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 Medium
\[
\sqrt{x^2}=5
\]
What are all possible solutions to the given equation?
A) -25 and 25
B) -5 and 5
C) -25 only
D) 5 only
▶️Answer/Explanation
Ans:B
The given equation is:
\[
\sqrt{x^2} = 5
\]
We know that \(\sqrt{x^2} = |x|\). This means the equation can be rewritten as:
\[
|x| = 5
\]
The absolute value equation \(|x| = 5\) has two possible solutions:
\[
x = 5 \quad \text{or} \quad x = -5
\]
Question medium
If \(5 \sqrt{3 x}-2=13\), what is the value of \(3 x\) ?
▶️Answer/Explanation
Ans:9
\(5 \sqrt{3x} – 2 = 13\)
Add 2 to both sides:
\[5 \sqrt{3x} = 15\]
Divide both sides by 5:
\[\sqrt{3x} = 3\]
Square both sides to isolate \(3x\):
\[(\sqrt{3x})^2 = 3^2\]
\[3x = 9\]
So, the value of \(3x\) is \(9\).
Question medium
If 3 \(\sqrt{ x − 3} + 10 = 22\), what is the value of x − 3 ?
▶️Answer/Explanation
16
To solve for \(x – 3\) in the equation \(3 \sqrt{x – 3} + 10 = 22\), we first isolate the square root term and then solve for \(x – 3\).
Subtract \(10\) from both sides:
\[ 3 \sqrt{x – 3} = 22 – 10 \]
\[ 3 \sqrt{x – 3} = 12 \]
Next, divide both sides by \(3\):
\[ \sqrt{x – 3} = \frac{12}{3} \]
\[ \sqrt{x – 3} = 4 \]
Now, to solve for \(x – 3\), we square both sides of the equation:
\[ ( \sqrt{x – 3} )^2 = 4^2 \]
\[ x – 3 = 16 \]
Question Medium
$$
\sqrt{x^2-9}=4
$$
What is the positive solution to the given equation?
▶️Answer/Explanation
5
Questions
. Which of the following is equivalent to $\sqrt[4]{x^2+8 x+16}$, where $x>0$ ?
A. $(x+4)^4$
B. $(x+4)^2$
C. $(x+4)$
D. $(x+4)^{\frac{1}{2}}$
▶️Answer/Explanation
Ans: D