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SAT Math : SAT Mathematics

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Example Questions

Example Question #33 : Algebraic Functions

In the xy-plane, a line with the equation $\dpi{100} \small y=\frac{1}{2}x-6$ crosses the y-axis at the point with the coordinates (m, n). What is the value of n?

Possible Answers:

–6

$\dpi{100} \small \frac{1}{2}$

Correct answer:

–6

Explanation:

This problem states that the given line crosses the y-axis at a certain point (m, n). By crossing the y-axis, we know that this point must be the y-intercept of this line. All y-intercepts lie on the y-axis and, therefore, have an x-coordinate of 0. If we plug in 0 for x in the equation of the line, $\dpi{100} \small y=\frac{1}{2}x-6$ , we will get

$\dpi{100} \small y=\frac{1}{2}\left (0 \right )-6$

y = –6

The y-intercept must be at the point

(0, –6)

so n must be –6.

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Example Question #2782 : Sat Mathematics

If $f(x)= x^3 + c$ and $\dpi{100} \small f(-3)=7$ . What is $\dpi{100} \small c$ ?

Possible Answers:

$31$

$7$

$30$

$-7$

$34$

Correct answer:

$34$

Explanation:

Plugging in $-3$ for $x$ and 7 for $f(x)$ into $f(x)= x^3 + c$ and solving for $c$ , we obtain $c=34$ .

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Example Question #2781 : Sat Mathematics

Solve for :

$3-z=3+z$ .

Possible Answers:

Correct answer:

Explanation:

Solving for yields

$2z=0\ or\ z=0$ .

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Example Question #2782 : Sat Mathematics

if $f(x) = x^{2} + x - 2$ and $g(x) = x - 3$ , solve $f(g(x))$ .

Possible Answers:

$f(g(x)) = x^{2} - 5x + 4$

$f(g(x)) = x^{2} + 1$

$f(g(x)) = x^{2} + x - 3$

$f(g(x)) = x^{2} + 2x - 5$

$f(g(x)) = x^{2} - 3$

Correct answer:

$f(g(x)) = x^{2} - 5x + 4$

Explanation:

We are solving for a composite function by substituting $g(x)$ into $f(x)$ to get: $f(g(x)) = (x - 3)^{2} + (x - 3) - 2$ before simplification.

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Example Question #2785 : Sat Mathematics

If $f(x)=2x^2-5$ where is an integer, which of the following could be a value of f(x) ?

II.

III.

Possible Answers:

II only

I only

I, II and III

I and III only

II and III only

Correct answer:

II and III only

Explanation:

Choice I is incorrect because to equal 0, $x^2=5$ , and since is an integer, this cannot be true.

Choice II is correct because f(x)=3 when x=2 or x=-2 .

Choice III is correct because f(x)=-3 when x=1 or x=-1 .

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Example Question #2783 : Sat Mathematics

Jamie is three times her little brother's age, and her little brother is two years younger than his older brother. Collectively, the three of them are 27 years old. How old is Jamie?

Possible Answers:

None of the available answers

Correct answer:

Explanation:

The algebraic expression for being Jamie's youngest brother's age is:

3x+x+(x+2)=27

5x+2=27

5x=25

x=5

Jamie's youngest brother is five, the next oldest brother is seven, and Jamie is 15.

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Example Question #2784 : Sat Mathematics

Consider the function defined as follows:

$a \Delta b = (a-b)^3 +b$

Find:

$(3 \Delta 5) \times (2 \Delta 0)$

Possible Answers:

Correct answer:

Explanation:

The notation used above can be confusing. Let:

$a \Delta b = f(a,b)$

We can now find the answer by substituting the appropriate values into the equation:

$a \Delta b= f(a,b) = (a-b)^3 +b$

Therefore:

$3 \Delta 5 = f(3,5) = (3-5)^3 + 5 = (-2)^3 + 5 = -3$

$2 \Delta 0 = f(2,0) = (2-0)^3 + 0 = 8$

Finally:

$(3 \Delta 5) \times (2 \Delta 0) = (-3) \times 8 = -24$

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Example Question #2785 : Sat Mathematics

Solve for f(2) .

f(x)= 2x-22

Possible Answers:

$\frac{1}{18}$

$-\frac{1}{11}$

Correct answer:

Explanation:

To solve for f(2) , we actually have to solve for f(x) , when x=2 . We simply replace any $\small x$ with a $\small 2$ .

f(x) = 2x - 22

f(2)= 2(2)-22

f(2)= 4-22

f(2)= -18

The answer of f(x) when x=2 is .

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Example Question #2663 : Act Math

If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?

Possible Answers:

Correct answer:

Explanation:

With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.

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Example Question #2664 : Act Math

g(x) = 4x – 3

h(x) = .25πx + 5

If f(x)=g(h(x)). What is f(1)?

Possible Answers:

19π – 3

π + 17

13π + 3

Correct answer:

π + 17

Explanation:

First, input the function of h into g. So f(x) = 4(.25πx + 5) – 3, then simplify this expression f(x) = πx + 20 – 3 (leave in terms of π since our answers are in terms of π). Then plug in 1 for x to get π + 17.

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #33 : Algebraic Functions

Example Question #2782 : Sat Mathematics

Example Question #2781 : Sat Mathematics

Example Question #2782 : Sat Mathematics

Example Question #2785 : Sat Mathematics

Example Question #2783 : Sat Mathematics

Example Question #2784 : Sat Mathematics

Example Question #2785 : Sat Mathematics

Example Question #2663 : Act Math

Example Question #2664 : Act Math

All SAT Math Resources

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