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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1175 : Concepts

is a number less than 24.

Which of the following gives a solution of the equation

| x + 15 | + C = 24

in terms of ?

Possible Answers:

x = C -9

x = C -39

x = C +9

x = C+39

Correct answer:

x = C -39

Explanation:

| x + 15 | + C = 24

| x + 15 | + C - C = 24 - C

| x + 15 | = 24 - C

C < 24 , so 24 - C is positive, so solutions exist; either

x + 15 = 24 - C or x + 15 = - ( 24 - C) .

We examine both cases.

x + 15 = 24 - C

x + 15 - 15= 24 - C - 15

x = 9 - C = -C + 9

x + 15 = - ( 24 - C)

x + 15 = C -24

x + 15 - 15 = C -24 - 15

x = C -39

Only x = C -39 is among the choices.

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Example Question #1171 : Concepts

x+y = -17

y+z = -34

x+z = 45

Evaluate .

Possible Answers:

insufficient information is given to determine the value of

y = -48

y = 14

y = 31

Correct answer:

y = -48

Explanation:

(x+y) + (y+z)+ (x+z)= -17 + (-34)+ 45

2x+ 2y+2z = - 6

$(2x+ 2y+2z) \div 2 = - 6 \div 2$

x+y+z = -3

(x+y+z )- (x+z ) = -3 - 45

y = -48

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Example Question #1172 : Concepts

Axes 4

In the above diagram, which of the four points is the -intercept of the line of the equation 4x+5y = -40 ?

Possible Answers:

Correct answer:

Explanation:

The -coordinate of the -intercept of the line of an equation can be found by setting y= 0 and solving for :

4x+5y = -40

$4x+5 \cdot 0 = -40$

4x+ 0 = -40

4x= -40

$4x\div 4 = -40 \div 4$

x = -10

The -intercept is the point (-10, 0) , which is ten units left of the origin. This is the point marked in the diagram.

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Example Question #1173 : Concepts

Axes 4

Refer to the above diagram. Which line has the same slope of the line of the equation 4x+6y =17 ?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation in slope-intercept form y = mx+b as follows:

4x+6y =17

4x+6y - 4x =17 - 4x

6y =- 4x+ 17

$\frac{1}{6} \cdot 6y =\frac{1}{6} \cdot (- 4x+ 17)$

$y = -\frac{4}{6}x+ \frac{17}{6}$

$y = -\frac{2}{3}x+ \frac{17}{6}$

The slope of this line is the coefficient of , which is $-\frac{2}{3}$ .

The slope of a line is its ratio of rise to run. The slopes of the four lines in the diagram are given below, with their justification shown.

Axes 4

Of the four lines, the line marked also has slope $-\frac{2}{3}$ .

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Example Question #561 : Algebra

Axes 4

Refer to the above diagram. Which line is perpendicular to the line of the equation 8x - 12y = 71 ?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation of the perpendicular line in slope-intercept form y = mx+b as follows:

8x - 12y = 71

8x - 12y- 8x = 71 - 8x

- 12y =- 8x+ 71

$-\frac{1}{12} \cdot (- 12y )= -\frac{1}{12} \cdot (- 8x+ 71)$

$y = \frac{8}{12}x - \frac{71}{12}$

$y = \frac{2}{3}x - \frac{71}{12}$

The slope of the line is the coefficient of , which is $\frac{2}{3}$ . The slope of a line perpendicular to this is the opposite of the reciprocal of $\frac{2}{3}$ , which is $-\frac{3}{2}$ .

The slope of a line is its ratio of rise to run. The slopes of the four lines in the diagram are given below, with their justification shown.

Axes 4

Of the four lines, the line marked has slope $-\frac{3}{2}$ .

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Example Question #562 : Algebra

Axes 4

Refer to the above diagram. Which of the above points is on the line of the equation y = 2x+ 7 ?

Possible Answers:

Correct answer:

Explanation:

All four points on the diagram have -coordinate , so set x= -1 in the equation to find the corresponding -coordinate:

y = 2x+ 7

y = 2(-1)+ 7 = -2 + 7 = 5

The correct point is the one with coordinates (-1, 5) . This point is one unit left and five units up from the orgin - the point at this location is .

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Example Question #1181 : Concepts

Axes 4

Refer to the above diagram. Which line is parallel to the line of the equation 8x - 12y = 55 ?

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation of the parallel line in slope-intercept form y = mx+b as follows:

8x - 12y = 55

8x - 12y- 8x = 55 - 8x

- 12y =- 8x+ 55

$-\frac{1}{12} \cdot (- 12y )= -\frac{1}{12} \cdot (- 8x+ 55)$

$y = \frac{8}{12}x - \frac{55}{12}$

$y = \frac{2}{3}x - \frac{55}{12}$

The slope of the line is the coefficient of , which is $\frac{2}{3}$ . The slope of a line parallel to this is also $\frac{2}{3}$ .

The slope of a line is its ratio of rise to run. The slopes of the four lines in the diagram are given below, with their justification shown.

Axes 4

Of the four lines, the line marked also has slope $\frac{2}{3}$ .

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Example Question #1182 : Concepts

Solve for :

$10=\frac{x}{3}+5$

Possible Answers:

x=10

x=30

x=15

x=5

Correct answer:

x=15

Explanation:

To get by itself, you must first get rid of the constant.

To undo the positive , you must subtract it from both sides leaving us with,

$5=\frac{x}{3}$ .

Then you must multiple both sides by and that means,

x=5*3=15 .

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Example Question #1771 : Hspt Mathematics

What is the area of a triangle with a base of 5 and a height of 20?

Possible Answers:

100

Correct answer:

Explanation:

When searching for the area of a triangle we are looking for the amount of the space enclosed by the triangle.

The equation for area of a triangle is $\frac{1}{2}(base)(height)= Area\: of\: Triangle$

Plug in the numbers for base and height into the equation yielding $\frac{1}{2}(5)(20)= Area\: of\: Triangle$

Then multiply the numbers together to arrive at the answer which is .

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Example Question #1772 : Hspt Mathematics

A trapezoid has height 32 inches and bases 25 inches and 55 inches. What is its area?

Possible Answers:

$800\; \textrm{in}^{2}$

$1,920\; \textrm{in}^{2}$

$1,760\; \textrm{in}^{2}$

$1,280 \; \textrm{in}^{2}$

$1,375\; \textrm{in}^{2}$

Correct answer:

$1,280 \; \textrm{in}^{2}$

Explanation:

Use the following formula, with B = 55,b = 25,h=32 :

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (55+25) \cdot 32 = 1,280$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1175 : Concepts

Example Question #1171 : Concepts

Example Question #1172 : Concepts

Example Question #1173 : Concepts

Example Question #561 : Algebra

Example Question #562 : Algebra

Example Question #1181 : Concepts

Example Question #1182 : Concepts

Example Question #1771 : Hspt Mathematics

Example Question #1772 : Hspt Mathematics

All HSPT Math Resources

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