Honors Trigonometry - Start up Review
A fanatic is a man who consciously over-compensates a secret doubt.-(Aldous Huxley)
1. Simplify the expression: 8 ÷ 4 - 2 ⋅ 5 + 2⋅ 3
2. The fifth and sixth terms of 10 data items, arranged in order from least to greatest
x+5
3x + 1
are
and
. What is the median of the data?
x
2x
3. Solve for x: 4x - 3(2x + 4) = 6x - 5
4x - 3 2x − 4
+
when x = -2
3
3
5. Write an equation for the given sentence:
Four times a number decreased by 12 is equal to the number decreased by 7
4. Evaluate:
6. True or False:
12 - 8 = 12 − 8
7. Simplify: 5 8 - 8 + 2 3 − 4 + 5
Solve for the indicated variable, indicate any restrictions on the variables.
8. ax + t = y solve for x
9. dc + d = x + y solve for d
Solve and graph the solution set
10. 2(x - 9) + 3 > -5
11. 5x - 1≥ 4 and 2x -1 ≤ 3
Solve and check: (graph the solution set)
12. - 2 < x + 1 < 5
13. 3 2x + 3 + 3 = 3
14. 2x + 1 < 5
On the coordinate plane provided, graph and label the following lines:
-3
x +1
4
Determine if the following relations are functions:
15. 3x - 4y = -12
16. y =
17. {(7,-2),(9,-4),(11,-6),(13,-8),(15,-10),(17,-12)}
18. {(10,-1),(11,-1),(12,-2),(13,-2),(14,-3),(15,-3)}
19. Given f(x) = 3x 2 − 2x + 1 and g(x) = 2x + 4, evaluate f(g(-2))
3
20. Find the inverse (f -1) of the function f(x) = x − 2
5
21. Write the equation of a line that passes through the points (-1,-2) and (3, 0)
2
x − 7 and passing through the point (6,-3)
3
3
23.. Write the equation of a line perpendicular to y = x + 1 and passing through (3,-2)
5
22. Write the equation of a line parallel to y =
24. If y varies directly as x, and y = 96 when x = 36:
Find x when y = 24
25. Solve the system of equations by addition:
⎧-5x + 7y = 11
⎨
⎩-2x - 3y = -13
Simplify:
28. (3x 2 + 7) − (x 2 − 4x + 2)
29. (2y - 3)(4y 2 + 6y + 9)
Factor:
26. Solve the system of equations by substitution:
30. 9c 2 d 2 − 25 f 2
⎧x = y - 2
⎨
⎩3x - y = 6
32. 2x 2 + 3x − 5
31. 8x 3 + y 3
27. Solve the system of equations by addition:
33. 25x 2 − 70xy + 49y2
⎧2x + 3y − z = 5
⎪
⎨x + y + z = 9
⎪ x − 2y − z = −7
⎩
34. 3ax 2 − 27a + 2x 2 − 18
35.The width of a rectangle is 5 meters more than one-half its length. The perimeter is 286 meters. Find
the length and width.
36.Rockford and Chicago are 126 miles apart by train. An express train leaves Chicago at the same time
a passenger train leaves Rockford. The express train travels 15 miles per hour faster than the passenger
train. The two trains pass each other in 0.7 hours. How fast is each train traveling?
37.Floyd has 16 coins in pennies, nickels, and dimes. The number of dimes is equal to the sum of the
number of pennies and the number of nickels. If the total value of the coins is $1.08, how many of each
kind does he have?
38. Find two consecutive even integers whose product is 288.
39.A boat travels at a rate of 15 kilometers per hour in still water. It travels 60 kilometers upstream in
the same time it travels 90 kilometers downstream. What is the rate of the current?
40. Write in scientific notation: 23, 400,000
41. Write in scientific notation: .0000000876
Simplify
Simplify:
8
-7x 2 y 5 z3
x- 2
42.
7 3
x
14x y z
48.
16
x− 3
x 2 + x − 20
x
43.
2
3x 2 − 9x − 12
x + 11x + 28 x + 7
49.
÷
14z
7z
x 2 − 16
x−7
44.
÷
2
22x y 2xy
2
x − 4x − 5
1
50. 2
−
x 2 + 2x − 3 x 2 + 13x + 36
x + 6x + 5 x + 5
45. 2
⋅
x + 8x − 9
x 2 + 3x
x2 + 1 x 2 + 1
46.
+
5x − 1
4x
2x − 3 2x
47.
−
3x + 2 6
Solve:
5
4
+
=2
x+8 x-8
x
6
1
52. 2
+
=
x − 36 x - 6 x + 6
6
4
53.
−
=1
x x +1
2 8
54.
+
= −4
x 9x
51.