Trigonometry – Mr.Troesch Winter Break Homework!
Name: ________________________
Directions: ONLY TURN-IN PAGES 1 AND 2 after the break! Show all work for the non-multiple
choice problems.
Part I:
1._____
5._____
6._____
9._____
10._____
14
Factor completely:
3._____
4. _____
7. _____
8. _____
10ax 2 − 23ax − 5a
15
Classical mathematics uses the term "Golden Ratio" for the ratio (1 + 5 ): 2. The Golden Ratio was used by
many famous artists to determine the dimensions of their paintings. If the ratio of the length to the width of a
painting is (1 + 5 ): 2, find the length, in feet, of a painting that has a width of 14 feet. Express your answer in
simplest radical form.
16
If 2 + 3i is one root of a quadratic equation with real coefficients, what is the sum of the roots of the equation?
1
17
Simplify completely when x −1
18
Solve
19
Express in simplest form (the second sign is a division symbol): 2x 2 −12x + 4 = 0
− 1 is divided by x − 1 .
by completing the square, expressing the result in simplest radical form.
4x + 8 2 − x
x2 − 4
•
÷
x + 1 3x − 15 2x 2 − 8x − 10
2
Part I
Answer all questions in this part. Each correct answer will receive 2
credits. No partial credit will be allowed. For each question, write on the
separate answer sheet the numeral preceding the word or expression that best
completes the statement or answers the question.
1 The roots of the equation 2x 2 + 7x − 3 = 0 are
(1) −
1
and − 3
2
1
and 3
2
(2)
(3)
−7 ± 73
4
3
The expression
4
Which ratio represents cot A in the diagram below?
7 ± 73
4
(3 − 7i)2 is equivalent to
(1) −40 + 0i (2) −40 − 42i
(3) 58 + 0i (4) 58 − 42i
(1)
5
(4)
25
24
(2)
25
7
(3)
24
7
(4)
7
24
Which values of x are in the solution set of the following system of
equations?
y = 3x − 6
y = x2 − x − 6
(1) 0, −4
6
(2) 0, 4
(3) 6, −2
(4) −6, 2
If the length of a rectangular garden is represented by
width is represented by
garden?
(1) x
(2) x + 5
x2 + 2x
and its
x 2 + 2 x − 15
2x − 6
, which expression represents the area of the
2x + 4
x2 + 2x
2( x + 5)
x
(4)
x +5
(3)
3
7
Which graph represents the solution set of
6x − 7 ≤ 5 ?
1)
2)
3)
4)
8
9
If 2 x − 1 + 2 = 5, then x is equal to
(1) 1
(3) 5
(2) 2
(4) 4
7
The expression
is equivalent to
2− 3
(1) 14 − 7 3
(2) 14 + 7 3
10
2+ 3
7
14 + 3
(4)
7
(3)
2
The roots of the equation 9x + 3x − 4 = 0 are
(1) imaginary
(2) real, rational, and equal
(3) real, rational, and unequal
(4) real, irrational, and unequal 4