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SSAT Upper Level Math : Coordinate Geometry

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 #16 : How To Graph Complex Numbers

Define an operation $\wedge$ as follows:

For all complex numbers a,b ,

$a \wedge b = a \div (b+ 3)$

Evaluate $7i \wedge 5i$

Possible Answers:

$-\frac{ 35 }{16} + \frac{ 21}{16} i$

$\frac{ 35 }{34}-\frac{ 21}{34} i$

$\frac{ 35 }{16} - \frac{ 21}{16} i$

$\frac{ 35 }{34} + \frac{ 21}{34} i$

$-\frac{ 35 }{16} - \frac{ 21}{16} i$

Correct answer:

$\frac{ 35 }{34} + \frac{ 21}{34} i$

Explanation:

$a \wedge b = a \div (b+ 3) = \frac{a}{b+3}$

$7i \wedge 5i = \frac{7i }{5i+3} = \frac{7i }{3+ 5i}$

Multiply both numerator and denominator by the conjugate of the denominator, 3-5i , to rationalize the denominator:

$7i \wedge 5i = \frac{7i (3-5i)}{(3+ 5i)(3-5i)}$

$= \frac{7i \cdot 3-7i \cdot 5i}{3^{2}+ 5^{2}}$

$= \frac{21i -35 \cdot i^{2}}{9+25}$

$= \frac{21i-35 (-1)}{34}$

$= \frac{21i+35}{34}$

$= \frac{ 35+21i}{34}$

$= \frac{ 35 }{34} + \frac{ 21}{34} i$

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Example Question #17 : How To Graph Complex Numbers

Subtract 7 - 9i from its complex conjugate. What is the result?

Possible Answers:

18i

2 +16i

2 - 2i

Correct answer:

18i

Explanation:

The complex conjugate of a complex number a - bi is a + bi , so the complex conjugate of 7 - 9i is 7 + 9i . Subtract the former from the latter:

$\left ( 7+9i\right ) - \left ( 7-9i\right ) = 7 + 9i - 7 + 9i = 7 - 7 +9i + 9i = 18i$

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Example Question #91 : Graphing

Give the product of 5+ 4 i and its complex conjugate.

Possible Answers:

25-16i

16+25i

25+16i

16 -25i

The correct answer is not given among the other responses.

Correct answer:

The correct answer is not given among the other responses.

Explanation:

The product of a complex number a + bi and its conjugate a - bi is

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

which will always be a real number. Therefore, all four given choices, all of which are imaginary, can be immediately eliminated. The correct response is that the correct answer is not given among the other responses.

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Example Question #631 : Ssat Upper Level Quantitative (Math)

Add 4+ 7i to its complex conjugate. What is the result?

Possible Answers:

11 + 11i

14i

11-3i

Correct answer:

Explanation:

The complex conjugate of a complex number a + bi is a - bi , so 4+7i has 4-7i as its complex conjugate; the sum of the two numbers is

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

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Example Question #20 : How To Graph Complex Numbers

Multiply the complex conjugate of 3 + 7i by . What is the result?

Possible Answers:

28 + 12i

-12 + 28i

12 - 28 i

-28+12i

12 + 28 i

Correct answer:

28 + 12i

Explanation:

The complex conjugate of a complex number a + bi is a - bi , so the complex conjugate of 3 + 7i is 3 - 7i . Multiply this by :

$(3-7i) \cdot 4i = 3 \cdot 4i - 7 i \cdot 4i$

$= 12i - 7 \cdot 4 \cdot i \cdot i$

$= 12i -28 \cdot (-1)$

= 12i + 28

= 28 + 12i

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Example Question #21 : How To Graph Complex Numbers

Multiply the complex conjugate of 8 by 5 i . What is the result?

Possible Answers:

None of the other responses gives the correct product.

40i

-40i

Correct answer:

40i

Explanation:

The complex conjugate of a complex number a + bi is a - bi . Since 8=8+0i , its complex conjugate is 8-0i = 8 itself. Multiply this by :

$8 \cdot 5i = 40 i$

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Example Question #92 : Graphing

Multiply the complex conjugate of by 3 i . What is the result?

Possible Answers:

-21i

None of the other responses gives the correct product.

21i

Correct answer:

Explanation:

The complex conjugate of a complex number a + bi is a - bi . Since 7i = 0+7i , its complex conjugate is 0-7i = -7i .

Multiply this by :

Recall that by definition i^2=-1 .

$-7i \cdot 3i = -7 \cdot 3 \cdot i \cdot i = -21 (-1) = 21$

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Example Question #351 : Coordinate Geometry

Multiply the following complex numbers:

$\left (5 + i \right )\left (5 + 2i \right )$

Possible Answers:

27 + 5i

23 + 15i

27 - 15i

23 + 5i

23 - 15i

Correct answer:

23 + 15i

Explanation:

FOIL the product out:

$\left (5 + i \right )\left (5 + 2i \right )$

To FOIL multiply the first terms from each binomial together, multiply the outer terms of both terms together, multiply the inner terms from both binomials together, and finally multiply the last terms from each binomial together.

$=5 \cdot 5 + 5 \cdot 2i + 5 \cdot i + i\cdot 2i$

$=25 + 10i + 5 i + 2i^{2}$

Recall that i is an imaginary number and by definition i^2=-1 . Substituting this into the function is as follows.

=25 + 10i + 5 i + 2 (-1)

=25 -2 + 10i + 5 i

=23 + 15i

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Example Question #1 : How To Graph Inverse Variation

Give the equation of the vertical asymptote of the graph of the equation $y = \frac{7}{9x+4}$ .

Possible Answers:

$x= \frac{7}{9}$

$x= - \frac{7}{4}$

x = 9

$x= -\frac{4}{9}$

x=-4

Correct answer:

$x= -\frac{4}{9}$

Explanation:

The vertical asymptote of an inverse variation function is the vertical line of the equation x = a , where is the value for which the expression is not defined. To find , set the denominator to and solve for :

9x+4 = 0

9x= -4

$x= -\frac{4}{9}$ is the equation of the asymptote.

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Example Question #2 : How To Graph Inverse Variation

Give the -intercept of the graph of the equation $y = \frac{5}{2x-7}$ .

Possible Answers:

$\left ( \frac{7}{2}, 0 \right )$

(7,0)

The graph has no -intercept.

(5,0)

$\left ( \frac{5}{2}, 0 \right )$

Correct answer:

The graph has no -intercept.

Explanation:

The -intercept of the graph of an equation is the point at which it intersects the -axis. Its -coordinate is 0, so set y = 0 and solve for :

$y = \frac{5}{2x-7}$

$0= \frac{5}{2x-7}$

$0\cdot (2x-7) = \frac{5}{2x-7} \cdot (2x-7)$

0 = 5

This is identically false, so the graph has no -intercept.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Coordinate Geometry

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #16 : How To Graph Complex Numbers

Example Question #17 : How To Graph Complex Numbers

Example Question #91 : Graphing

Example Question #631 : Ssat Upper Level Quantitative (Math)

Example Question #20 : How To Graph Complex Numbers

Example Question #21 : How To Graph Complex Numbers

Example Question #92 : Graphing

Example Question #351 : Coordinate Geometry

Example Question #1 : How To Graph Inverse Variation

Example Question #2 : How To Graph Inverse Variation

All SSAT Upper Level Math Resources

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