Name_________________
AIMS Review Problems similar to #31 in packet
Recall: Always look for a GCF then try to factor what remains into two binomials. Ex.
(x+1)(x-2). Be aware of special cases like the difference of perfect squares. Ex. 9x² - 25
Name______________________
AIMS Review Problems similar to #32 in packet
Recall: Parallel = lines have same slope (different y-intercepts), Perpendicular = slopes are
opposite reciprocals, Coinciding = the lines are exactly the same (same slope, same y-intercept)
5. Factor the polynomial completely.
1. What is the complete factorization of the
polynomial shown?
2 x 4 + x3 + 4 x 2 − 2 x
a.
x 2 (2 x 2 + x ) − 2 x (2 x + 1)
b.
x (2 x 3 + x 2 + 4 x − 2)
x ( x 2 − 2)(2 x + 1)
3
2
d. x (2 x + x ) − 4
1. Given the following equations, decide which
statement is true about the lines graphed from
the equations.
6x2 − 5x − 4
(3 x + 4)(2 x + 1)
(3x − 4)(2 x + 1)
c. (6 x + 2)( x − 4)
d. (6 x − 1)( x + 4)
a.
b.
c.
2. Factor the polynomial completely.
− x 4 + 2 x3
a.
x(− x3 + 2 x 2 )
3
c.
2 x (− x + 1)
−4( x + 2)
d.
− x 3 ( x − 2)
b.
3. Find the complete factorization for the
polynomial below.
x2 −1
( x − 1)( x + 1)
b. prime
c. ( x − 1)( x − 1)
d. ( x + 1)( x + 1)
a.
4. What is the complete factorization of the
polynomial shown?
x 2 + x − 20
( x + 4)( x − 5)
( x + 4)( x + 5)
c. ( x − 4)( x + 5)
d. ( x − 4)( x − 5)
a.
b.
Answers: c. d. a. c. b. b. c.
DOK Problems:
6. The surface area of a rectangular box with a
square base and a height of 5 inches is 112
square inches. The surface area is given by
2
A=2x +4xh. Find x.
a. The equation is not factorable,
therefore the box cannot exist.
b. x = 4 inches
c. x = -14 inches
d. The answer is negative which is
impossible so there is not solution.
7. You throw a ball up into the air. At 4
meters above the ground the ball leaves your
hand with an initial vertical velocity of 19 feet
per second. The vertical motion model is:
2
h = - 5t + vt +s.
(t=time, s= starting height)
*Write an equation that gives the height of the
ball as a function of the time.
*After how many seconds does the ball land on
the ground?
a. h(t ) = −5t 2 + vt + s, and t=0
2
b. h(t ) = −5t + 4t + 19, and t = 19
c. h(t ) = −5t 2 + 19t + 4, and t = 4
1
d. h(t ) = −5t + 19t + 4, and t = −
5
2
j − 12 = 3k , and
e.
f.
g.
h.
1
k + j = −4
3
They coincide
They are parallel
They are perpendicular
They intersect but are not
perpendicular
2. What do you know about the lines of the
following equations?
−12 a − 13 = −b, and 7 + b = 12a
e.
f.
g.
h.
They coincide
They are parallel
They are perpendicular
They intersect but are not
perpendicular
3. Decide which statement best describes the
lines graphed from the given equations.
y−2=
e.
f.
g.
h.
1
1
x, and − x + y = 2
2
2
They coincide
They are parallel
They are perpendicular
They intersect but are not
perpendicular
4. What happens when the two equations are
graphed on the same axis?
5. What can you tell about the lines of the
following equations?
2
3
− x + y = 4, and − 3 + y = − x
3
2
e.
f.
g.
h.
They coincide
They are parallel
They are perpendicular
They intersect but are not
perpendicular
DOK Problems:
6. Given the following coordinates determine
if lines AB and CD are parallel, perpendicular,
or intersecting but not perpendicular and
explain why.
A(4, 6) B(6, 9) C(10, 6) D(13, 4)
e. The lines are parallel because they have
the same slope.
f. The lines are perpendicular because
their slopes are opposite reciprocals of
each other.
g. The lines intersect but are not
perpendicular because they have
different slopes.
h. The lines are perpendicular because
their slopes are the same.
7. Determine what type of quadrilateral is
formed by the following points:
A(-5, 0) B (-3, 2) C(2, -2) D(0, -4)
b + 1 = 3 x, and − 5b + 2 x = −b
a. Parallelogram
e.
f.
g.
h.
b. Trapezoid
They coincide
They are parallel
They are perpendicular
They intersect but are not
perpendicular
Answers: c. b. a. d. c. b. a.
c. Rectangle
d. Rhombus
Name_______________
PRACTICE AIMS QUESTION #33
Finding the measures of arcs
AIMS Review Question #34 Triangle Congruency Shortcuts.
There
thT are several formulas for finding the measure of arcs.
1) Locate the picture on the AIMS reference that most closely matches
your question.
2) Identify the “intercepted arcs”
3) Plug the numbers into the formula.
a. Remember a complete circle = 360 degrees.
In order to prove that two triangle are congruent you would normally have to prove that
all corresponding sides are congruent and all corresponding angles are congruent.
However, instead of finding all 6 sides and 6 angles (3 sides and 3 angles from each
triangle) you can instead use one of these five congruence shortcuts. They are:
Solve for the indicated measure. Pictures may not be drawn to scale.
SSS (side-side-side)
SAS (side-angle-side)
ASA (angle-side-angle)
SAA or AAS (side-angle-angle)
And if you have a right triangle you can use HL (hypotenuse-leg)
1.
The shortcuts that don’t work are:
2. Find the m < AEB
b) 45o
a) 30o
c) 60o
d) 75o
1. sovle for x
a) 40o
b) 88o
d) 128o
c) 100o
112º
A
D
128º
160o
E
D
xº
48º
Decide if the following triangles are congruent and state a postulate that supports your
choice.
T
F
Q
C
B
50o
C
AAA (angle-angle-angle)
ASS (angle-side-side)
1.
C
100o
B 72º A
2.
D
S
A
B
E
R
135
3.
T
o
B
E
A
AC is a diameter, find the m < AED
C
o
a) 60
D
o
b) 75
o
c) 30
3.
d) 15
O
C
25o
5.
B
a) 51
C
b) 72o
c) 91.5o
d) 116.5o
= 112° , then find the m < AED
If m AD = 38° and mBC
a) 37o
A
D
G
A
xo
4.
E
D
o
105o
127o
U
b) 74o
c) 75o
d) 105o
Answers: 1. B 2. D 3. A 4. C 5. A
4. Given segment AC is the perpendicular bisector of segment DE at point F and
segment DE is the perpendicular bisector of segment AC at point F. Connect points A
and D, points D and C, points C and E, and points E and A. Name all congruent triangles
formed and the postulates that prove congruency.
Name_______________
PRACTICE AIMS QUESTION #35
#1 Which conclusion makes the following argument valid?
Quadrilateral ABCD is a parallelogram.
All parallelograms have 2 pairs of congruent sides.
A)
B)
C)
D)
Quadrilateral
Quadrilateral
Quadrilateral
Quadrilateral
ABCD
ABCD
ABCD
ABCD
is a
has
has
has
#5 Decide if the reasoning is valid or not
If 2 parallel lines are cut by a transversal, then each pair of
corresponding angles is congruent.
<E and <F are congruent, therefore <E and <F are corresponding
angles.
A) Valid
B) Invalid
square.
4 congruent sides.
four congruent angles.
2 pairs of congruent sides.
#6 Identify the converse of the given conditional statement.
If a polygon has just 5 sides, then it is a pentagon.
#2 Based solely on the statement and premise, which
conclusion is MOST valid?
Statement: If 2 angles are right angles, then they are both 900.
Premise: < Y and < Z are both right angles.
A) Angles Y and Z are both 900.
B) Angles Y and Z belong to a single square.
C) Angles Y and Z belong to 2 right triangles.
D) Angles Y and Z are both alternate exterior angles.
#3 Decide if the reasoning is valid or not
A person who lives in Arizona also lives in the United States.
Mike lives in the Unites States, therefore, Mike lives in Arizona.
A) Valid
B) Invalid
A)
B)
C)
D)
E)
If
If
If
If
If
it
it
it
it
it
is not a polygon, then it is not a pentagon.
is not a polygon, then it does not have 4 sides.
a polygon has just 5 sides, then it is not a pentagon.
is not a pentagon, then it doesn’t have just 5 sides.
is a pentagon, then it has just 5 sides.
#7 Identify the contrapostive of the given conditional
statement.
If a polygon has just 4 sides, then it is a quadrilateral.
A) If a polygon does not have 4 sides, then it is not a
quadrilateral.
B) If it is a quadrilateral, then it has just 4 sides.
C) If a polygon is not a quadrilateral, then it does not have just 4
sides.
D) If it is not a polygon, then it doesn’t have 4 sides.
#4 Decide if the reasoning is valid or not
If a 4-sided polygon has 4 right angles, then it is a rectangle.
Polygon ABCD has four right angles, therefore, polygon ABCD is a
rectangle.
A) Valid
B) Invalid
Answers
1) D
2) A
7) C
3) B
4) A
5) B
6) E