SAT Math Module 2

Math Module 2

The question asks for the function that represents values given in a table. In function notation, the number inside the parentheses is the $ x $-value that goes into the function, or the input, and the value that comes out of the function is the $ y $-value, or the output. Together, they represent points on the graph of the function.

The table shows pairs of values for $ x $ and $ f(x) $, and the correct function must work for every point on the graph. Plug in values from the table and eliminate functions that don’t work. Try the point $ (0, 15) $ and plug $ x = 0 $ and $ f(x) = 15 $ into the answer choices:
* Choice (A) becomes $ 15 = 3(0) + 12 $, or $ 15 = 12 $. This is not true, so eliminate (A).
* Choice (B) becomes $ 15 = 3(0) + 15 $, or $ 15 = 15 $. This is true, so keep (B), but check the remaining answers just in case.
* Choice (C) becomes $ 15 = 15(0) + 12 $, or $ 15 = 12 $; eliminate (C).
* Choice (D) becomes $ 15 = 15(0) + 15 $, or $ 15 = 15 $; keep (D).

Two answers worked for the first point, so try a second point from the table and plug $ x = 1 $ and $ f(x) = 18 $ into the remaining answers:
* Choice (B) becomes $ 18 = 3(1) + 15 $, or $ 18 = 18 $; keep (B).
* Choice (D) becomes $ 18 = 15(1) + 15 $, or $ 18 = 30 $; eliminate (D).

The correct answer is (B).

1 / 22

When the linear function $ y = f(x) $ is graphed in the $ xy $-plane, the graph contains the corresponding values of $ x $ and $ f(x) $ shown in the table above. Which of the following could represent the function?

$ f(x) = 15x + 15 $

$ f(x) = 15x + 12 $

$ f(x) = 3x + 15 $

$ f(x) = 3x + 12 $

2 / 22

15a – (6a – 2a)
Which of the following expressions is equivalent to the given expression?

11a

23a

3 / 22

33, 34, 38, 41, 43, 44, 47
Which of the following is the median of the given data?

4 / 22

Right triangle ABC has sides of the following lengths: AB = 165, BC = 280, and AC = 325. Another triangle, LMN, is similar to ABC such that A corresponds to L and B corresponds to M. What is the value of cos(L)?

$ \frac{33}{65} $

$ \frac{33}{56} $

$ \frac{65}{33} $

$ \frac{56}{65} $

5 / 22

The function $ g $ is defined as $ g(x) = x^{2}-1 $. What is the value of $ g(x) $ when $ x=3 $?

6 / 22

Which equation represents the relationship between the numbers a and b if a is half of b?

$ a = b – 2 $

$ a = b + 2 $

$ b = \frac{1}{2} a $

$ a = \frac{1}{2} b $

7 / 22

A total of 200 pets were adopted at an event. If 70% of the adopted pets were dogs, how many of the pets were dogs?

8 / 22

A rectangle has a height of 23 inches (in) and a width of 9 in. What is its perimeter, in inches?

207

1,024

9 / 22

The function $ f $ is given as $ f(x) = \frac{2}{3}x $. When $ x = 6 $, what is the value of $ f(x) $?

10 / 22

The production cost p(x), in dollars, to produce x units of an item when materials cost $2 per item is given by p(x) = 2x + 150. What is the total cost to produce 2,000 units of this item?

$3,850

$4,150

$1,850

$2,300

11 / 22

Which of the following equations correctly expresses $ r $ in terms of $ p $ and $ s $ if the relationship between the numbers $ p $, $ r $, and $ s $ can be expressed as $ p = 13r – 6s $?

$ r = 13p + 6s $

$ r = \frac{1}{13}p + 6s $

$ r = \frac{p + 6s}{13} $

$ r = \frac{-6s – p}{13} $

12 / 22

Function $ f $ is defined by $ f(x) = x^{3} + 1 $. Which of the following tables gives three values of $ x $ and their corresponding values of $ y $?

13 / 22

$ 3x – 4y = 17 $

In the $ xy $-plane, the graph of a line with an $ x $-intercept of $ (c, 0) $ and a $ y $-intercept of $ (0, k) $, where $ c $ and $ k $ are constants, can be represented by the given equation. What is the value of $ \frac{c}{k} $?

$ \frac{4}{3} $

$ \frac{3}{4} $

$ -\frac{4}{3} $

$ -\frac{3}{4} $

14 / 22

A postal machine processes mail at a constant rate of 21 pieces of mail per minute. At this rate, how many pieces of mail would the machine process in 7 minutes?

147

15 / 22

James must drive 100 miles before he can take his driver’s license test. He knows that when he drives around town running errands, he drives at an average speed of 20 miles per hour. If James maintains this average speed, how many hours must he drive to meet the requirement for his driver’s license test?

100

16 / 22

Stella had 211 invitations to send for an event. She has already sent 43 invitations and will send them all if she sends 24 each day for the next d days. Which of the following equations represents this situation?

24d – 43 = 211

43d + 24 = 211

24d + 43 = 211

43d – 24 = 211

17 / 22

If h(–1) = 3 and h(0) = 5 in linear function h, which of the following is the equation of function h?

h(x) = 2x + 3

h(x) = 2x

h(x) = 3x + 5

h(x) = 2x + 5

18 / 22

What is the value of the solution to the equation 22 = y – 10?

19 / 22

What is the value of 4y – 16 if y – 4 = 11?

20 / 22

The height of a rocket launched from a rooftop can be modeled by the equation $ h = -16s^{2} + 64s + 21 $, where $ h $ is the height of the rocket above the ground, in feet, and $ s $ is the number of seconds since the rocket was launched. Which of the following represents the height, in feet, of the rooftop from which the rocket was launched?