Regents Prep: Math A
Multiple-Choice Questions
Regents Prep Math A: Topical Multiple-Choice Question Archive
Use of Topical Archive Multiple-Choice Questions
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Feel free to copy and paste any of the multiple-choice questions below for use in creating your own Regents-style assessments.

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Modeling/Multiple Representation: Question 1 of 25
What is the image of point (2,5) under the translation that shifts (x,y) to (x+3,y-2)?
  1. (0,3)
  2. (0,8)
  3. (5,3)
  4. (5,8)

Correct Answer Number: 3

Explanation: For the point that you are given (2,5), 2 is the x-coordinate, and 5 is the y-coordinate. Simply substitute x=2 and y=5 into the new translation (x+3,y-2). You will get (2+3, 5-2) which is (5,3).

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Modeling/Multiple Representation: Question 2 of 25
The direct distance between city A and city B is 200 miles. The direct distance between city B and city C is 300 miles. Which could be the direct distance between city C and city A?
  1. 50 miles
  2. 350 miles
  3. 550 miles
  4. 650 miles

Correct Answer Number: 2

Explanation: Picture the three cities forming a triangle. (According to the answers, the three cities do not form a straight line.) The sides of a triangle are related in such a manner that the adding of any two sides of the triangle must give a value larger than any single side of the triangle. The value 350 is the only choice that will uphold this relationship.

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Modeling/Multiple Representation: Question 3 of 25
At a concert, $720 was collected for hot dogs, hamburgers, and soft drinks. All three items sold for $1.00 each. Twice as many hot dogs were sold as hamburgers. Three times as many soft drinks were sold as hamburgers. The number of soft drinks was
  1. 120
  2. 240
  3. 360
  4. 480

Correct Answer Number: 3

Explanation: Represent the number of hamburgers by x. The cost of a hamburger is one dollar times x, which is still represented by x. Since they all sold for the same amount of money, the cost of the hotdogs is represented by 2x and the cost of the soft drinks is 3x. Your equation is x + 2x + 3x = 720. Solving for x, you will get 6x = 720 and x = 120. BE CAREFUL!! The question asks for the number of soft drinks or 3x.


Modeling/Multiple Representation: Question 4 of 25
If x = -3 and y = 2, which point on the graph below represents the location (-x,-y)?
 

  1. P
  2. Q
  3. R
  4. S

Correct Answer Number: 2

Explanation: (-x,-y) = (-(-3),-2) = (3,-2)

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Modeling/Multiple Representation: Question 5 of 25
The diagram below shows triangle ABC with segment AB extended to point D, exterior angle CBD measuring 145º, and angle C measuring 75º. What is the measure of angle CAB?
 

  1. 35º
  2. 70º
  3. 110º
  4. 220º

Correct Answer Number: 2

Explanation: Since angle ABC and angle DBC form a straight angle, the measure of angle ABC=35º. The angles in a triangle add to 180º. Therefore the measure of angle CAB=70º. This problem could also be done using the exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

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Modeling/Multiple Representation: Question 6 of 25
Two tin cans are shown in the diagram below. The shape of these cans is best described as a
 

  1. rectangular solid
  2. pyramid
  3. cone
  4. cylinder

Correct Answer Number: 4

Explanation: Cans are cylinders.

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Modeling/Multiple Representation: Question 7 of 25
When the point (2,-5) is reflected in the x-axis, what are the coordinates of its image?
  1. (-5,2)
  2. (-2,5)
  3. (2,5)
  4. (5,2)

Correct Answer Number: 3

Explanation: Draw yourself a sketch and think of folding the point over the x-axis.

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Modeling/Multiple Representation: Question 8 of 25
The image of the point (5,6) reflected in the y-axis is
  1. (6,5)
  2. (-6,5)
  3. (5,-6)
  4. (-5,6)

Correct Answer Number: 4

Explanation: Draw a sketch and fold along the y-axis. Your new point is in the 2nd Quadrant. It is the same distance away from the y-axis as the original point (5,6).

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Modeling/Multiple Representation: Question 9 of 25
If the sides of a triangle are 6, 8 and x, how many integer values of x could be the measure of the third side of the triangle?
  1. 11
  2. 5
  3. 6
  4. 8

Correct Answer Number: 1

Explanation: Remember that the sum of any two sides of a triangle must be larger than the third side. The third side could be as small as 3, or as large as 13, and still make this rule true. This is a total of 11 values.

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Modeling/Multiple Representation: Question 10 of 25
The distance between parallel lines p and m is 12 units. Point A is on line p. How many points are equidistant from lines p and m and 8 units from point A?
  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer Number: 2

Explanation: This is a compound locus problem. Do each part separately and see where the results intersect. First, the points equidistant from the two parallel lines is a third parallel line half way between the two given lines (in this problem, 6 units from each line). Draw this line as a dotted line. Second, the points equidistant from point A form a circle of radius 8. Draw the circle dotted. Look for the intersections of the dotted drawings. The dotted circle intersects the dotted line in two places.

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Modeling/Multiple Representation: Question 11 of 25
If the number represented by n - 3 is an odd integer, which expression represents the next greater odd integer?
  1. n - 5
  2. n - 2
  3. n - 1
  4. n + 1

Correct Answer Number: 3

Explanation: Think of a numerical example of this problem so that you can clearly see what the pattern will be. If you start with the number 3, the next greater odd integer is 5. To get from 3 to 5 it was necessary to add 2. The pattern for generating odd numbers when you start with an odd number, is to add 2. So, if you start with n - 3, the next greater odd integer will be (n - 3) + 2 = n - 1.

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Modeling/Multiple Representation: Question 12 of 25
The distance from point A to point B is seven units. How many points are equidistant from A and B and also four units from point A?
  1. 0
  2. 1
  3. 2
  4. 3

Correct Answer Number: 3

Explanation: This is a compound locus problem. Do each part separately and find the points of intersection. First, the points equidistant from A and point B form a line half way between A and B (the perpendicular bisector of segment AB). In this problem, this line is 3.5 units from both A and B. Draw this line dotted. Second, the points equidistant from point A form a circle of radius 4. Draw the circle dotted. Look to where the dotted line and the dotted circle intersect (2 locations).

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Modeling/Multiple Representation: Question 13 of 25
Two supplementary angles are in the ratio of 2 to 3. The number of degrees in the smaller angle is:
  1. 18
  2. 36
  3. 54
  4. 72

Correct Answer Number: 4

Explanation: Supplementary angles add to 180º. Represent the angles as 2x and 3x. 2x + 3x = 180 and 5x = 180 therefore x = 36. BE CAREFUL!! The question asked for the smaller angle (2x). 2x = 72.

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Modeling/Multiple Representation: Question 14 of 25
Triangle ABC is congruent to triangle DEF with segment AB congruent to segment DE. If AB = 2x + 10, and DE = 4x - 20, find the value of x.
  1. 5
  2. 10
  3. 15
  4. 60

Correct Answer Number: 3

Explanation: Congruent means equal. 2x+10=4x-20
30=2x
15=x

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Modeling/Multiple Representation: Question 15 of 25
The two legs of a right triangle measure 5 and 12. The leg and hypotenuse of another right triangle measure 12 and 13 respectively. What can be said about these two triangles?
  1. The triangles are congruent.
  2. The triangles are not congruent.
  3. The triangles are both equilateral triangles.
  4. The triangles are both isosceles triangles.

Correct Answer Number: 1

Explanation: In the first triangle with legs of 5 and 12, the hypotenuse is 13 (use the Pythagorean Theorem).
In the second triangle with leg 12 and hypotenuse 13, the missing leg is 5 (use the Pythagorean Theorem).
These triangles are exactly the same size and shape (congruent).

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Modeling/Multiple Representation: Question 16 of 25
Which of the following triangles are always similar?
  1. right triangles
  2. isoscelse triangles
  3. equilateral triangles
  4. scalene triangles

Correct Answer Number: 3

Explanation: The only triangle choice which guarantees TWO angles of the same size in each triangle would be the equilateral triangles where each equilateral triangle contains three 60º angles.

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Modeling/Multiple Representation: Question 17 of 25
If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining 3 angles.
  1. 60, 60, 60
  2. 30, 60, 90
  3. 60, 120, 120
  4. 60, 120, 150

Correct Answer Number: 3

Explanation: By the properties of a parallelogram we know that the opposite angles are equal and the consecutive angles are supplementary.

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Modeling/Multiple Representation: Question 18 of 25
The construction below shows a perpendicular from a point off the line. The reason that PA is perpendicular to line l is
 

  1. the locus of points equidistant from two given points is a perpendicular bisector of the segment formed by the two points.
  2. perpendicular lines always form right angles.
  3. two congruent triangles are formed illustrating SAS.
  4. the locus of points equidistant from a given point is a circle.

Correct Answer Number: 1

Explanation: This construction is based upon the locus theorem that the locus of points equidistant from two points is the perpendicular bisector of that segment.

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Modeling/Multiple Representation: Question 19 of 25
Under a translation of 5 units up and 2 units to the left, the point (3,4) will become
  1. (8,2)
  2. (1,9)
  3. (-2,6)
  4. (-2,2)

Correct Answer Number: 2

Explanation: "UP" is moving in a positive direction and "LEFT" is moving in a negative direction. Add 5 to the y-coordinate and subtract 2 from the x-coordinate. Drawing a picture is often helpful in obtaining the correct location.

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Modeling/Multiple Representation: Question 20 of 25
Which set of numbers canNOT represent the sides of a triangle?
  1. 3,4,5
  2. 4,5,7
  3. 3,4,7
  4. 10, 12, 14

Correct Answer Number: 3

Explanation: The sum of any two sides of a triangle must be greater than the third side. This is not true in #3. 3 + 4 is not greater than 7.

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Modeling/Multiple Representation: Question 21 of 25
If the point T(-1,5) is reflected over the x-axis, the coordinates of its image will be
  1. (1,-5)
  2. (-1,-5)
  3. (1,5)
  4. (5,-1)

Correct Answer Number: 2

Explanation: Reflecting over the x-axis is "folding" over the x-axis. The x-coordinate stays the same, but the y-coordinate changes to the negative value.

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Modeling/Multiple Representation: Question 22 of 25
What is the total number of points equidistant from two parallel lines and also equidistant from two points on one of these lines?
  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer Number: 1

Explanation: Try to visualize this situation. Equidistant from two parallel lines is one line between the parallels. Equidistant from two points is the perpendicular bisector of the segment joining the two points. These two lines intersect in one point.

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Modeling/Multiple Representation: Question 23 of 25
The sides of a triangle are 3, 5 and 7. What is the length of the shortest side of a similar triangle whose longest side is 21?
  1. 9
  2. 15
  3. 6
  4. 10

Correct Answer Number: 1

Explanation: The ratio of similitude is 1:3=7:21. The shortest side of the first triangle is 3. Its corresponding side in the larger triangle is 9. 1:3 = 9:x

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Modeling/Multiple Representation: Question 24 of 25
Two complementary angles measure x and 65º. How many degrees are there in x ?
  1. 25º
  2. 115º
  3. 35º
  4. 125º

Correct Answer Number: 1

Explanation: Complementary angles add to 90º.

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Modeling/Multiple Representation: Question 25 of 25
Under a dilation, A(0,0), B(0,4) and C(6,0) become A'(0,0), B'(0,10) and C'(15,0). What is the scale factor of dilation?
  1. 2
  2. 2.5
  3. 3
  4. 4

Correct Answer Number: 2

Explanation: Remember to look to see what each coordinate is multiplied by to form the new coordinates.

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