HiSET: Math : HiSet: High School Equivalency Test: Math

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #1 : Rotations

Hexagon

Rotate the above hexagon  counterclockwise, then reflect it about . Call  the image of  after these transformations.

 will be located in the same position as which of the following points?

Possible Answers:

Correct answer:

Explanation:

 rotation is equivalent to  of a complete rotation, so rotate as follows:

Hexagon

The image of  under this rotation, which we will call , is at .

Now, construct , and reflect the hexagon about this line:

Hexagon

The image of  under this reflection - the desired  - is located at  itself.

 

Example Question #61 : Measurement And Geometry

Between 6:15 and 6:40, the minute hand of a clock undergoes which of the following clockwise rotations?

Possible Answers:

Correct answer:

Explanation:

Between 6:15 and 6:40,

minutes elapse.

The minute hand of a clock rotates one complete clockwise turn about its mount over the course of 60 minutes. Therefore, over 25 minutes, the minute hand rotates clockwise.

Example Question #62 : Measurement And Geometry

Over the course of 20 minutes, the hour hand of a clock undergoes which of the following rotations?

Possible Answers:

Correct answer:

Explanation:

The hour hand of a clock makes one complete  clockwise rotation over the course of 12 hours, or

minutes.

Therefore, over the course of 20 minutes, the hour hand rotates

.

Example Question #123 : Hi Set: High School Equivalency Test: Math

Over the course of one minute and forty seconds, the minute hand of a clock undergoes which of the following clockwise rotations?

Possible Answers:

Correct answer:

Explanation:

The minute hand of a clock rotates one complete clockwise turn about its mount over the course of 60 minutes, or, equivalently, since there are 60 seconds in a minute, every

seconds.

Over the course of 1 minute 40 seconds - or, since one minute is equal to 60 seconds,  seconds - the minute hand rotates clockwise

.

Example Question #1 : Rotations

Letters

Examine the figures in the above diagram. The figure at right is the result of performing which of the following transformations on the figure at left?

Possible Answers:

 clockwise rotation

 counterclockwise rotation

 clockwise rotation

 counterclockwise rotation

 rotation

Correct answer:

 clockwise rotation

Explanation:

Examine the figure below:

1

If we connect the horizontal line with the line along the rotated nine at right, we see that it is the result of a one-third turn clockwise; the angle between them 

Example Question #11 : Rotations

Letters

Examine the figures in the above diagram. The figure at right is the result of performing which of the following transformations on the figure at left?

Possible Answers:

 clockwise rotation

 counterclockwise rotation

 counterclockwise rotation

 clockwise rotation

None of the other choices gives the correct response.

Correct answer:

 clockwise rotation

Explanation:

Examine the figure below:

1

If we connect the horizontal line with the line along the rotated nine at right, we see that it is the result of a one-eighth turn clockwise; the angle between them .

Example Question #11 : Rotations

Letters

Examine the figures in the above diagram. The figure at right is the result of performing which of the following transformations on the figure at left?

Possible Answers:

 clockwise rotation

 counterclockwise rotation

 counterclockwise rotation

 rotation

 clockwise rotation

Correct answer:

 counterclockwise rotation

Explanation:

Examine the figure below. 

1

If we connect the horizontal line with the line along the rotated "omega" at right, we see that it is the result of a one-sixth turn counterclockwise; the angle between them is one sixth of , or  .

Example Question #121 : Hi Set: High School Equivalency Test: Math

Over the course of one hour and twenty minutes, the hour hand of a clock undergoes which of the following clockwise rotations?

Possible Answers:

Correct answer:

Explanation:

The hour hand of a clock makes one complete  clockwise rotation over the course of 12 hours, or, since one hour is equal to 60 minutes,

Therefore, over the course of 1 hour 20 minutes - which is equal to minutes - the hour hand rotates

.

Example Question #1 : Dilations

Right triangle

On the above right triangle perform a dilation of scale factor  with the center of the dilation at the circumcenter of the triangle. Let the images of , and  be ,  and , respectively.

Which of the following correctly shows  relative to  ?

Possible Answers:

Right triangle

Right triangle

Right triangle

Right triangle

Right triangle

Correct answer:

Right triangle

Explanation:

The circumcenter of a triangle can be located by finding the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisectors are shown below, with point of intersection  :

Right triangle

It can be seen that, as is characteristic of a right triangle, this point is the midpoint of the hypotenuse. Construct . A dilation of scale factor   with center  can be performed by letting , and  be the midpoints of , and , respectively: 

Right triangle

Removing the perpendicular bisectors and , we see that the correct choice is the figure

Right triangle

Example Question #1 : Dilations

Right triangle

On the above right triangle perform a dilation of scale factor  with the center of the dilation at the centroid of the triangle. Let the images of , and  be ,  and , respectively.

Which of the following correctly shows  relative to  ?

Possible Answers:

Right triangle

Right triangle

Right triangle

Right triangle

Right triangle

Correct answer:

Right triangle

Explanation:

The centroid of a triangle can be located by finding the intersection of the three medians of the triangle - the segments that connect each vertex to the midpoint of its opposite side. The medians are shown below, with point of intersection  :

Right triangle

A dilation of scale factor   with center  can be performed by letting , and  be the midpoints of , , and , respectively: 

Right triangle

Removing the medians and , we see that the correct choice is the figure

Right triangle

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