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SSAT Upper Level Math : Geometry

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 #51 : Geometry

Find the circumference of a circle with a diameter of 2.

Possible Answers:

$\Pi$

$2\Pi$

$4\Pi$

Correct answer:

$2\Pi$

Explanation:

There are two possible formulas for finding the circumference of a circle. They are as follows:

$C=2\Pi \cdot r$

And:

$C=\Pi \cdot d$

Where C is circumference, r is radius, and d is diameter.

For this problem, we are given the diameter is 2, meaning we can plug our numbers into the second equation. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$C=\Pi \cdot 2= 2\Pi$

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Example Question #52 : Geometry

Find the circumference of a circle with a radius of 12.

Possible Answers:

$24\Pi$

$12\Pi$

$6\Pi$

$144\Pi$

Correct answer:

$24\Pi$

Explanation:

There are two possible formulas for finding the circumference of a circle. They are as follows:

$C=2\Pi \cdot r$

And:

$C=\Pi \cdot d$

Where C is circumference, r is radius, and d is diameter.

For this problem, we are given the radius is 12, meaning we can plug our numbers into the first equation. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$C=\Pi \cdot 2 \cdot 12= 24\Pi$

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Example Question #53 : Geometry

Find the circumference of a circle with a radius of 13.

Possible Answers:

$13\Pi$

$26\Pi$

$169\Pi$

$39\Pi$

Correct answer:

$26\Pi$

Explanation:

There are two possible formulas for finding the circumference of a circle. They are as follows:

$C=2\Pi \cdot r$

And:

$C=\Pi \cdot d$

Where C is circumference, r is radius, and d is diameter.

For this problem, we are given the radius is 13, meaning we can plug our numbers into the first equation. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$C=\Pi \cdot 2 \cdot 13= 26\Pi$

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Example Question #54 : Geometry

Find the circumference of a circle with a radius of 27.

Possible Answers:

$27\Pi$

$54\Pi$

$12\Pi$

$9\Pi$

Correct answer:

$54\Pi$

Explanation:

There are two possible formulas for finding the circumference of a circle. They are as follows:

$C=2\Pi \cdot r$

And:

$C=\Pi \cdot d$

Where C is circumference, r is radius, and d is diameter.

For this problem, we are given the radius is 27, meaning we can plug our numbers into the first equation. Since pi is an irrational constant, it is okay to leave the answer in terms of pi.

$C=\Pi \cdot 2 \cdot 27= 54\Pi$

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Example Question #525 : Sat Mathematics

Given the graph of the line below, find the equation of the line.

Act_math_160_04

Possible Answers:

$y=\frac{10}{3}x-4$

y=-5x-4

y=x-4

y=-x

Correct answer:

$y=\frac{10}{3}x-4$

Explanation:

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

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Example Question #2 : Coordinate Geometry

Which line passes through the points (0, 6) and (4, 0)?

Possible Answers:

y = 2/3x –6

y = 2/3 + 5

y = 1/5x + 3

y = –3/2 – 3

y = –3/2x + 6

Correct answer:

y = –3/2x + 6

Explanation:

P₁ (0, 6) and P₂ (4, 0)

First, calculate the slope: m = rise ÷ run = (y₂ – y₁)/(x₂– x₁), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula:

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

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Example Question #3 : Coordinate Geometry

What line goes through the points (1, 3) and (3, 6)?

Possible Answers:

–3x + 2y = 3

2x – 3y = 5

4x – 5y = 4

–2x + 2y = 3

3x + 5y = 2

Correct answer:

–3x + 2y = 3

Explanation:

If P₁(1, 3) and P₂(3, 6), then calculate the slope by m = rise/run = (y₂ – y₁)/(x₂ – x₁) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

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Example Question #61 : Lines

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

Possible Answers:

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

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

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

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

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

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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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 #51 : Geometry

Example Question #52 : Geometry

Example Question #53 : Geometry

Example Question #54 : Geometry

Example Question #525 : Sat Mathematics

Example Question #2 : Coordinate Geometry

Example Question #3 : Coordinate Geometry

Example Question #61 : Lines

Example Question #1441 : Gre Quantitative Reasoning

Example Question #101 : Algebra

All SSAT Upper Level Math Resources

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