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SSAT Upper Level Math : Algebra

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 #5 : How To Find The Equation Of A Line

Lines

Examine the above diagram. What is x + y ?

Possible Answers:

145

135

125

Correct answer:

125

Explanation:

Use the properties of angle addition:

$\left ( x - 13\right )+ (y + 25) +43= 180$

x + y + 25+43- 13= 180

x + y + 55= 180

x + y + 55-55= 180-55

x + y = 125

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Example Question #5 : How To Find The Equation Of A Line

Are the following two equations parallel?

y=2x+13

5y=10x+95

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

When two lines are parallal, they must have the same slope.

Look at the equations when they are in slope-intercept form, y=mx+b where b represents the slope.

We must first reduce the second equation since all of the constants are divisible by .

This leaves us with y=2x+19 . Since both equations have a slope of , they are parallel.

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Example Question #2 : How To Find The Equation Of A Line

Reduce the following expression:

$\frac{10a^{3}b^{5}c^{-2}}{2a^{2}}$

Possible Answers:

$\frac{5ab^{5}}{c^{2}}$

$10a^{1.5}b^{-5}c^{2}$

$10a^{1.5}b^{5}c^{2}$

$\frac{5ab^{3}}{c^{2}}$

$\frac{5a^{5}b^{5}}{c^{2}}$

Correct answer:

$\frac{5ab^{5}}{c^{2}}$

Explanation:

For this expression, you must take each variable and deal with them separately.

First divide you two constants 10/2=5 .

Then you move onto and when you divide like exponents you must subtract the exponents leaving you with .

is left by itself since it is already in a natural position.

Whenever you have a negative exponential term, you must it in the denominator.

This leaves the expression of $\frac{5ab^{5}}{c^{2}}$ .

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Example Question #6 : How To Find The Equation Of A Line

Give the equation of a line that passes through the point (4,7) and has an undefined slope.

Possible Answers:

x = 7

y = 4

x = 4

x + y = 11

y = 7

Correct answer:

x = 4

Explanation:

A line with an undefined slope has equation x = a for some number ; since this line passes through a point with -coordinate 4, then this line must have equation x = 4

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Example Question #7 : How To Find The Equation Of A Line

Give the equation of the line through (2,9) and (8,1) .

Possible Answers:

4x+3y=35

3x+4y=28

-3x+4y=30

3x-4y=20

4x-3y=29

Correct answer:

4x+3y=35

Explanation:

First, find the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{9-1}{2-8}=\frac{8}{-6}=-\frac{4}{3}$

Apply the point-slope formula:

$y-y_{1}= m (x-x_{1})$

$y-1= -\frac{4}{3} (x-8)$

$y-1= -\frac{4}{3} x- \left (-\frac{4}{3} \right )8$

$y-1= -\frac{4}{3} x+ \frac{32}{3}$

$y= -\frac{4}{3} x+ \frac{35}{3}$

Rewriting in standard form:

$\frac{4}{3} x + y= \frac{35}{3}$

4x+3y=35

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Example Question #1 : Algebraic Word Problems

Michael scores a 95, 87, 85, 93, and a 94 on his first 5 math tests. If he wants a 90 average, what must he score on the final math test?

Possible Answers:

Correct answer:

Explanation:

To solve for the final score:

Add the five past test scores and you get 454. Then set up an algebraic equation where you add 454 to , which is the final test score, and divide by six, because you want the average for 6 tests now. You make this equation equal to 90 because that is the average Michael wants and solve for :

$\left ( 454+x\right )\div6 = 90$

454+x = 540

x=86

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Example Question #2 : Algebraic Word Problems

If David wants to drive to his friend's house, which is 450 miles away, in 6 hours, what is the average speed David has to drive at?

Possible Answers:

$60\ mph$

$75\ mph$

$80\ mph$

$65\ mph$

$50\ mph$

Correct answer:

$75\ mph$

Explanation:

$Distance=rate\times time$

Plug in the the values for distance and time, and solve for rate.

$450 = r\times 6$

and

r = 75

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Example Question #1 : Algebraic Word Problems

If the sum of the smallest and largest of three consecutive even numbers is 28, what is the value of the second largest number in the series?

Possible Answers:

Correct answer:

Explanation:

The three numbers would be

, x+2 , and x+4 .

Add the first and third value and you get

2x+4 = 28

and

x=12 .

The second largest value is x+2=14 .

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Example Question #2 : Algebraic Word Problems

Beth and Sam are 500 miles apart. If Beth travels at 60mph and leaves her house at 1pm, what time will she arrive at Sam's house?

Possible Answers:

9:00 PM

9:30 PM

9:20 PM

9:33 PM

8:33 PM

Correct answer:

9:20 PM

Explanation:

Using $Distance = rate\times time$ , the time would be 8.333 hours, which is hours and minutes. If you add that to 1pm, you get 9:20pm.

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Example Question #1 : Algebraic Word Problems

Greg is trying to fill a 16 oz. bottle with water. If Greg fills the bottle at 1 oz per second and the bottle leaks .2 oz per second, how long would it take for Greg to fill the bottle?

Possible Answers:

$16\ seconds$

$22\ seconds$

$20\ seconds$

$24\ seconds$

$8\ seconds$

Correct answer:

$20\ seconds$

Explanation:

You first find the rate at which the bottle is being filled at, which is

1 oz. -0.2 oz = 0.8 oz .

Then you divide the entire bottle, which is 16 oz. by the rate of .8 oz , and you get $20\ seconds$ .

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Algebra

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #5 : How To Find The Equation Of A Line

Example Question #5 : How To Find The Equation Of A Line

Example Question #2 : How To Find The Equation Of A Line

Example Question #6 : How To Find The Equation Of A Line

Example Question #7 : How To Find The Equation Of A Line

Example Question #1 : Algebraic Word Problems

Example Question #2 : Algebraic Word Problems

Example Question #1 : Algebraic Word Problems

Example Question #2 : Algebraic Word Problems

Example Question #1 : Algebraic Word Problems

All SSAT Upper Level Math Resources

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