Home / Digital SAT Math : Nonlinear functions -Practice Questions

# Digital SAT Math : Nonlinear functions -Practice Questions

## SAT MAth Practice questions – all topics

• Advanced Math Weightage: 35% Questions: 13-15
• Equivalent expressions
• Nonlinear equations in one variable and systems of equations in two variables
• Nonlinear functions

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question   Easy

The line graph shows the number of near-Earth asteroids discovered by the Spacewatch survey from 2003 to 2010.

During which period was the increase in the number of near-Earth asteroids discovered the greatest?
A) From 2003 to 2004
B) From 2004 to 2005
C) From 2005 to 2006
D) From 2007 to 2008

Ans:D

We will compare the increase in the number of near-Earth asteroids discovered from year to year by examining the vertical distances between points on the graph.

1. From 2003 to 2004:
In 2003, the number of asteroids discovered is approximately 50.8.
In 2004, the number of asteroids discovered is approximately 70.2.
Increase: $$70.2 – 50.8 = 19.4$$.

2. From 2004 to 2005:
In 2004, the number of asteroids discovered is approximately 70.2.
In 2005, the number of asteroids discovered is approximately 80.3.
Increase: $$80.3 – 70.2 = 10.1$$.

3. From 2005 to 2006:
In 2005, the number of asteroids discovered is approximately 80.3.
In 2006, the number of asteroids discovered is approximately 90.9.
Increase: $$90.9 – 80.3 = 10.6$$.

4. From 2007 to 2008:
In 2007, the number of asteroids discovered is approximately 40.8.
In 2008, the number of asteroids discovered is approximately 80.4.
Increase: $$80.4 – 40.8 = 39.6$$.

By comparing these increases, we see that the greatest increase occurred from 2007 to 2008.

[Calc]  Question  Easy

The average price of regular gasoline, per gallon, in the United States in 2001 was $$\ 1.42$$. Each year from 2001 to 2008 , the average price increased by approximately $$12 \%$$ of the previous year’s average price. Which equation best models this situation, where $$y$$ is the average price, in dollars, of regular gasoline, per gallon, and $$x$$ is the number of years since 2001 ?
A) $$y=1.12^x$$
B) $$y=1.42^x$$
C) $$y=1.12(1.42)^x$$
D) $$y=1.42(1.12)^x$$

Ans:D

The average price of regular gasoline in the United States in 2001 was $$\1.42$$. Each year from 2001 to 2008, the average price increased by approximately $$12\%$$ of the previous year’s average price. We need to determine the equation that best models this situation.

The price of gasoline increases by $$12\%$$ each year, so the price in the next year is $$112\%$$ of the previous year’s price, which is equivalent to multiplying by $$1.12$$.

Let’s define:
$$y$$ as the average price of gasoline in dollars,
$$x$$ as the number of years since 2001.

In 2001 ($$x = 0$$), the price is $$\1.42$$.
Each year, the price is multiplied by $$1.12$$. Therefore, the equation modeling this situation is:
$y = 1.42 (1.12)^x$

[No-Calc]  Question  Easy

$$f(x)=5^{x}+3$$

If the given function f is graphed in the xy-plane, where y=f(x), what is the y-intercept of the graph?

A. (0,3)

B. (0,4)

c. (0,5)

D. (0,8)

Ans: B

To find the $$y$$-intercept of the graph of the function $$f(x) = 5^x + 3$$, we set $$x = 0$$ and solve for $$y$$.

$f(0) = 5^0 + 3 = 1 + 3 = 4$

So, the $$y$$-intercept of the graph is at the point $$(0, 4)$$.

Therefore, the correct answer is option B) $$(0, 4)$$.

[Calc]  Question  Easy

What is the minimum number of books in the book drop recorded during this time?
A. 5
B. 4
C. 3
D. 1

Ans: D

So from graph  the minimum number of books in the book drop recorded during this time is 1.

[No-Calc]  Question  Easy

The function N models the amount of nickel-56, in Earth masses, remaining t days after a massive star explodes. About how many Earth masses of nickel-56 were there when the star exploded?

A) 3,000

B) 8,000

C) 12,000

D) 24,000

D)  24,000

From the graph, the curve appears to start around 24,000 Earth masses at time t = 0 days.

Therefore, the best option that approximates the initial amount of nickel-56 when the star exploded is:

D) 24,000 Earth masses

[No-Calc]  Question  Easy

The graph of the function f is shown. What is the value of f(0) ?

3

When x=0 value of y is 3.

So f(0)=3

[Calc]  Question  Easy

A touring company purchased a new tour bus for $100,000. The graph models the value of the bus as a function of the time, in years, since it was purchased. Which of the following is closest to the number of years after the company purchased the bus that the value of the bus will be half of the purchase price? A. 1 B. 6 C. 10 D. 25 ▶️Answer/Explanation Ans: B To determine how many years after purchase the value of the bus will be half of the purchase price ($50,000), I will analyze the graph showing the declining value over time.

The initial purchase price of $100,000 corresponds to the y-intercept of the graph. To find when the value reaches$50,000, we need to locate the point on the curve where the y-value (bus value) is 50,000.

[Calc]  Questions Foundation

The table gives some values of $$\mathrm{x}$$ and their corresponding values of $$f(x)$$. Which of the following graphs could be the graph of $$y=f(x)$$ in the xy-plane?

Ans:C

f(x) is being zero at  x=-2 and x= -1

and at x= 0 value of y = -2

So option – C best fit.

[Calc]  Question   Easy

The graph shown models the value, in dollars, of an investment account over time, in years, after an original amount is deposited.

According to the graph, how many year does it take for the value of the investment account to double?
A) 2
B) 3
C) 7
D) 14

D) 14

[Calc]  Question  Easy

The function $g$ is defined by $g(x)=4 x^2-3$. For what positive value of $x$ is $g(x)=13$ ?
A) 2
B) 4
C) $\frac{\sqrt{10}}{4}$
D) $\frac{\sqrt{10}}{2}$

A

Questions

The graph above shows the temperature in a room during a day when the thermostat malfunctioned. For which of the following two-hour periods was difference between the maximum and minimum temperatures greatest?

1. 1:00 to 3:00
2. 3:00 to 5:00
3. 5:00 to 7:00
4. 7:00 to 9:00

Ans: B

Question

$y=(x-h)^2(x+h)(x+k)$ The equation above is graphed in the $x y$-plane. If $h$ and $k$ are positive constants and $h \neq k$, how many distinct $x$ intercepts does the graph have?
A. 1
B. 2
C. 3
D. 4

Ans: C

Questions

\begin{aligned} & P=2,000 x \\ & P=500\left(2^x\right) \end{aligned}

A website administrator is considering using one of the two models above to predict the total number of purchases, $P$, made $x$ weeks after the website’s advertising campaign begins. How many more purchases are predicted by the exponential model than by the linear model 5 weeks after the advertising campaign begins?
A. 6,000
B. 8,000
C. 10,000
D. 16,000

Ans: A

Question

A ball was dropped from a height of 1.5 meters and hit the ground several times. The graph above represents the height $$h$$, in meters, of the ball $$t$$ seconds after it was dropped. Of the following, which best approximates the maximum height, in meters, of the ball between the second and third time it hit the ground?

1. 0.2
2. 0.4
3. 0.8
4. 1.5

Ans: B

Question

If $x^4-y^4=-15$ and $x^2-y^2=-3$, what is the value of $x^2+y^2$ ?
A. 5
B. 4
C. 2
D. 1