ETS Math Test I. A+ Graded End Term Exam
In the figure shown, quadrilateral ABFG is a square and quadrilateral FCDE is a rectangle. Which of the
following statements must be true about the figure?
Select all that apply. - ✔✔A G lies on the x-axis.
D D is in the fourth quadrant.
E The area of the polygon ABCDEFG is 27 square units.
Options (A), (D), and (E) are correct. The question requires an understanding of the coordinate plane
and area of polygons. Since the x-axis is the horizontal axis, point G lies on the x-axis and has
coordinates (-3, 0). The points in the fourth quadrant have a positive x-coordinate and a negative y-
coordinate. Since point D has coordinates (4, -3), point D is in the fourth quadrant. The polygon is made
of a square, a right triangle, and a rectangle. The length of the side of the square is 3 units; therefore,
the area of the square is 9 square units. The lengths of the sides of the right triangle are 3 and 4 units,
respectively; therefore, the area of the right triangle is 6 square units. The lengths of the sides of the
rectangle are also 3 and 4 units, respectively; therefore, the area of the rectangle is 12 square units.
Finally, the area of the polygon is the sum of the areas of its parts; that is, 9 + 6 + 12, or 27 square units.
Which of the following is equal to 5(10^0)? - ✔✔C. 5
A pencil is 18 centimeters in length. How long is the pencil in millimeters? - ✔✔C. 180
If the geometric sequence below continues to increase in the same way, what is the next number in the
sequence?
2, 6, 18, 54, 162, ... - ✔✔C. 486
3x^5+7x^3−5
Which of the following lists the coefficients and degrees of the terms in the polynomial shown? -
✔✔A.Coefficients: 3, 7, −5−5 ; Degrees: 5, 3, 0
In which quadrant is the point (−8,2) located? - ✔✔B. Quadrant II
, Elisa's number: 5,723,683
Troy's number: 2,678,533
Both Elisa and Troy wrote a number, as shown. The digit 7 in Elisa's number represents how many times
what the digit 7 represents in Troy's number? - ✔✔A. 10
3y+2y
What is the value of the algebraic expression shown when y = 5 ? - ✔✔B. 25
Which of the following could be used to describe the polygon shown? - ✔✔D. Irregular and concave
The question requires an understanding of polygons and their properties. The polygon can be described
as irregular because its sides are of different lengths, and the polygon can be described as concave
because it is possible to connect two vertices of the polygon with a segment that is not contained in the
interior of the polygon.
Sara went to the store to buy some clothes. She bought six shirts, half as many pairs of pants as shirts,
and a fourth as many sweaters as shirts. How many pieces of clothing did Sara buy?
Which of the following statements about the solution to the word problem shown must be true? - ✔✔D.
Because of the real-world context, the solution must belong to the set of all natural numbers; therefore,
the solution is not acceptable.
Option (D) is correct. The question requires an understanding of how to evaluate the reasonableness of
a solution to a contextual word problem. The solution to the given word problem must belong to the set
of all natural numbers because the unit is pieces of clothing, which is a positive and discrete unit.
According to the word problem, Sara bought 6 shirts, 3 pairs of pants, and 112112 sweaters, totaling
10121012 pieces of clothing. The solution is, therefore, not acceptable since it is not a natural number.
In the figure shown, quadrilateral ABFG is a square and quadrilateral FCDE is a rectangle. Which of the
following statements must be true about the figure?
Select all that apply. - ✔✔A G lies on the x-axis.
D D is in the fourth quadrant.
E The area of the polygon ABCDEFG is 27 square units.
Options (A), (D), and (E) are correct. The question requires an understanding of the coordinate plane
and area of polygons. Since the x-axis is the horizontal axis, point G lies on the x-axis and has
coordinates (-3, 0). The points in the fourth quadrant have a positive x-coordinate and a negative y-
coordinate. Since point D has coordinates (4, -3), point D is in the fourth quadrant. The polygon is made
of a square, a right triangle, and a rectangle. The length of the side of the square is 3 units; therefore,
the area of the square is 9 square units. The lengths of the sides of the right triangle are 3 and 4 units,
respectively; therefore, the area of the right triangle is 6 square units. The lengths of the sides of the
rectangle are also 3 and 4 units, respectively; therefore, the area of the rectangle is 12 square units.
Finally, the area of the polygon is the sum of the areas of its parts; that is, 9 + 6 + 12, or 27 square units.
Which of the following is equal to 5(10^0)? - ✔✔C. 5
A pencil is 18 centimeters in length. How long is the pencil in millimeters? - ✔✔C. 180
If the geometric sequence below continues to increase in the same way, what is the next number in the
sequence?
2, 6, 18, 54, 162, ... - ✔✔C. 486
3x^5+7x^3−5
Which of the following lists the coefficients and degrees of the terms in the polynomial shown? -
✔✔A.Coefficients: 3, 7, −5−5 ; Degrees: 5, 3, 0
In which quadrant is the point (−8,2) located? - ✔✔B. Quadrant II
, Elisa's number: 5,723,683
Troy's number: 2,678,533
Both Elisa and Troy wrote a number, as shown. The digit 7 in Elisa's number represents how many times
what the digit 7 represents in Troy's number? - ✔✔A. 10
3y+2y
What is the value of the algebraic expression shown when y = 5 ? - ✔✔B. 25
Which of the following could be used to describe the polygon shown? - ✔✔D. Irregular and concave
The question requires an understanding of polygons and their properties. The polygon can be described
as irregular because its sides are of different lengths, and the polygon can be described as concave
because it is possible to connect two vertices of the polygon with a segment that is not contained in the
interior of the polygon.
Sara went to the store to buy some clothes. She bought six shirts, half as many pairs of pants as shirts,
and a fourth as many sweaters as shirts. How many pieces of clothing did Sara buy?
Which of the following statements about the solution to the word problem shown must be true? - ✔✔D.
Because of the real-world context, the solution must belong to the set of all natural numbers; therefore,
the solution is not acceptable.
Option (D) is correct. The question requires an understanding of how to evaluate the reasonableness of
a solution to a contextual word problem. The solution to the given word problem must belong to the set
of all natural numbers because the unit is pieces of clothing, which is a positive and discrete unit.
According to the word problem, Sara bought 6 shirts, 3 pairs of pants, and 112112 sweaters, totaling
10121012 pieces of clothing. The solution is, therefore, not acceptable since it is not a natural number.
