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HSPT Math : Concepts

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Example Questions

Example Question #1471 : Concepts

What is the total degrees of the angles in a square?

Possible Answers:

360

180

270

Correct answer:

360

Explanation:

A square has four right angles which each have degrees.

To get the total you just multiple the measure of one by to get

90*4=360 .

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Example Question #11 : Geometry

Angle $\angle ABC$ measures $20^{\circ}$

$\overrightarrow{BD}$ is the bisector of $\angle ABC$

$\overrightarrow{BE}$ is the bisector of $\angle CBD$

What is the measure of $\angle ABE$ ?

Possible Answers:

$5^{\circ}$

$15^{\circ}$

$40^{\circ}$

$30^{\circ}$

$10^{\circ}$

Correct answer:

$15^{\circ}$

Explanation:

Angle pic

Let's begin by observing the larger angle. $\angle ABC$ is cut into two 10-degree angles by $\overrightarrow{BD}$ . This means that angles $\angle ABD$ and $\angle CBD$ equal 10 degrees. Next, we are told that $\overrightarrow{BE}$ bisects $\angle CBD$ , which creates two 5-degree angles. $\angle ABE$ consists of $\angle ABD$ , which is 10 degrees, and $\angle DBE$ , which is 5 degrees. We need to add the two angles together to solve the problem.

$\angle ABE=\angle ABD+\angle DBE$

$\angle ABE=10^{\circ}+5^{\circ}$

$\angle ABE=15^{\circ}$

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Example Question #181 : Coordinate Geometry

If $\overleftrightarrow{FH} \parallel \overleftrightarrow{AD}$ , $\overline{BE}\perp \overleftrightarrow{GC}$ , and $m\angle HGC=58^\circ$ , what is the measure, in degrees, of $\angle ABE$ ?

Alternate interior angles

Possible Answers:

148

122

Correct answer:

148

Explanation:

The question states that $\overleftrightarrow{FH} \parallel \overleftrightarrow{AD}$ . The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:

$m\angle GCA = 58^\circ$

The sum of angles of a triangle is equal to 180 degrees. The question states that $\overline{BE}\perp \overleftrightarrow{GC}$ ; therefore we know the following measure:

$m \angle BEC = 90^\circ$

Use this information to solve for the missing angle: $\angle EBC$

$180^\circ=m\angle EBC+58^\circ+90^\circ$

$m\angle EBC=32^\circ$

The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:

$180^\circ=m\angle ABE+32^\circ$

$m\angle ABE=148^\circ$

The measure of $\angle ABE$ is 148 degrees.

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Example Question #1472 : Concepts

What is the slope of a line through the points (2,5) and (-2,3) ?

Possible Answers:

$-\frac{1}{2}$

Undefined slope

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

Use the slope fomula, setting $x_{1} = -2, x_{2} = 2,y_{1} = 3, y_{2} = 5$

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{5-3}{2-(-2)} = \frac{2}{4} =\frac{1}{2}$

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Example Question #1473 : Concepts

In which quadrant, or on which axis, is the point with coordinates (6,-6) located?

Possible Answers:

Quadrant III

Quadrant II

Quadrant I

Quadrant IV

The -axis

Correct answer:

Quadrant IV

Explanation:

Any point with a positive -coordinate and a negative -coordinate is located in the lower right quadrant - Quadrant IV.

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Example Question #1474 : Concepts

Which of the following is an equation of a line with slope 0?

Possible Answers:

y = -5

$y=x^{2} +1$

y = x+7

x+y= 10

x = 6

Correct answer:

y = -5

Explanation:

A line with slope 0 has equation y = b for some real value .

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Example Question #1475 : Concepts

Axes

Give the equation of the red line in slope-intercept form.

Possible Answers:

$y =- \frac{7}{4}x + 6$

$y = \frac{7}{4}x + 6$

$y = \frac{4}{7}x + 6$

$y =- \frac{7}{4}\left (x + 6 \right )$

$y = -\frac{4}{7}x + 6$

Correct answer:

$y = \frac{7}{4}x + 6$

Explanation:

The slope of the line is

$m = \frac{y_{2}- y_{1}}{x_{2}- x_{1}} = \frac{6- (-1)}{0-(-4)} = \frac{7}{4}$

The -intercept of the line has -coordinate b= 6

The slope-intercept form can be written:

y = mx+b

Replace:

$y = \frac{7}{4}x+6$

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Example Question #1476 : Concepts

Axes_2

The green and blue lines are perpendicular: What is the slope of the blue line?

Possible Answers:

It cannot be determined from the information given.

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

The slope of the blue line, being perpendicular to the green line, is the opposite of the reciprocal of the slope of the green line. The slope of the green line can be found using the slope formula:

$m = \frac{y_{2}- y_{1}}{x_{2}- x_{1}} = \frac{10-0}{0-30} = -\frac{1}{3}$

The opposite of the reciprocal of $-\frac{1}{3}$ is 3, and this is the slope of the blue line.

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Example Question #1477 : Concepts

A line segment on the coordinate plane has endpoints (a-5,-b) and (b+8, a-4) . In terms of and , as applicable, give the -coordinate of its midpoint.

Possible Answers:

a - b - 4

a + b + 3

$\frac{a + b + 3}{2}$

$\frac{a - b - 4}{2}$

$\frac{a - b - 13}{2}$

Correct answer:

$\frac{a + b + 3}{2}$

Explanation:

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$x= \frac{(a-5)+(b+8)}{2} = \frac{a+b-5+8}{2} = \frac{a+b+3}{2}$ .

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Example Question #1478 : Concepts

A line segment on the coordinate plane has endpoints (a-5,-b) and (b+8, a-4) . In terms of and , as applicable, give the -coordinate of its midpoint.

Possible Answers:

a + b + 3

a - b - 4

$\frac{a - b - 4}{2}$

$\frac{a + b + 3}{2}$

$\frac{a + b - 4}{2}$

Correct answer:

$\frac{a - b - 4}{2}$

Explanation:

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$y= \frac{(a-4)+(-b)}{2} = \frac{a-b-4}{2}$ .

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1471 : Concepts

Example Question #11 : Geometry

Example Question #181 : Coordinate Geometry

Example Question #1472 : Concepts

Example Question #1473 : Concepts

Example Question #1474 : Concepts

Example Question #1475 : Concepts

Example Question #1476 : Concepts

Example Question #1477 : Concepts

Example Question #1478 : Concepts

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