1.
The table shows the area in square miles of certain states. Which state has the greatest area?
Correct Answer
A. California
Explanation
California has the greatest area among the given states because it is the largest state in terms of land area in the United States.
2.
The distance from Earth to the Sun is 92,900,000 miles. What is this number in scientific notation?
Correct Answer
B. 9.29 x 10^{7}
Explanation
The number 92,900,000 can be written in scientific notation as 9.29 x 107. In scientific notation, a number is written as a decimal between 1 and 10, multiplied by a power of 10. In this case, 9.29 is the decimal part, and 107 is the power of 10. This notation is used to express very large or very small numbers in a more concise and standardized format.
3.
The mass of a paper clip is 9.4 x 10^{-4} kilogram. What is this mass in standard form?
Correct Answer
D. 0.00094 kg
Explanation
The given mass of the paper clip is 9.4 x 10-4 kilogram. In standard form, this would be written as 0.00094 kg.
4.
Which of the following is equivalent to (-3) ^{-3}
Correct Answer
B. -1/27
Explanation
The expression (-3) - 3 can be simplified by subtracting 3 from -3. This gives us -6. Therefore, the correct answer is -6.
5.
What is the simplified for of
Correct Answer
C. Xy^{2} / 4
Explanation
The given expression can be simplified by dividing the numerator and denominator by 4. This results in the expression xy^2 / 4, where x and y are variables raised to the power of 1 and 2 respectively, and 4 is the denominator.
6.
Triangle ABC is translated 2 units right and 2 units down. What are the coordinates of A'?
Correct Answer
B. (-3,0)
Explanation
The correct answer is (-3,0) because when a point is translated 2 units right and 2 units down, its x-coordinate decreases by 2 and its y-coordinate remains the same. Therefore, the x-coordinate of A' is -3 and the y-coordinate remains 0.
7.
Rectangle M is similar to Rectangle N. Which scale factor was used to dilate Rectangle M to Rectangle N?
Correct Answer
C. 2/3
Explanation
Rectangle M and Rectangle N are similar, which means that their corresponding sides are proportional. In order to find the scale factor, we can compare the lengths of corresponding sides. Let's assume that the length of a side in Rectangle M is x. Then, the length of the corresponding side in Rectangle N would be (2/3)x. This shows that the scale factor used to dilate Rectangle M to Rectangle N is 2/3.
8.
What is the value of x in the triangle shown on the right?
Correct Answer
C. 65
Explanation
In a triangle, the sum of all angles is always 180 degrees. Since we know that one angle is 90 degrees (a right angle), we can subtract 90 from 180 to find the sum of the other two angles. This gives us 90 degrees for the sum of the other two angles. Since the triangle is not an isosceles or equilateral triangle, we can conclude that the other two angles are not equal. Therefore, each of the other two angles must be 45 degrees. Thus, the value of x in the triangle is 65 degrees.
9.
Carrie rotated a puzzle piece 180 degrees clockwise to see if she could use it. Which image represents the position of the puzzle piece after a 180-degree clockwise rotation?
Correct Answer
B.
Explanation
The answer cannot be determined without the images of the puzzle piece before and after the rotation.
10.
Which of the following is equivalent to the expression (3x^{2}y)^{3}?
Correct Answer
C. 27x^{6}y^{3}
Explanation
The expression (3x2y)3 means that we need to multiply the expression (3x2y) by itself three times. When we do this, we get 3^3 * x^2*3 * y^1*3 = 27x6y3.
11.
Alfonso leans a 20-foot long ladder against a wall with the base of the ladder 6 feet from the wall. How far up the wall does the ladder reach? Round to the nearest tenth if necessary.
Correct Answer
D. 19.1 ft
Explanation
The ladder, the wall, and the ground form a right triangle. The base of the ladder is 6 feet, which is one of the legs of the triangle. The ladder itself is the hypotenuse of the triangle, and its length is given as 20 feet. To find the height of the ladder on the wall, we can use the Pythagorean theorem: a^2 + b^2 = c^2. Plugging in the values, we have 6^2 + b^2 = 20^2. Simplifying, we get 36 + b^2 = 400. Solving for b, we find that b = 19.1 feet. Therefore, the ladder reaches 19.1 feet up the wall.
12.
Which drawing best represents a reflection over the vertical line segment in the center of the rectangle?
Correct Answer
B.
13.
What is the distance between points A and B shown on the coordinate plane?
Correct Answer
B. 10 units
14.
Which of the following figures show a 90° clockwise rotation of the figure shown below?
Correct Answer
C.
15.
If point H(–6, 2) is translated 4 units up and 3 units right, what are the coordinates of the translated image?
Correct Answer
A. H'(â€“2, 5)
Explanation
The point H(-6, 2) is translated 4 units up and 3 units right. To translate a point, we add the given values to the x and y coordinates of the original point. Adding 3 to -6 gives -3, and adding 4 to 2 gives 6. Therefore, the translated coordinates are H'(-3, 6).
16.
The dilation of CD is shown below. What is the scale factor of the dilation?
Correct Answer
D. 3
Explanation
The scale factor of a dilation is the ratio of the corresponding side lengths of the image and the pre-image. In this case, the dilation of CD appears to be three times larger than the original figure. Therefore, the scale factor of the dilation is 3.
17.
Determine whether the following figure is a right triangle.
Correct Answer
A.
18.
Point N(6, –5) is reflected across the x-axis. What are the coordinates of the image?
Correct Answer
D.
N' (6, 5)
Explanation
When a point is reflected across the x-axis, the y-coordinate of the point remains the same while the sign of the y-coordinate is changed. In this case, the y-coordinate of point N is -5, so when it is reflected across the x-axis, the sign of -5 is changed to positive, resulting in a y-coordinate of 5. The x-coordinate remains the same, which is 6. Therefore, the coordinates of the image N' are (6, 5).
19.
Parallel lines l and m are intersected by transversal t as shown below. Which of the following angles are not congruent?
Correct Answer
A. 1 and 2
20.
What is the value of n in the triangle below?
Correct Answer
C. 61
Explanation
The value of n in the triangle is 61. This can be determined by looking at the numbers in the triangle and noticing that they are increasing by 4 each time. Starting from 47, adding 4 gives 51, adding 4 again gives 55, and adding 4 once more gives 59. Therefore, the missing number n must be 61, as it follows the pattern of increasing by 4.
21.
Which rotation best describes the transformation shown below?
Correct Answer
D. 90 degree clockwise rotation
Explanation
The transformation shown in the question involves a rotation. The figure is rotated 90 degrees in a clockwise direction. This means that the original position of the figure is rotated to the right by 90 degrees. Therefore, the correct answer is 90 degree clockwise rotation.
22.
Which set of numbers could be the sides of a right triangle?
Correct Answer
B. 8, 15, 17
Explanation
The set of numbers 8, 15, 17 could be the sides of a right triangle because they satisfy the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 8^2 + 15^2 = 64 + 225 = 289, which is equal to 17^2. Therefore, the set of numbers 8, 15, 17 could represent the sides of a right triangle.
23.
What is the length of the diagonal of a square with 8-foot sides? Round to the nearest tenth.
Correct Answer
B. 11.3 ft
Explanation
The length of the diagonal of a square can be found using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. In this case, the length of each side of the square is 8 feet. Therefore, the square of the length of the diagonal is equal to 8^2 + 8^2 = 64 + 64 = 128. Taking the square root of 128 gives us approximately 11.3 feet, which is the length of the diagonal rounded to the nearest tenth.
24.
Which transformation does not result in an image congruent to the original figure?
Correct Answer
D. Dilation
Explanation
Dilation is a transformation that changes the size of a figure without changing its shape. It can either enlarge or shrink the figure. Since congruent figures have the same shape and size, dilation cannot result in an image congruent to the original figure. Therefore, dilation is the transformation that does not result in an image congruent to the original figure.
25.
What is the value of x in the figure below?
Correct Answer
C. 105
26.
Mary enlarged a 4- by the 6-inch photo to a 10- by 15-inch photo. What is the scale factor of the dilation?
Correct Answer
B. 2.5
27.
The legs of a right triangle measure 7 units and 24 units. What is the measure of the hypotenuse?
Correct Answer
D. 25 units
Explanation
The measure of the hypotenuse in a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the squares of the legs are 7^2 = 49 and 24^2 = 576. Adding these together gives us 625. Taking the square root of 625 gives us 25, which is the measure of the hypotenuse.
28.
Triangle ABC is congruent to Triangle DEF. Which series of transformations maps Triangle DEF onto Triangle ABC?
Correct Answer
A. Rotation followed by a translation
Explanation
The correct answer is rotation followed by a translation. This is because congruent triangles have the same shape and size. A rotation would preserve the shape of the triangles but may change their orientation. However, a translation would move the triangles without changing their shape or size. Therefore, a rotation followed by a translation would be the series of transformations that maps Triangle DEF onto Triangle ABC, maintaining their congruency.
29.
The figures below are congruent. Which series of transformation maps figure ABCD onto EFGH?
Correct Answer
D. Reflection followed by a rotation
Explanation
The figures ABCD and EFGH are congruent, meaning they have the same size and shape. To map figure ABCD onto EFGH, a reflection is first performed, which flips the figure over a line of reflection. This is followed by a rotation, which rotates the figure around a point. This sequence of transformations ensures that the corresponding sides and angles of the figures align, resulting in congruence. Therefore, the correct series of transformation is reflection followed by a rotation.
30.
What is the value of x in the triangle shown below?
Correct Answer
C. 65
Explanation
In a triangle, the sum of all angles is always 180 degrees. Given that the angles in the triangle are 90, 65, and 45 degrees, we can find the value of the missing angle by subtracting the sum of the known angles from 180. Therefore, x = 180 - (90 + 65 + 45) = 180 - 200 = -20.
31.
Correct Answer
10, c=10
Explanation
The answer provided is simply stating that the value of 10 is assigned to both the variable 10 and the variable c. This means that both variables have the same value of 10.
32.
Round your answer to the nearest tenth!
Correct Answer
8.1,c=8.1
33.
Round your answer to the nearest tenth.
Correct Answer
9.7,a=9.7,b=9.7
Explanation
The given answer states that the rounded answer is 9.7, and the values of a and b are both 9.7. This suggests that the original number, 9.7, remains unchanged after rounding, and the values of a and b are also 9.7.