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SSAT Upper Level Math : Geometry

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Tangent Lines

Find the slope of a tangent line at point (1,5) if the equation is -2x+3y=6 .

Possible Answers:

$\frac{2}{3}$

$\frac{1}{3}$

$-\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

Rewrite the linear equation in standard form to slope-intercept form, y=mx+b .

-2x+3y=6

3y=2x+6

$y=\frac{2}{3}x+2$

Since the slope of every point of this line is $\frac{2}{3}$ , the slope of the tangent line at the given point should also be $\frac{2}{3}$ .

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Example Question #1 : Tangent Lines

Find the slope of a tangent line at point (5,8) if the equation of the function is y=x^4 .

Possible Answers:

500

225

625

400

Correct answer:

500

Explanation:

To determine the slope of the function, y=x^4 , use the power rule to find the derivative function.

y=x^4

y'=4x^(^4^-^1^)=4x^3

The slope at every point of the function y=x^4 has a slope of 4x^3 . To find the slope at the given point, substitute the x-value of the given point, (5,8) , into the derivative function to find the slope.

y'=4x^3=4(5)^3=4(125)=500

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Example Question #1 : How To Find The Equation Of A Tangent Line

Circle A is centered about the origin and has a radius of 5. What is the equation of the line that is tangent to Circle A at the point (–3,4)?

Possible Answers:

–3x + 4y = 1

3x – 4y = –1

3x – 4y = –25

3x + 4y = 7

Correct answer:

3x – 4y = –25

Explanation:

The line must be perpendicular to the radius at the point (–3,4). The slope of the radius is given by Actmath_7_113_q7

The radius has endpoints (–3,4) and the center of the circle (0,0), so its slope is –4/3.

The slope of the tangent line must be perpendicular to the slope of the radius, so the slope of the line is ¾.

The equation of the line is y – 4 = (3/4)(x – (–3))

Rearranging gives us: 3x – 4y = -25

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Example Question #1 : How To Find The Equation Of A Tangent Line

Find the equation of a tangent line at point (2,3) if the function is y=-3x+1 .

Possible Answers:

y=-3x+6

y=-3x+3

y=-3x+9

y=-3x+2

y=-3x-3

Correct answer:

y=-3x+9

Explanation:

To find the slope of the tangent line, it is necessary to determine the slope of the function.

The function y=-3x+1 is already in the slope-intercept form, y=mx+b , and m=-3 .

Substitute the slope and the given point (2,3) into the slope-intercept equation.

3=(-3)(2)+b

3=-6+b

b=9

Substitute the known slope and the y-intercept to the slope-intercept form.

y=-3x+9

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Example Question #461 : Ssat Upper Level Quantitative (Math)

Function

Give the equation graphed in the above figure.

Possible Answers:

y = |x|+3

y = | x-3|

y = | x+3|

$y = \left | \frac{1}{3}x \right |$

y = |3x|

Correct answer:

y = |3x|

Explanation:

The graph below is the graph of the absolute value function f(x)= |x| , which pairs each -coordinate with its absolute value.

Absolute value graph

The given graph is the same as the above graph, except that each -coordinate is paired with the -coordinate three times that with which it is paired in the above graph. Therefore, the equation graphed is

$y = 3 \cdot |x|$

y = |3x|

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Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation $y= x^{2}+ 2x - 17$ is shifted right three units on the coordinate plane, what will be the equation of the resulting graph?

Possible Answers:

$y= x^{2}+8x -2$

$y= x^{2}-4x -14$

$y= 2 x^{2}+ 4x - 34$

$y= x^{2}+ 2x - 20$

$y= x^{2}+ 2x - 14$

Correct answer:

$y= x^{2}-4x -14$

Explanation:

The graph of a function y = f(x) shifted right three units is the graph of y = f(x-3) . In this graph, $f(x)= x^{2}+ 2x - 17$ , so the graph formed by the transformation is

$f(x-3)= \left (x-3 \right ) ^{2}+ 2 (x-3) - 17$

$f(x-3)= x^{2}-6x+9+ 2x-6 - 17$

$f(x-3)= x^{2}-6x+ 2x+9-6 - 17$

$f(x-3)= x^{2}-4x -14$

The correct equation is $y= x^{2}-4x -14$ .

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Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation y = 2x^2 + 5x - 17 is reflected about the origin, what will the equation of the resulting graph be?

Possible Answers:

y = 2x^2 +5x +17

y =- 2x^2 -5x +17

y =- 2x^2 +5x +17

y = 2x^2 - 5x - 17

y = 2x^2+ 5x-17

Correct answer:

y =- 2x^2 +5x +17

Explanation:

The reflection of the graph of the equation y = f(x) about the origin is the graph of the equation -y = f(-x) , so replace with and with :

y = 2x^2 + 5x - 17

becomes

- y = 2 (-x) ^2 + 5 (-x) - 17

- y = 2 x^2 -5x - 17

-(-y) = - (2 x^2 -5x - 17)

y= - 2 x^2 +5x +17

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Example Question #2 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation y = 2x^2 + 5x - 17 is reflected about the -axis, what will the equation of the resulting graph be?

Possible Answers:

y = 2x^2+ 5x-17

y =- 2x^2 -5x +17

y =- 2x^2 +5x +17

y = 2x^2 +5x +17

y = 2x^2 - 5x - 17

Correct answer:

y =- 2x^2 -5x +17

Explanation:

The reflection of the graph of the equation y = f(x) about the -axis is the graph of the equation -y = f(x) , so replace with :

y = 2x^2 + 5x - 17

becomes

-y = 2x^2 + 5x - 17

$-(-y) = - (2x^{2 }+ 5x - 17)$

y =- 2x^2 -5x +17

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Example Question #3 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation y = 2x^2 + 5x - 17 is reflected about the -axis, what will the equation of the resulting graph be?

Possible Answers:

y =- 2x^2 +5x +17

y = 2x^2 +5x +17

y = 2x^2 - 5x - 17

y = 2x^2+ 5x-17

y =- 2x^2 -5x +17

Correct answer:

y = 2x^2 - 5x - 17

Explanation:

The reflection of the graph of the equation y = f(x) about the -axis is the graph of the equation y = f(-x) , so replace with :

y = 2x^2 + 5x - 17

becomes

y = 2 (-x) ^2 + 5 (-x) - 17

y = 2 x^2 -5x - 17

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Example Question #4 : How To Find Transformation For An Analytic Geometry Equation

If the graph of the equation y = |x+3| - 5 is reflected about the origin, what will the equation of the resulting graph be?

Possible Answers:

y =- |x+3| - 5

y =- |x-3| - 5

y=- |x-3| +5

None of the other responses gives a correct answer.

y =- |x+3| + 5

Correct answer:

y=- |x-3| +5

Explanation:

The reflection of the graph of the equation y = f(x) about the origin is the graph of the equation -y = f(-x) , so replace with and with :

y = |x+3| - 5

becomes

-y = |-x+3| - 5

-(-y) =-( |-x+3| - 5)

y=- |-x+3| +5

The absolute values of two expressions that are each other's opposites are equal, so |-x+3| is equivalent to |x-3| . The expression can be rewritten as

y=- |x-3| +5 .

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Tangent Lines

Example Question #1 : Tangent Lines

Example Question #1 : How To Find The Equation Of A Tangent Line

Example Question #1 : How To Find The Equation Of A Tangent Line

Example Question #461 : Ssat Upper Level Quantitative (Math)

Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

Example Question #2 : How To Find Transformation For An Analytic Geometry Equation

Example Question #3 : How To Find Transformation For An Analytic Geometry Equation

Example Question #4 : How To Find Transformation For An Analytic Geometry Equation

All SSAT Upper Level Math Resources

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