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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #141 : Coordinate Geometry

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

Possible Answers:

$\dpi{100} \small y=2x-3$

$\dpi{100} \small y=-4x+6$

$\dpi{100} \small y=4x+6$

$\dpi{100} \small y=-2x+3$

$\dpi{100} \small y=4x-6$

Correct answer:

$\dpi{100} \small y=4x-6$

Explanation:

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

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Example Question #1441 : Gre Quantitative Reasoning

A line is defined by the following equation:

7x+28y=84

What is the slope of that line?

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

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Example Question #101 : Algebra

If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?

Possible Answers:

$y=-\frac{1}{8}x+14.375$

$y=\frac{1}{8}x+14.375$

y=-8x+38

$y=-\frac{1}{8}x+13.625$

y=-8x-38

Correct answer:

$y=-\frac{1}{8}x+14.375$

Explanation:

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 – 14) / (–5 –3)

= (1 )/( –8)

=–1/8

y = –(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = –(1/8)3 + b

14 = –3/8 + b

b = 14 + (3/8)

b = 14.375

y = –(1/8)x + 14.375

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Example Question #61 : Geometry

What is the equation of a line that passes through coordinates $\dpi{100} \small (2,6)$ and $\dpi{100} \small (3,5)$ ?

Possible Answers:

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=3x+2$

$\dpi{100} \small y=x+7$

$\dpi{100} \small y=-x+8$

$\dpi{100} \small y=2x-4$

Correct answer:

$\dpi{100} \small y=-x+8$

Explanation:

Our first step will be to determing the slope of the line that connects the given points.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be . Using slope-intercept form, our equation will be y=(-1)x+b . Use one of the give points in this equation to solve for the y-intercept. We will use $\dpi{100} \small (2,6)$ .

6=(-1)(2)+b

6=-2+b

8=b

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

y=(-1)x+8

y=-x+8

This is our final answer.

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

Which of the following equations does NOT represent a line?

Possible Answers:

x+y=10

x-y=10

x^2+y=10

5y=10

x=10

Correct answer:

x^2+y=10

Explanation:

The answer is x^2+y=10 .

A line can only be represented in the form x=z or y=mx+b , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

x^2+y=10 represents a parabola, not a line. Lines will never contain an x^2 term.

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Example Question #101 : Coordinate Plane

Let y = 3x – 6.

At what point does the line above intersect the following:

$2x =\frac{2}{3}y+4$

Possible Answers:

(–5,6)

(–3,–3)

(0,–1)

They intersect at all points

They do not intersect

Correct answer:

They intersect at all points

Explanation:

If we rearrange the second equation it is the same as the first equation. They are the same line.

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Example Question #2 : Lines

A line has a slope of and passes through the point (8, 1) . Find the equation of the line.

Possible Answers:

y=15x+2

y=2x+1

y=2x-15

y=2x-10

Correct answer:

y=2x-15

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

y=mx+b , where is the slope of the line and is its -intercept.

Plug the given conditions into the equation to find the -intercept.

1=2(8)+b

Multiply:

b+16=1

Subtract from each side of the equation:

b=-15

Now that you have solved for , you can write out the full equation of the line:

y=2x-15

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Example Question #62 : Geometry

Find the equation of a line that has a slope of and passes through the points (-2, 2) .

Possible Answers:

y=2x-2

y=2x+2

y=-2x+2

y=-2x-2

Correct answer:

y=-2x-2

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

y=mx+b , where is the slope of the line and is its -intercept.

Since the problem gives us the slope of the line (m) , we just need to use the point that is given to us to find the -intercept. Plug in known values for and taken from the given point into the y=mx+b equation to find the -intercept:

2=-2(-2)+b

Multiply:

b+4=2

Subtract from each side of the equation:

b=-2

Now that you've solved for , you can plug the given slope (m) and the -intercept (b) into the slope-intercept form of the equation of a line to figure out the answer:

y=-2x-2

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Example Question #63 : Geometry

Find the equation of the line that has a slope of and passes through the point (-5, 4) .

Possible Answers:

y=-3x-3

y=-3x-9

y=-3x+11

y=-3x-11

Correct answer:

y=-3x-11

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

y=mx+b , where is the slope of the line and is its -intercept.

4=-3(-5)+b

Multiply:

4=15+b

Subtract from each side of the equation:

b=-11

Now, we can write the final equation by plugging in the given slope (m) and the -intercept (b) :

y=-3x-11

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Example Question #64 : Geometry

Find the equation of the line that has a slope of and passes through the point (-1, -1) .

Possible Answers:

y=4x-9

y=4x+3

y=4x-3

y=4x+8

Correct answer:

y=4x+3

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

y=mx+b , where is the slope of the line and is its -intercept.

-1=4(-1)+b

Multiply:

-1=-4+b

Add to each side of the equation:

b=3

Now, we can write the final equation by plugging in the given slope (m) and the -intercept (b) :

y=4x+3

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #141 : Coordinate Geometry

Example Question #1441 : Gre Quantitative Reasoning

Example Question #101 : Algebra

Example Question #61 : Geometry

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

Example Question #101 : Coordinate Plane

Example Question #2 : Lines

Example Question #62 : Geometry

Example Question #63 : Geometry

Example Question #64 : Geometry

All SSAT Upper Level Math Resources

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