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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

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

Example Questions

Example Question #1 : Graphing Functions

Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. Give the equation of that line in slope-intercept form.

Possible Answers:

$y = \frac{1}{2}x + 8$

$y = - \frac{1}{2}x + 8$

$y = \frac{1}{2}x + 4$

$y = \frac{1}{2}x - 4$

$y = - \frac{1}{2}x + 4$

Correct answer:

$y = - \frac{1}{2}x + 8$

Explanation:

First, we need to find the slope of the above line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be $m = -\frac{1}{2}$ . Since we want this line to have the same -intercept as the first line, which is the point (0,8) , we can substitute $m = -\frac{1}{2}$ and b = 8 in the slope-intercept form:

y = mx + b

$y = - \frac{1}{2}x + 8$

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Example Question #2 : Graphing Functions

Axes

Refer to the above diagram. If the red line passes through the point $\left ( N, 4\right )$ , what is the value of ?

Possible Answers:

N = -5

$N = -7\frac{1}{3}$

$N = -3\frac{1}{3}$

$N = -4\frac{2}{3}$

$N= -1\frac{1}{3}$

Correct answer:

$N = -4\frac{2}{3}$

Explanation:

One way to answer this is to first find the equation of the line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$ :

$m = \frac{18-0}{0-(-6)} = \frac{18}{6} = 3$

The line has slope 3 and -intercept (0,18) , so we can substitute m = 3, b = 18 in the slope-intercept form:

y = mx+b

y = 3x+18

Now substitute 4 for and for and solve for :

4= 3N+18

-14 =3N

$N = -\frac{14}{3}= -4\frac{2}{3}$

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Example Question #1 : How To Graph Complex Numbers

Multiply:

$\left (7 - 2i \right )\left (7 - 3i \right )$

Possible Answers:

55 +7i

43 -35i

49 + 6i

43 -7i

55 -35i

Correct answer:

43 -35i

Explanation:

FOIL the product out:

$\left (7 - 2i \right )\left (7 - 3i \right )$

$= 7 \cdot 7 - 7 \cdot 3i - 7 \cdot 2i + 2i \cdot 3i$

$= 49 -21i - 14i + 6 i^{2}$

= 49 -21i - 14i + 6 (-1)

= 49 -6 -21i - 14i

= 43 -35i

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Example Question #2 : How To Graph Complex Numbers

Simplify:

$\left ( 8 - 3i\right ) ^{2}$

Possible Answers:

55 - 48i

73- 48i

55 +48i

Correct answer:

55 - 48i

Explanation:

Use the square of a binomial pattern to multiply this:

$\left ( 8 - 3i\right ) ^{2}$

$= 8 ^{2}- 2 \cdot8\cdot3i + \left ( 3i\right )^{2}$

$= 64- 48i + 3^{2}i^{2}$

= 64- 48i + 9 (-1)

= 64-9 - 48i

= 55 - 48i

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Example Question #3 : How To Graph Complex Numbers

Multiply:

(1.1 + 0.6i )(1.1 - 0.6i )

Possible Answers:

1.21 - 0.36i

1.57 - 1.32i

0.85 + 1.32i

0.85

1.57

Correct answer:

1.57

Explanation:

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

$\left (a + bi \right )\left (a -bi \right ) = a^{2} + b ^{2}$

$\left (1.1 + 0.6i \right )\left (1.1 -0.6 i \right ) = 1.1^{2} + 0.6 ^{2} = 1.21 + 0.36 = 1.57$

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Example Question #4 : How To Graph Complex Numbers

Multiply:

$\left (5 - 3i \right )\left (5 +3i \right )$

Possible Answers:

16 -30i

25 -9i

34 +30i

Correct answer:

Explanation:

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

$\left (a - bi \right )\left (a +bi \right ) = a^{2} + b ^{2}$

$\left (5 - 3i \right )\left (5 +3i \right ) = 5 ^{2} + 3 ^{2}= 25 + 9 = 34$

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Example Question #5 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers a,b ,

$a*b = a ^{5}-b^{3}$

Evaluate $\left (2 i \right )* \left (3i \right )$

Possible Answers:

-27+32i

27 -32i

32 - 27i

59i

Correct answer:

59i

Explanation:

$a*b = a ^{5}-b^{3}$

$\left (2 i \right )* \left (3i \right ) = \left (2 i \right ) ^{5}-\left (3i \right ) ^{3}$

$= 2^{5} i^{5} - 3^{3} i ^{3}$

$= 32\cdot i^{4} \cdot i - 27 \cdot (-i )$

$= 32\cdot 1 \cdot i +27 i$

= 32 i +27 i

= 59 i

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Example Question #5 : How To Graph Complex Numbers

Define an operation as follows:

For all complex numbers a,b ,

a*b = a+3ib

Evaluate (4+7i) * (3-8i)

Possible Answers:

28 +16 i

13+31i

35-35i

13-17i

-20 + 16i

Correct answer:

28 +16 i

Explanation:

a*b = a+3ib

(4+7i) * (3-8i) = (4+7i) + 3i (3-8i)

$= 4+7i + 3i \cdot 3- 3i \cdot 8i$

$= 4+7i + 9i - 24i ^{2}$

= 4+7i + 9i - 24 (-1)

= 4+7i + 9i- (-24)

= 4+7i + 9i +24

= 28 +16i

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Example Question #341 : Coordinate Geometry

Evaluate $(3i)^{-5}$ .

Possible Answers:

$- \frac{1}{243} i$

$\frac{1}{243} i$

-243 i

The expression is undefined.

243i

Correct answer:

$- \frac{1}{243} i$

Explanation:

$(3i)^{-5} = \frac{1}{(3i)^{5} }= \frac{1}{3^{5}i^{5} } = \frac{1}{243 i^{4} \cdot i } = \frac{1}{243 \cdot 1 \cdot i }$

$= \frac{1}{243 i } \cdot = \frac{1\cdot i}{243 i \cdot i } = \frac{i}{243 (-1)} = - \frac{1}{243} i$

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Example Question #8 : How To Graph Complex Numbers

Define an operation $\wedge$ as follows:

For all complex numbers a,b ,

$a \wedge b = a \div (b+ 2i)$

Evaluate $8 \wedge 4$

Possible Answers:

$-\frac{8}{3} + \frac{ 4}{3}i$

$-\frac{8}{5} + \frac{ 4}{5}i$

$\frac{8}{3} - \frac{ 4}{3}i$

$\frac{8}{5} + \frac{ 4}{5}i$

$\frac{8}{5} - \frac{ 4}{5}i$

Correct answer:

$\frac{8}{5} - \frac{ 4}{5}i$

Explanation:

$a \wedge b = a \div (b+ 2i) = \frac{a}{b+2i}$

$8 \wedge 4 = \frac{8}{4+2i}$

Multiply both numerator and denominator by the conjugate of the denominator, 4 - 2i , to rationalize the denominator:

$8 \wedge 4 = \frac{8(4-2i)}{(4+2i)(4-2i)}$

$= \frac{8\cdot 4-8\cdot 2i}{4^{2}+2^{2}}$

$= \frac{32-16i}{16+4}$

$= \frac{32-16i}{20}$

$= \frac{32 }{20} - \frac{ 16}{20}i$

$= \frac{8}{5} -\frac{ 4}{5}i$

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All SSAT Upper Level Math Resources

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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 #1 : Graphing Functions

Example Question #2 : Graphing Functions

Example Question #1 : How To Graph Complex Numbers

Example Question #2 : How To Graph Complex Numbers

Example Question #3 : How To Graph Complex Numbers

Example Question #4 : How To Graph Complex Numbers

Example Question #5 : How To Graph Complex Numbers

Example Question #5 : How To Graph Complex Numbers

Example Question #341 : Coordinate Geometry

Example Question #8 : How To Graph Complex Numbers

All SSAT Upper Level Math Resources

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