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
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
▶️Answer/Explanation
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.
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) \(y=1.42(1.12)^x\)
▶️Answer/Explanation
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:
\[
y = 1.42 (1.12)^x
\]
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)
▶️Answer/Explanation
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) \((0, 4)\).
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
▶️Answer/Explanation
Ans: D
So from graph the minimum number of books in the book drop recorded during this time is 1.
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
▶️Answer/Explanation
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