – (b – 3)

b = 2 

300

(1/2)n – 6 = (1/4)n – 2

n = 16

400

Darren drives to school in rush hour traffic and averages 36 mph. He returns home in mid-afternoon when there is less traffic and averages 45 mph. What is the distance between his home and school if the total traveling time is 1hr 30min? 

Hint: make a "d=rt" table!

30mi 

1.3 factoring review

100

Factor: 

10x² + 9x + 2

(2x + 1)(5x + 2) 

200

Simplify and write in standard a + bi form: 

5 – (-12)^1/2

5 – 2i√3

300

Simplify and write in a + bi form 

12 + 17i
     22

6 + 17i
11   22

400

Answer in a + bi form

(238 + 14i) – (64 + 19i) 

174 – 5i

1.4 quadratic equations

100

Solve 

x² – 18x + 5 = 0

x = 9 ± 2√19

200

Solve using the zero product property: 

3y² = 27y 

Hint: keep it simple! 

x = 0
x = 9 

300

Solve by completing the square: 

3x² + 12x = –90 

-2 ± i√26

400

Solve 

2x(x – 3) = –7 

Hint: pop goes the weasel! 

3/2 + (√(5)/2)i 

1.6 polynomials

100

Solve 

x⁴ – 3x² – 4 = 0

x = ±2
x = ±i

200

Solve 

(c² + 3)² + 2(c² + 3) – 24 = 0

c = ±3i
c = ±1

300

Simplify WITHOUT a calculator 

–81^–3/4

– 1
 27

400

Solve 

√(x + 7) = x – 5

x = 9

1.6 radicals

100

5x² + 20x + 15  ⋅  x – 1
     10x + 30         x² – 1

= 1/2

200

35r²s²   ÷   5rs²
(r – 2)      (r – 2)²

= 7r(r – 2)

300

x² + 21x + 40   +   x + 1
     x² – 25              x + 5

2x+7
 x-5

400

Carmen drives between Miami, Florida, and West Palm Beach, Florida. She drives 30 mi in clear weather and then encounters a thunderstorm for the last 36 mi. She drives 22 mph slower through the thunderstorm than she does in clear weather. If the total time for the trip is 2.75 hr, determine her average speed in nice weather and her average speed driving in the thunderstorm.

Hint: make a table! 

18 mph in the thunderstorm 

40 mph in nice weather