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HSPT Math : HSPT Mathematics

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Example Questions

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Example Question #2 : How To Find X Or Y Intercept

Give the -intercept, if there is one, of the graph of the equation

$y = 3(x-2)^{2} + 4 (x-7)$ .

Possible Answers:

The graph does not have a -intercept.

(0, 8)

(0, -42)

(0, -16)

(0, -64)

Correct answer:

(0, -16)

Explanation:

The -intercept is the point at which the graph crosses the -axis; at this point, the -coordinate is 0, so substitute for in the equation:

$y = 3(x-2)^{2} + 4 (x-7)$

$y = 3(0-2)^{2} + 4 (0-7)$

$y = 3( -2)^{2} + 4 ( -7)$

$y = 3 \cdot 4 + 4 ( -7)$

y = 12+ 4 ( -7)

y = 12+ (-28)

y = -16

The -intercept is the point (0, -16) .

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Example Question #286 : Geometry

Give the slope of the line that passes through (5,3) and (-1, 5) .

Possible Answers:

$\frac{4}{3}$

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

Use the slope formula, substituting $x_{1}= 5, y_{1}=3,x_{2}= -1, y_{2}=5$ :

$m =\frac{ y_{2}- y_{1} }{x_{2} - x_{1}}=\frac{ 5-3 }{-1-5} = \frac{ 2 }{-6} =-\frac{1 }{3}$

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Example Question #281 : Geometry

What is the slope of the line that passes through (4,4) and (8,8) ?

Possible Answers:

2.5

1.5

0.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-4}{8-4}=\frac{4}{4}=1$

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Example Question #282 : Geometry

What is the slope of the line that passes through (4,7) and (-3,-7) ?

Possible Answers:

3.5

1.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-7-7}{-3-4}=\frac{-14}{-7}=2$

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Example Question #2081 : Hspt Mathematics

What is the slope given the points (3,6) and (-4,5) ?

Possible Answers:

$\frac{1}{7}$

$-\frac{1}{7}$

Correct answer:

$\frac{1}{7}$

Explanation:

Write the slope equation, substitute the point values, and solve for the slope.

$m=\frac{y_2-y_1}{x_2-x_1}= \frac{5-6}{-4-3}= \frac{-1}{-7}= \frac{1}{7}$

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Example Question #302 : Geometry

A point (2,-4) is shifted $\textup{3 units}$ to the left and $\textup{5 units}$ down. What is the new point?

Possible Answers:

(5,9)

(1,-9)

(-1,-9)

(-1,1)

(3,5)

Correct answer:

(-1,-9)

Explanation:

A point is defined as (x,y) . If the point is shifted left or right, the value will be added or subtracted. If the point is shifted up or down, then the value will be added or subtracted.

3 units to the left is: x=2-3 =-1

5 units down is: y= -4-5 =-9

The new point is: (-1,-9)

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Example Question #303 : Geometry

Shift (-1,-1) up $\textup{3 units}$ and left $\textup{3 units}$ . State the new point.

Possible Answers:

(-3,-2)

(2,-4)

(3,2)

(3,-4)

(-4,2)

Correct answer:

(-4,2)

Explanation:

The movement of a point left and right will change the x-value of the point, as movement up and down will change the y-value of the point.

Three units up is adding three to the y-value.

(-1,-1+3) = (-1,2)

Left three units is subtracting three from the x-value.

(-1-3,2) = (-4,2)

The point is: (-4,2)

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Example Question #2082 : Hspt Mathematics

Begin at the point (3, -2) on the coordinate plane and move six units to the left. Where are you now?

Possible Answers:

(9, -2)

(3, 4)

(3, -8)

(-3, -2)

Correct answer:

(-3, -2)

Explanation:

Moving six units to the left changes the -coordinate of the point by subtracting six from it, while preserving the -coordinate. The ordered pair of the new location is (3-6, -2) , or (-3, -2) .

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Example Question #2083 : Hspt Mathematics

Begin at the point (1, - 5) on the coordinate plane and move four units to the right. Next, move six units up. Where are you now?

Possible Answers:

(7, -1)

(-5, -9)

(-3, -11)

(5, 1)

Correct answer:

(5, 1)

Explanation:

Moving four units to the right increases the -coordinate by 4; moving six units up increases the -coordinate by 6. The current location is

(1+4, - 5+6) , or (5, 1) .

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Example Question #311 : Geometry

On the coordinate plane, how do you get from (-3, 4) to (7, 2) ?

Possible Answers:

Move left ten units and up two units

Move down ten units and left two units

Move right ten units and down two units

Move up ten units and right two units

Correct answer:

Move right ten units and down two units

Explanation:

The -coordinate changes by 7 - (-3) = 10 units; therefore, you must move ten units in a positive horizontal direction - right.

The -coordinate changes by 2 - 4 = -2 units; therefore, you must move two units in a negative vertical direction - down.

The correct response is to move right ten units and down two units.

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #2 : How To Find X Or Y Intercept

Example Question #286 : Geometry

Example Question #281 : Geometry

Example Question #282 : Geometry

Example Question #2081 : Hspt Mathematics

Example Question #302 : Geometry

Example Question #303 : Geometry

Example Question #2082 : Hspt Mathematics

Example Question #2083 : Hspt Mathematics

Example Question #311 : Geometry

All HSPT Math Resources

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