Download and log4 64 ∙ 256 - Blaine School District

2016 Northwest High School Math Championship
Advanced Algebra – Trigonometry Test
Grades 11-12
æ of the x3 and x4 terms in the simplified binomial
1. Calculate the sum of the coefficients
5
expansion of (x + 2) .
1
1
1
1. If
3
+
4
= x , then x =
2. It is given that sin(θ) = 3/5, where
θ lies
Quadrant
II. Find the values
of the five remaining
2. A
goldin bar
is a rectangular
solid measuring
2 ⇥ 3 ⇥ 4. It is melted d
standard trigonometric functions (of
θ). [Note:
is an
angle in standard
position,
its is the length of a si
equal
cubesθare
constructed
from this
gold. with
What
terminal edge lying in Quadrant II.]
3. What is the area of a triangle whose sides have length 10, 13, and 13
3. In triangle ABC, AB = 25, AC =4.24,The
andperimeter
BC = 23. Let
be the point
which rectangle is three time
of D
a rectangle
is on
28.ACAfor
second
BD ⊥ AC. What is the value of ADfirst,
− DC?
and twice as wide. The perimeter of the second rectangle is 72. W
of the first rectangle?
4. Find the sum of log !
!
!"
and log
∙ 256 . is 20 feet high. How many feet away from the base of th
! 64
5. A
lamppost
person who is 5 feet tall stand in order to cast an 8-foot shadow?
5. Given that csc(72 · x°) · cos(54°)
1, what is
x?
6. =Workers
inthe
an least
o⌅cepositive
have a value
coffeeofmachine
and make 1 12 cents profit o
The profits were split at the end of the year, and everyone got $2.50
6. Consider the equation 3q2 + 21 = 9q,
let a andafter
b be that.
the complex
of this that
equation.
$25and
remaining
It wasroots
suggested
instead everyone sh
Given that the imaginary part of b that
is less
than
the
imaginary
part
of
a,
simplify
the
would have left three people with no money. How many cups of c
expression 20a + 16b + ab.
7. In a circle whose diameter is 30, a chord is drawn perpendicular to
the chord intersects the radius to the
7. Find the simplified value of !
.
radius
is
3.
What
is
the
length
of the chord?
!
!
!
!
!
!
! !!! !⋯!!"!
! !!""
! !!"#
!
from the
point
where
!! !!distance
!
! !! !! !⋯!!" !!" !!"
A 8. What is the smallest number of coins (possible denominations 1, 5,
8. The two right triangles shown at right
have
equalwill
perimeters.
Theto pay the exact price for any item cos
cents)
which
enable one
B hypotenuse of triangle BDC is oneup
legtoofand
triangle
ABC
stacked
on (100 cents)?
including one dollar
top of it. If the smallest angle of triangle BDC is 35 degrees, what
9. What
is the
solutionABC?
set of the inequality x3 + x2
is the degree measure of the smallest
angle
of triangle
Round your answer to the nearest hundredth.
D 2x ⇧ 0?
10. In the diagram below, line v is perpendicular to line h, and theC angle at
A light ray has angle of reflection equal to angle of incidence. Our
the(5,angle
which
is ⌅
90 degrees.
A rayathas
9. A triangle has its vertices at (0, 0),consider
(4, 2), and
1). What
is the
tangent
of the angle
the initial angle of i
of 50 degrees. It follows a path in which it next hits wall h, then s, a
vertex (4, 2)?
What will be the number of degrees of its angle of incidence with wal
time?
...
...
..
10. In the diagram to the right, line v is perpendicular to line h, and
.....
.
.
...
...
.
.....
.....
.....
...
...
.
... .....
...
... .......
...
the angle at B is 75 degrees. A light ray has angle of reflection
....
...
............
...
...
...
equal to angle of incidence. Our convention is to consider the
...
...
s.........
...
...v
...
angle that is less than or equal to 90 degrees. A ray has initial
...
...
...
...
...
...
angle of incidence with v of 50 degrees. It follows a path in which
...
...
...
...
...
.
h
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.....
it next hits wall h, then s, and then v again. What will be the
A
B
number of degrees of its angle of incidence with wall v this
11. What is the smallest positive integer p for which there is a positive int
(second) time?
2n+p ⇤ 2n mod 100? (This p is the period of the sequence ⌃2n mod
considers the last two digits of the numbers.)
12. A polynomial has remainder 2 when divided by x 1, and has rem
divided by x 2. What remainder is obtained when this polynomi
(x 1)(x 2)?
1