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SAT Math : Algebra

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Example Questions

Example Question #421 : Algebra

What is the sixth term of the sequence: $\frac{1}{3}, \frac{1}{2}, \frac{3}{4}, \frac{9}{8} ... ?$

Possible Answers:

$\frac{3}{2}$

$\frac{81}{32}$

$\frac{27}{16}$

$2$

$\frac{81}{16}$

Correct answer:

$\frac{81}{32}$

Explanation:

Each term equals the previous term multiplied by $\frac{3}{2}$ .

The fifth term in the sequence is $\frac{9}{8} \cdot \frac{3}{2} = \frac{27}{16}$ .

The sixth term in the sequence is thus $\frac{27}{16} \cdot \frac{3}{2} = \frac{81}{32}$ .

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Example Question #2516 : Sat Mathematics

If $\dpi{100} \small z-3=n$ , then $\dpi{100} \small 2z=$ ?

Possible Answers:

$\dpi{100} \small 2n+6$

$\dpi{100} \small n+6$

$\dpi{100} \small 3n+6$

$\dpi{100} \small n$

$\dpi{100} \small n+3$

Correct answer:

$\dpi{100} \small 2n+6$

Explanation:

Begin by rearranging the equation to solve for z:

$\dpi{100} \small z=n+3$

This means that $\dpi{100} \small 2z=2\left ( n+3 \right )$ , which can be rewritten as $\dpi{100} \small 2n+6$ .

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Example Question #2518 : Sat Mathematics

If 5x-4 = 21 , what is the value of 3x + 1 ?

Possible Answers:

Correct answer:

Explanation:

First, solve the equation 5x-4 = 21 to find .

If 5x-4 = 21 , then must equal .

5x=21+4

5x=25

x=5

Then, plug the value for into the second equation, 3x+1 .

3(5)+1 = 16 .

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Example Question #51 : Expressions

3x = 4w

5y = 7x

9z = 8y

Which of the following is a correct statement?

Possible Answers:

135z = 224 w

15z= 14w

189 z= 160w

160z= 189w

224 z = 135 w

Correct answer:

135z = 224 w

Explanation:

9z = 8y

$\frac{9z }{9}= \frac{8y}{9}$

$z= \frac{8}{9}y$

Similarly, $y = \frac{7}{5}x$ and $x= \frac{4}{3} w$ .

Using some substitution:

$z= \frac{8}{9}y = \frac{8}{9} \cdot \frac{7}{5}x = \frac{8}{9} \cdot \frac{7}{5} \cdot \frac{4}{3} w = \frac{8 \cdot 7 \cdot 4}{9 \cdot 5 \cdot 3} \cdot w = \frac{224}{135}w$

Multiply:

$z= \frac{224}{135}w$

$135 \cdot z =135 \cdot \frac{224}{135}w$

135z = 224 w

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Example Question #743 : Algebra

$3^{3}+7\cdot5=?$

Possible Answers:

142

170

162

Correct answer:

Explanation:

The purpose of this question is to practice using the correct order of operations, which is the proper way to simplify this expression. Using PEMDAS (parentheses, exponent, multiplication, division, addition, subtraction) the exponent is treated first,

3^3=27

then the multiplication,

$7\cdot 5=35$

and the addition operation is handled last.

Executing the exponent simplifies the expression to

$27+7\cdot5$ ,

then executing the multiplication simplifies the expression to

27+35 ,

which adds together to be .

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Example Question #2521 : Sat Mathematics

A plane takes off from Airport A. It travels due north at 400 mi/hr for 2.5 hours, then it turns and travels due east at 430 mi/hr for 3 hours and lands at Airport B. How far is Airport B from Airport A? Round to the nearest mile, assume a straight line path.

Possible Answers:

$1660\ mi$

$2290\ mi$

$830\ mi$

$1632\ mi$

$1631\ mi$

Correct answer:

$1632\ mi$

Explanation:

The purpose of this question is to utilize the method of drawing a triangle to match the situation. Multiply the velocity by the time to find the distance traveled.

So,

$400\cdot \frac{5}{2}=1000$ mi for the first part of the trip and $430\cdot3=1290$ mi for the second part of the trip.

This forms a triangle with a vertical side of 1000 mi and a horizontal side of 1290 mi.

The side which we need to find is the hypotenuse, or the distance between the two airports. This is done by using the Pythagorean Theorem ( $A^{2}+B^{2}=C^{2}$ ), which means that squaring the dimensions of both the vertical and horizontal sides, adding them together, and then taking the square root of that yields the length of the hypotenuse.

$c=\sqrt{1000^2+1290^2}$

$c=\sqrt{2664100}\approx 1632.2$

This method leaves an answer of 1632.207 mi.

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Example Question #41 : How To Evaluate Algebraic Expressions

If a=0 , b=4 , c=-4 , and d=2 , then what is the value of the given expression?

x^a+2^b -c+d

Possible Answers:

x+22

Correct answer:

Explanation:

Substitution in our given values, we get

x^0+2^4 -(-4)+2 .

Simplifying this expression, we get

1+16+4+2=23

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Example Question #744 : Algebra

Given: a=3 , b=-2 , c=4 , find the value of a^2-2ab^2+c .

Possible Answers:

Correct answer:

Explanation:

We substitute the values for a, b, and c into the equation:

a^2-2ab^2+c

Given:

a=3 , b=-2 , c=4

the equation becomes,

(3)^2-2(3)(-2)^2+(4)

From here simplify but using order of operations PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

9-2(3)(4)+4

=9-6(4)+4

=9-24+4

=-15+4

=-11

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Example Question #41 : Evaluating Expressions

If a=4b , b=2c , and c=3d , then what is the value of $\frac{d}{b}$ ?

Possible Answers:

$\frac{1}{6}$

$\frac{3}{2}$

None of the given answers.

Correct answer:

$\frac{1}{6}$

Explanation:

If c=3d ,

then

$d=\frac{c}{3}$ .

Therefore,

$\frac{d}{b}=\frac{\frac{c}{3}}{2c}=\frac{c}{3}\cdot\frac{1}{2c}=\frac{c}{6c}=\frac{1}{6}$

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Example Question #42 : Evaluating Expressions

High and low

Above is a graph which gives the high and low temperatures, in degrees Fahrenheit, over a one week period for Jefferson City. Temperature given in degrees Fahrenheit can be converted to the Celsius scale using the following formula, where and are the temperature expressed in degrees Celsius and degrees Fahrenheit, respectively:

$C = \frac{5}{9} (F-32)$

In degrees Celsius, what was the lowest temperature of the week shown (nearest whole degree)?

Possible Answers:

$-4^{\circ }C$

$-7^{\circ }C$

$-11^{\circ }C$

$-19^{\circ }C$

$-15^{\circ }C$

Correct answer:

$-11^{\circ }C$

Explanation:

The lowest temperature of the week shown was $13 ^{\circ } F$ , on Wednesday and Thursday. This can be converted to degrees Celsius by setting F= 13 in the given formula and evaluating as follows:

$C = \frac{5}{9} (F-32)$

$C = \frac{5}{9} (13 -32)$

$= \frac{5}{9} (-19)$

$= -10\frac{5}{9}$

To the nearest integer, this is $-11^{\circ }C$ .

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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #421 : Algebra

Example Question #2516 : Sat Mathematics

Example Question #2518 : Sat Mathematics

Example Question #51 : Expressions

Example Question #743 : Algebra

Example Question #2521 : Sat Mathematics

Example Question #41 : How To Evaluate Algebraic Expressions

Example Question #744 : Algebra

Example Question #41 : Evaluating Expressions

Example Question #42 : Evaluating Expressions

All SAT Math Resources

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