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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Measurement: Question 1 of 31
During a recent winter, the ratio of deer to foxes was 7 to 3 in one county of New York State. If there were 210 foxes in the county, what was the number of deer in the county?
  1. 90
  2. 147
  3. 280
  4. 490

Correct Answer Number: 4

Explanation: Since the ratio of deer to foxes is 7 to 3, you can represent the number of deer by 7x and the number of foxes by 3x. If there are 210 foxes, you know that 3x = 210 and x = 70. This means that the number of deer (7x) must be 7(70)=490.

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Measurement: Question 2 of 31
The Pentagon building in Washington, D.C., is shaped like a regular pentagon. If the length of one side of the Pentagon is represented by n + 2, its perimeter would be represented by
  1. 5n + 10
  2. 5n + 2
  3. n + 10
  4. 10n

Correct Answer Number: 1

Explanation: A regular pentagon has 5 sides of equal length. The perimeter would be 5(n+2) which equals 5n+10.

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Measurement: Question 3 of 31
The ratio of the corresponding sides of two similar squares is 1 to 4. What is the ratio of the area of the smaller square to the area of the larger square?
  1. 1:2
  2. 1:4
  3. 1:8
  4. 1:16

Correct Answer Number: 4

Explanation: If two figures are similar, the ratio of their areas is the square of the ratio of their corresponding sides.

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Measurement: Question 4 of 31
What is the diameter of a circle whose circumference is 5?
 

  1. A
  2. B
  3. C
  4. D

Correct Answer Number: 4

Explanation: Notice that the problem is asking for the DIAMETER. Use the formula for circumference which utilizes the diameter, C=(pi)d. The formula becomes 5=(pi)d. Solving for d gives answer choice 4.

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Measurement: Question 5 of 31
In the figure below, ACDH and BCEF are rectangles, AH=2, GH=3, GF=4, and FE=5. What is the area of BCDG?
 

  1. 6
  2. 8
  3. 10
  4. 20

Correct Answer Number: 3

Explanation: The area of a rectangle is A=bh. Sides DG and EF are equal. Sides AH and BG are equal. Therefore, the area is 5 times 2 which is 10 square units.

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Measurement: Question 6 of 31
What is the slope of the line shown in the figure below?
 

  1. 4/3
  2. 3/4
  3. -(3/4)
  4. -(4/3)

Correct Answer Number: 1

Explanation: Remember that slope is the rise over the run. Simply counting the rise and run between the two points shown in the diagram will give the slope.

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Measurement: Question 7 of 31
If 6 and x have the same mean (average) as 2, 4, and 24, what is the value of x?
  1. 5
  2. 10
  3. 14
  4. 36

Correct Answer Number: 3

Explanation: The mean of 2, 4, and 24 is (2+4+24)/3=10. This means that (6+x)/2=10. Solving for x, we get 6+x=20 and x=14.


Measurement: Question 8 of 31
Sterling silver is made of an alloy of silver and copper in the ratio of 37:3. If the mass of a sterling silver ingot is 600 grams, how much silver does it contain?
  1. 48.65 g
  2. 200 g
  3. 450 g
  4. 555 g

Correct Answer Number: 4

Explanation: Represent this problem with the equation 37x + 3x = 600. Combining terms gives 40x = 600. Solving for x shows that x = 15. Now, the amount of silver is represented by 37x, so substitution is necesssary 37(15)=555.

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Measurement: Question 9 of 31
What is the distance between points A(3,1) and B(5,-3)?
 

  1. A
  2. B
  3. C
  4. D

Correct Answer Number: 3

Explanation: Use the Distance formula to solve this problem OR plot the points on graph paper, form a right triangle, and use the Pythagorean theorem.

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Measurement: Question 10 of 31
For what value of x will x and 12 have the same mean (average) as 4 and 30?
  1. 4
  2. 48
  3. 22
  4. 12

Correct Answer Number: 3

Explanation: The average of 4 and 30 is 34/2 = 17. In order for 2 numbers to have an average of 17, they must ADD to 34. The missing value must be 22 so that 22 + 12 = 34.


Measurement: Question 11 of 31
If the edge of a cube is 9 inches and the edge of a second cube is 7 inches, the difference in the volumes of these cubes is:
  1. 32
  2. 63
  3. 343
  4. 386

Correct Answer Number: 4

Explanation: The volume of the first cube is (9)(9)(9)=729. The volume of the second cube is (7)(7)(7)=343. The difference is 386.

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Measurement: Question 12 of 31
The perimeter of a rectangle is 40. One of the sides is 5. Find the lengths of the other three sides.
  1. 10, 10, 10
  2. 5, 10, 10
  3. 5, 15, 15
  4. 10, 15, 15

Correct Answer Number: 3

Explanation: Perimeter is the distance around the outside. A rectangle has opposite sides equal. One of the other sides is 5, which leaves 30 units (from the 40 in the perimeter) to be split between the other two sides.

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Measurement: Question 13 of 31
Find the area of a circle whose diameter is 10. Express answer to the nearest tenth.
  1. 628.4
  2. 314.2
  3. 78.5
  4. 39.2

Correct Answer Number: 3

Explanation: Be Careful! This problem give the diameter (10), but the area formula requires the radius (5). Area of a circle is pi times the radius squared.

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Measurement: Question 14 of 31
If the legs of a right triangle are 6 and 10, find the length of the hypotenuse to the nearest tenth.
  1. 8.0
  2. 11.7
  3. 12.0
  4. 13.6

Correct Answer Number: 2

Explanation: Use the Pythagorean Theorem c²=a²+b²

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Measurement: Question 15 of 31
What are the coordinates of the y-intercept of the equation y - 3x = 5?
  1. (0,5)
  2. (0,-5)
  3. (0,3)
  4. (0,-3)

Correct Answer Number: 1

Explanation: Put the equation in y=mx+b form and read the value for b.
y=3x+5 and b=5. The y-intercept is at 5. The coordinates are (0,5).

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Measurement: Question 16 of 31
What is the equation of line whose slope is 3 and passes through the point (1,2)?
  1. y=3x+2
  2. y=x+2
  3. y=3x+1
  4. y=3x-1

Correct Answer Number: 4

Explanation: Use the point-slope form. y-y1=m(x-x1)
y-2=3(x-1)
y-2=3x-3
y=3x-1

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Measurement: Question 17 of 31
The measures of the angles in a triangle are in the ratio of 1:2:6. Find the number of degrees in the largest angle of the triangle.
  1. 20º
  2. 40º
  3. 90º
  4. 120º

Correct Answer Number: 4

Explanation: The angles of a triangle add to 180º. x + 2x + 6x = 180
9x=180
x=20
Be careful! The question asks for the LARGEST angle. Substitute:6x=6(20)=120º

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Measurement: Question 18 of 31
If the lengths of the sides of a square are doubled, then the area of the sqaure would be multiplied by
  1. 1
  2. 2
  3. 4
  4. 8

Correct Answer Number: 3

Explanation: Set up an example: If the side is 3, the area is 9. If the side is doubled(6), the area is 36. The area is multiplied by 4.

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Measurement: Question 19 of 31
The slope of a vertical line is
  1. 0
  2. 1
  3. -1
  4. undefined

Correct Answer Number: 4

Explanation: A vertical line has "rise" but no "run". Thus, the denominator in the rise/run formula is 0 and it is an undefined fraction.

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Measurement: Question 20 of 31
How many pounds of ground beef should you buy to make 120 hamburgers, if each burger patty will weigh 5 ounces before cooking?
  1. 16
  2. 32
  3. 38
  4. 60

Correct Answer Number: 3

Explanation: ? lbs/5 oz = 1 lb/16 oz
Solving for the question mark gives 0.313. Multiply times 120 and you get 37.5. Round to 38 for the number of pounds needed.

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Measurement: Question 21 of 31
If you needed to determine the size of an angle in an architectural drawing, which mathematical tool would you most likely use?
  1. a compass
  2. vernier caliphers
  3. a protractor
  4. a micrometer

Correct Answer Number: 3

Explanation: Protractors are used to measure angles.

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Measurement: Question 22 of 31
Find the median: 5, 15, 10, 15, 5, 10, 10, 20, 25, 15.
  1. 10
  2. 12.5
  3. 15
  4. There is no median value.

Correct Answer Number: 2

Explanation: Arrange the values into ascending order: 5, 5, 10, 10, 10, 15, 15, 15, 20, 25
Since both 10 and 15 fall in the middle, the median is the average of these two values. (10+15)/2=12.5


Measurement: Question 23 of 31
If sin A = 0.1908, find the number of degrees in angle A.
  1. 0.003º
  2. 3º
  3. 11º
  4. 13º

Correct Answer Number: 3

Explanation: Use your calculator. If using a scientific calculator, enter 0.1908 and hit the value ABOVE the sin key.

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Measurement: Question 24 of 31
A ladder 6 feet long leans against a wall and makes an angle of 71º with the ground. Find to the nearest tenth of a foot how high up the wall the ladder will reach.
  1. 2.0
  2. 3.5
  3. 5.7
  4. 6.0

Correct Answer Number: 3

Explanation: Draw a diagram. The right triangle has a hypotenuse of 6 and the angle of 71º should be placed between the ladder and the ground. Place x on the vertical side. The correct trig. function is sin 71º=x/6.

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Measurement: Question 25 of 31
Solve for x: x/(x+8) = 5/15
  1. 3
  2. 4
  3. 5
  4. 6

Correct Answer Number: 2

Explanation: Cross multiply and solve. 15x = 5(x + 8)
15x = 5x + 40
10x = 40
x = 4

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Measurement: Question 26 of 31
If one inch represents 10 feet, what dimensions would you use to make a scale drawing of a building 20 feet by 40 feet?
  1. 2 in. by 4 in.
  2. 10 in. by 40 in.
  3. 4 in. by 5 in.
  4. 5 in. by 10 in.

Correct Answer Number: 1

Explanation: Establish two proportions:
Width: 1/10=x/20
x=2 inches
Length: 1/10=y/40
y=4 inches

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Measurement: Question 27 of 31
In a magazine, 30 pages of the 80 pages are devoted to sports. What percent of the magazine is devoted to sports?
  1. 2.7%
  2. 3.75%
  3. 27%
  4. 37.5%

Correct Answer Number: 4

Explanation: Written literally: 30 = m% of 80
30 = (m/100)(80)
30 = (80m)/100
80m=3000
m=37.5

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Measurement: Question 28 of 31
Find the midpoint between the points (6,4) and (3,-4).
  1. (1.5,0)
  2. (9,8)
  3. (4.5,0)
  4. (9,0)

Correct Answer Number: 3

Explanation: Use the midpoint formula: (x,y)=((x1+x2)/2,(y1+y2)/2)
((6+3)/2,(4+(-4))/2)=(9/2,0/2)=(4.5,0)

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Measurement: Question 29 of 31
M is the midpoint of segment AB. The coordinates of A are (2,3) and the coordinates of M are (4.5,6). Find the coordinates of B.
  1. (9,18)
  2. (7,9)
  3. (3.25,4.5)
  4. (2.5,1.5)

Correct Answer Number: 2

Explanation: Use the midpoint formula and solve for the missing value: (x,y)=((x1+x2)/2,(y1+y2)/2)
(4.5,6)=((2+x2)/2,(3+y2)/2)
4.5=(2+x2)/2 and 9=2+x2 and 7=x2
6=(3+y2)/2 and 12=3+y2 and 9=y2

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Measurement: Question 30 of 31
Find the slope of a line perpendicular to the line whose equation is 3y + 2x = 6.
  1. 2
  2. -2
  3. -3/2
  4. 3/2

Correct Answer Number: 4

Explanation: Perpendicular lines have negative reciprocal slopes.
Rewrite the equation to read its slope: 3y=-2x+6
y=-2/3+2 so the slope is (-2/3). The negative reciprocal of (-2/3) is 3/2.

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Measurement: Question 31 of 31
Bosie, the cow, weighs 851 pounds, to the nearest pound. Which weight listed cannot be the actual weight of the cow?
  1. 850.6 pounds
  2. 851.0 pounds
  3. 851.4 pounds
  4. 851.6 pounds

Correct Answer Number: 4

Explanation: 851.6 pounds would round to 852 pounds to the nearest pound.

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