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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

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Example Questions

Example Question #11 : Geometry

Triangle6

Given a height of units and base of units, find the area of the triangle shown above.

Possible Answers:

$22 \text{ square units}$

$15 \text{ square units}$

$30 \text{ square units}$

$7.5 \text{ square units}$

Correct answer:

$15 \text{ square units}$

Explanation:

The area of any triangle is calculated by the formula:

$A = \frac{1}{2}\times base \times height$

Thus, the area of this triangle is:

$A =\frac{1}{2}\times 6 \times 5 = 15 \text{ square units}$

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Example Question #12 : Geometry

Triangle3

Given the above triangle has a base of and hypotenuse of , find the height of the triangle.

Possible Answers:

$3 + \sqrt{6}$

$\sqrt{34}$

Correct answer:

Explanation:

Use the Pythagorean Theorem,

c^2 = a^2 + b^2

where is the hypotenuse, is the base, and is the height.

Rearranging to solve for the height, , yields:

b^2 = c^2 - a^2 = 5^2 - 3^2 = 25 - 9 = 16

$b = \sqrt{16} = 4$

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Example Question #201 : Ssat Middle Level Quantitative (Math)

Which of the following points would be located in Quadrant III?

Possible Answers:

(1,3)

(7,-11)

(-2,-7)

(-2,0)

(-4,9)

Correct answer:

(-2,-7)

Explanation:

By definition, a point on the coordinate plane that is in Quadrant III must have both a negative coordinate and a negative coordinate. The only answer choice that satisfies both of these conditions is (-2,-7) .

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Example Question #202 : Ssat Middle Level Quantitative (Math)

In which quadrant or on what axis will you find the point (-5,7) ?

Possible Answers:

The -axis

Quadrant III

Quadrant IV

Quadrant I

Quadrant II

Correct answer:

Quadrant II

Explanation:

The point (-5,7) has a negative coordinate and a positive coordinate. By definition, any point on a coordinate plane with these characteristics is located in Quadrant II.

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Example Question #203 : Ssat Middle Level Quantitative (Math)

In which quadrant or on which axis will you find the point (0,7) ?

Possible Answers:

Quadrant II

The -axis

Quadrant I

Quadrant III

The -axis

Correct answer:

The -axis

Explanation:

The point (0,7) does not move in any direction on the -axis, but does move units up on the -axis. Therefore, the point is located only on the -axis.

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Example Question #204 : Ssat Middle Level Quantitative (Math)

Which of the following points is in Quadrant II on the coordinate plane?

Possible Answers:

(4,5)

(4,-5)

(-4,5)

(-4,0)

(-4,-5)

Correct answer:

(-4,5)

Explanation:

All points in Quadrant II have negative -coordinates and positive -coordinates. The only answer that fulfills these criteria is (-4,5) .

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Example Question #205 : Ssat Middle Level Quantitative (Math)

In which quadrant or on which axis will we find the point (7,0) ?

Possible Answers:

Quadrant II

Quadrant IV

The -axis

Quadrant I

Correct answer:

The -axis

Explanation:

By definition, any point in the coordinate plane that has a non-zero value -coordinate and a zero-value -coordinate is on the -axis.

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Example Question #2 : How To Find The Points On A Coordinate Plane

In which quadrant or on which axis of the coordinate plane will you find the point (6,-9) ?

Possible Answers:

Quadrant IV

Quadrant II

Quadrant I

Quadrant III

The -axis

Correct answer:

Quadrant IV

Explanation:

A point with a positive -coordinate and a negative -coordinate can be found in Quadrant IV.

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Example Question #204 : Ssat Middle Level Quantitative (Math)

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( - 10, -20 \right )$ and $\left ( -20,10 \right )$ . Give the coordinates of the midpoint of the segment.

Possible Answers:

(-5, -15)

(-15, -5)

(-30, -10)

(-10, -30)

Correct answer:

(-15, -5)

Explanation:

The -coordinate of the midpoint can be found by dividing the sum of the -coordinates of the endpoints by 2:

$\left [(-10 ) + (-20) \right ] \div 2 = \left [-(10 + 20) \right ] \div 2 = -30 \div 2 = -15$

The -coordinate of the midpoint is found similarly:

$\left [ (-20)+ 10 \right ] \div 2 = \left [-(20-10) \right ] \div 2 = -10 \div 2 = -5$

The coordinates of the midpoint are (-15, -5) .

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Example Question #2 : How To Find The Points On A Coordinate Plane

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( 4 \frac{1}{3}, - 4 \frac{1}{3}\right )$ and $\left ( 12, 12\right )$ . Give the coordinates of the midpoint of the segment.

Possible Answers:

$\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$

$\left ( 3 \frac{5}{6} , 8 \frac{1}{6} \right )$

$\left ( 7 \frac{2}{3}, 16 \frac{1}{3}\right )$

$\left ( 16 \frac{1}{3}, 7 \frac{2}{3} \right )$

Correct answer:

$\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$

Explanation:

The -coordinate of the midpoint is half the sum of the -coordinates of the endpoints:

$\frac{1}{2} \left ( 4 \frac{1}{3} + 12 \right )$

$= \frac{1}{2} \times 16 \frac{1}{3}$

$= \frac{1}{2} \times \frac{49}{3}$

$= \frac{49}{6}$

$=8 \frac{1}{6}$

The -coordinate of the midpoint is found similarly:

$\frac{1}{2} \left (- 4 \frac{1}{3} + 12 \right )$

$= \frac{1}{2} \left (12 - 4 \frac{1}{3} \right )$

$= \frac{1}{2} \times 7 \frac{2}{3}$

$= \frac{1}{2} \times \frac{23}{3}$

$= \frac{23}{6}$

$= 3 \frac{5}{6}$

The midpoint has coordinates $\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$ .

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All SSAT Middle Level Math Resources

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #11 : Geometry

Example Question #12 : Geometry

Example Question #201 : Ssat Middle Level Quantitative (Math)

Example Question #202 : Ssat Middle Level Quantitative (Math)

Example Question #203 : Ssat Middle Level Quantitative (Math)

Example Question #204 : Ssat Middle Level Quantitative (Math)

Example Question #205 : Ssat Middle Level Quantitative (Math)

Example Question #2 : How To Find The Points On A Coordinate Plane

Example Question #204 : Ssat Middle Level Quantitative (Math)

Example Question #2 : How To Find The Points On A Coordinate Plane

All SSAT Middle Level Math Resources

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