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WorksheetsMath 2 NCFE Review
Total questions: 95
Worksheet time: 48mins
The measures of two angles of a triangle are 70 and 55. This triangle is
a right triangle
a scalene triangle
an obtuse triangle
an isosceles triangle
In triangle QRS, m∠Q = x, m∠R = 8x - 40, and m∠S = 2x. Which type of triangle is triangle QRS?
isosceles
right
acute
obtuse
A right triangle contains a 38° angle whose adjacent side measures 10 centimeters. What is the length of the hypotenuse, to the nearest hundredth of a centimeter?
7.88
12.69
12.80
16.24
In the following diagram, triangle LMO is isosceles with LO = MO. If m∠L = 55 and m∠NOM = 28, what is m∠N?
27
28
42
70
The two acute angles of an isosceles right triangle must measure
30° and 60°
35° and 55°
40° and 50°
45° and 45°
Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram. What are the values of x and y?
x = 42 and y = 96
x = 69 and y = 69
x = 90 and y = 48
x = 96 and y = 42
In the accompanying diagram, triangle ABC is congruent to triangle XYZ. Which two statements identify corresponding congruent parts for these triangles?
AB ≅ XY and ∠C ≅ ∠Y
AB ≅ YZ and ∠C ≅ ∠X
BC ≅ XY and ∠A ≅ ∠Y
BC ≅ YZ and ∠A ≅ ∠X
In the accompanying diagram of triangle ABC, BC is extended to D, m∠A = 20, m∠ACD = 70, and m∠B = x. What is the value of x?
110
90
70
50
Two angles of a triangle measure 65° and 75°. Which is not the measure of an exterior angle of the triangle?
105°
115°
130°
140°
The lengths of the sides of a triangle are 8, 15, and 17. If the longest side of a similar triangle is 51, what is the length of the shortest side?
32
24
16
4
In the accompanying diagram, ∠B and ∠E are right angles, AB = 3, BC = 4, and AD = 15. What is the length of DE?
5
9
8
12
The sides of triangle ABC are 2, 3, and 4. Which set of numbers could represent the sides of a triangle similar to triangle ABC?
5, 6, 7
6, 9, 16
12, 13, 14
20, 30, 40
If a tree cast a 90-foot shadow at the same time a 3-foot pole held perpendicular to the ground casts a 5-foot shadow, what is the height of the tree, expressed in feet?
18
54
72
150
Jordan and Missy are standing together in a schoolyard. Jordan, who is 6 feet tall, casts a shadow that is 54 inches long. At the same time, Missy casts a shadow that is 45 inches long. How tall is Missy?
38 in
86.4 in
5 ft
5 ft 6 in
Parallelogram ABCD was translated to parallelogram A'B'C'D'. How many units and in what direction were the x-coordinates of parallelogram ABCD moved?
3 units to the right
3 units to the left
7 units to the right
7 units to the left
Ruby is making a calendar. Which shows a slide of the word "March" over the line?
A shape is shown in the accompanying picture. Which shows this shape transformed by a flip?
Joanne and Christopher are designing a quilt. They start by creating a triangle shape in the lower left quadrant as shown in the accompanying image. They transform it by rotating the triangle shown 90° clockwise about the origin. What does the new design look like?
Alyssa made the design shown in the accompanying diagram. Which transformation could be used to show that figure A is congruent to figure B?
add 5 to each x-coordinate
multiply each y-coordinate by -1
multiply each x-coordinate by -1
rotate the figure 90 degrees about the origin
Which graph shows a reflection of the rectangle across the horizontal dotted line?
Polygon A will be rotated counter-clockwise 90° about point P to form polygon A'. Which figure shows A'?
Which of the following is a single reflection of figure N over the y-axis to form N'?
Which figure shows the triangle in the accompanying picture reflected over the x-axis, then reflected over the y-axis?
Figure EFGH in the coordinate plane has vertices at (-5, 2), (-5, -2), (-1, -2), and (-1, 2). If the figure is translated 5 units to the right and 2 units up, what are the coordinates of E'F'G'H'?
(0, 4), (0, 0), (4, 0), (4, 4)
(-3, 7), (-3, 3), (1, 3), (1, 7)
(-10, 0), (-10, 4), (-6, -4), (-6, 0)
(-7, -3), (-7, -7), (-3, -7), (-3, -3)
A polygon has been rotated about the origin. Which statement must be true?
The lengths of the sides are doubled.
The area of the polygon did not change.
The coordinates of the vertices did not change.
The area of the polygon is 4 times its original area.
Three transformations will be performed on triangle ABC. Which set of transformations will always produce a congruent triangle?
dilation, rotation, translation
reflection, dilation, translation
rotation, reflection, dilation
rotation, translation, reflection
If triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A'?
(-5, -4)
(-5, 4)
(-4, 5)
(-4, -5)
The accompanying diagram shows triangle HIJ and its image triangle H'I'J' after a single transformation. Which of the following describes the transformation?
reflection over the x-axis
reflection over the y-axis
rotation 90° clockwise about the origin
rotation 90° clockwise about the origin
Triangle LMN is shown on the coordinate plane. Which coordinate plane shows triangle LMN after a 90° counterclockwise rotation about the origin?
A triangle is shown in the accompanying figure. Which triangle is congruent to the shown triangle?
A triangular tile is shown. Patrick needs another tile that is congruent to this tile for the design on his kitchen wall. Which tile is congruent to the original tile?
A flagpole casts a shadow 27 feet long. Larry is 6 feet tall and casts a 5-foot shadow. How tall is the flagpole? Round your answer to the nearest foot.
18 feet
25 feet
28 feet
32 feet
In triangle ABC, Z is the midpoint of AC and Y is the midpoint of BC. If YZ = 21 and AB = (2x - 4), what is x?
7.25
12.5
23
46
Triangle ABC and triangle CED are similar. Find the measure of ∠A.
65°
80°
90°
130°
A ball is thrown straight up with an initial velocity of 54 feet per second. The height of the ball t seconds after it is thrown is given by the formula h(t) = 54t - 12t2. How many seconds after the ball is thrown will it return to the ground?
9.2
6
4.5
4
The height of a swimmer's dive off a 10-foot platform into a diving pool is modeled by the equation y = 2x2 - 12x + 10, where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water's surface. What is the farthest depth below the water's surface that the swimmer will reach?
6 feet
8 feet
10 feet
12 feet
What is the solution of the equation x2 - 3x - 10 = 10.
-2, 5
-5, -2
2, 5
-5, 2
What is the solution set of x2 - x - 20 = 0?
-4, 5
-5, 4
-10, 2
-2, 10
what is the solution set of the equation 2x2 + x - 3 = 0?
-3, 1/2
-3/2, 1
-3, -1/2
1, 3/2
For which equation is the solution set -5, 2?
x2 + 3x - 10 = 0
x2 - 3x = 10
x2 + 3x = -10
x2 - 3x + 10 = 0
Which of the following represents the graph of y = x2 - 4?
Which of the following represents the graph of the equation y = -x2 + 2?
How many times does the graph of y = 2x2 - 2x + 3 intersect the x-axis?
none
one
two
three
What are the solutions of the equation 5x(x + 8) = 0?
x = -5; x = -8
x = 0; x = -8
x = 0; x = 8
x = 5; x = 8
Pedro throws a ball upward at a rate of 20 meters per second from an initial height of 2 meters. The height of the ball above the ground can be approximated by h = -5t2 + 20t + 2, where t represents the amount of time, in seconds, since the ball has been released. What is the maximum height that the ball reaches?
5 meters
6 meters
20 meters
22 meters
What is the sum of the solutions to the equation x2 - 12 = 4?
-4
0
4
12
The graph of a quadratic function is shown in the accompanying diagram. Which set includes the zeros of this function?
2, 4
-2, 4
-4, 2
-4, -2
If x2 - 6x - 16 is written in the form a(x - h)2 + k, what is the value of a + h + k?
-27
-21
12
29
Which of the following statements best describes the solution(s) of ⅓x2 + ⅙x = 3?
no solution
1 negative solution
1 positive solution and 1 negative solution
2 positive solutions
Suppose that the equation V = 20.8x2 - 458.3x + 3500 represents the value of a car from 1964 to 2002. What year did the car have the least value? (x = 0 in 1964)
1965
1970
1975
1980
The value of (8/27)-⅔ is
4/9
-4/9
-2/3
9/4
The expression 8-⅔ is the equivalent to
¼
-¼
-4
4
If x is a positive integer, 4x½ is equivalent to
2/x
2x
4√(x)
4*(1/x)
The graph of the equation y = 10x lies entirely in Quadrants
I and II
II and III
I and IV
III and IV
∛(9)⋅∛(81)
128^(1/9)
128^(1/6)
9
none of these
Solve ∛(x2 + 2) = 3
±√(5)
±√(7)
±1
±5
The solution set of √(2x + 1) = 1 is
-1, 0
0
the empty set
none of these
Simplify (3x-2y4)-3
27xy
9x2y12
(x6)/(27y12)
none of these
Which of the following has the apparent range of [0, ∞)?
What is the domain of the following graph?
All real numbers
-8 < x < 4
0 ≤ x < 4
0 < x < 4
What is the range of the function in the accompanying image?
[-4, 5]
[-3, 3]
[-2, 3]
[-4, -1]
What is the domain of the function in the accompanying image?
0 ≤ x ≤ 5
0 ≤ x ≤ 8
0 ≤ y ≤ 1
0 ≤ y ≤ 6
Which of these describes the range of the function graphed in the accompanying image?
[0, ∞)
[0, 5]
all real numbers
all whole numbers
The vertex of the quadratic function shown in the accompanying image is at (0, -4). If the graph of this function is translated 2 units down, which of the following best describes the range of the resulting graph?
All numbers greater than or equal to -6
All numbers less than or equal to -6
All numbers greater than or equal to -2
All real numbers
Which of the following graphs does not represent a function of x?
What is the domain of the following graph?
all real numbers
all real numbers except -4
all real numbers greater than or equal to 0
all real numbers greater than or equal to -4
The graph of a function is shown in the accompanying image. Which value is not in the range of the function?
0
3
4
5
Which of the following expressions is equivalent to (6xy)2?
12x2y2
6xy2
36x2y2
6x2y2
Which of the following is equivalent to (m + 1)(m + 5)?
2m + 6
m2 + 5
m2 + 5m + 6
m2 + 6m + 5
The graph of y = |x + 2| is shown in the accompanying figure. Which graph represents y = -|x + 2
Which is an equation of the graph shown in the diagram?
y = x2 - 4
y = -x2 + 4
x = y2 - 4
x = -y2 + 4
In a right triangle, m∠C = 90, m∠A = 55, and CA = 10. What is the length of AB to the nearest integer?
6
14
17
24
In the accompanying diagram of right triangle RUN, m∠U = 90, m∠N = 37, and RN = 21. What is the length of RU, expressed to the nearest tenth?
12.6
15.8
16.8
34.9
In the right triangle shown in the diagram below, what is the value of x to the nearest whole number?
12
14
21
28
A tree casts a 25-foot shadow on a sunny day, as shown in the accompanying diagram. If the angle of elevation from the tip of the shadow to the top of the tree is 32°, what is the height of the tree to the nearest tenth of a foot?
13.2
15.6
21.2
40.0
In right triangle ABC shown in the accompanying diagram, AB = 18.3 and BC = 11.2. What is the measure of ∠A, to the nearest tenth of a degree?
31.5
37.7
52.3
58.5
If a = 4, b = 6, and sinA = ⅗, then sinB equals
3/20
6/10
8/10
9/10
Given triangle ABC as pictured, AB = 6, and AC = 9, find BC.
45
3√(5)
5√(3)
117
A bag contains 2 red marbles and 3 blue marbles. If one marble is drawn at random, what is the probability that it is red?
⅕
⅖
⅗
⅘
If a letter is chosen at random from the word "BASEBALL," what is the probability that the letter chosen is not an L?
1/8
2/8
6/8
7/8
The probability of throwing two fours on a single toss of a pair of dice is
1/36
1/12
1/6
1/3
If two coins are tossed, the probability of getting two tails is
1/2
1/3
1/4
1/8
John has 6 pairs of pants and 3 shirts. How many possible outfits consisting of one shirt and one pair of pants can he select?
9
2
12
18
If Debbie has 3 blouses and 4 skirts, how many different outfits of a blouse and skirt can she wear?
12
7
3
4
A cafeteria offers a choice of five sandwiches, three salads, and three beverages. How many different meals can he choose if each meal consists of one sandwich, one salad, and one beverage?
1
5
11
45
If two fair dice are tossed, the probability of getting a sum of 12 is 1/36. What is the probability of not getting a sum of 12?
35/36
30/36
6/36
34/36
The spinner in the accompanying diagram is divided into eight equal regions and is spun once. What is the probability of not getting red?
3/5
3/8
5/8
7/8
A single card is drawn from a standard deck of 52 cards. What is the probability that the card is a five or a diamond?
17/52
15/32
16/52
18/52
An urn contains five red marbles, four green marbles, and three blue marbles. If one marble is drawn at random, what is the probability that it is either a green marble or a blue marble?
5/12
3/12
7/12
4/12
If two cards are drawn from a standard deck of 52 cards without replacement, what is the probability that both cards are fives?
2/53
(4/52)⋅(3/51)
(1/4)⋅(1/3)
(5/52)⋅(4/51)
A bag of marbles contains three blue, one black, and four yellow marbles. If two marbles are chosen at random without replacement, what is the probability that both marbles will be yellow?
3/14
7/56
1/3
1/4
Keisha is playing a game using a wheel divided into eight equal sectors, as shown in the diagram below. Each time the spinner lands on orange, she will win a prize.
1/64
1/56
1/16
1/4
A newspaper poll was taken to determine the probable winner in an election for mayor. The probability that Andrews will win is 0.4, while the probability that Egan will win is 0.3. What is the probability that either Andrews or Egan will win?
0.7
0.12
0.3
0.4
When a number is chosen at random from the set {1, 2, 3, 4, 5, 6}, which event has the greatest probability of occurring?
choosing an even number
choosing a prime number
choosing a number greater than 3
not choosing either 1 or 6
The party registration of the voters in Jonesville is shown in the table. If one of the registered Jonesville voters is selected at random, what is the probability that the person selected is not a democrat?
0.333
0.400
0.600
0.667
