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
▶️ Answer/Explanation
Answer: 14
Question Hard
The table shows three values of \( x \) and their corresponding values of \( g(x) \), where
\(
g(x) = \frac{f(x)}{x+3}
\)
and \( f \) is a linear function. What is the \( y \)-intercept of the graph of \( y = f(x) \) in the \( xy \)-plane?
\(
\begin{array}{ll}
\text{A. } (0, 36) \\
\text{B. } (0, 12) \\
\text{C. } (0, 4) \\
\text{D. } (0, -9)
\end{array}
\)
▶️Answer/Explanation
Ans: A
Question Hard
\(h(x)=2(x—4)^2-32\)
The quadratic function h is defined as shown. In the xy-plane, the graph of y= h(x) intersects the x-axis at the points (0,0)and (t,0), where t is a constant. What is the value of t ?
A1
B.2
C.4
D.8
▶️Answer/Explanation
Ans: D
\(h(0)=2(0—4)^2-32\)
\(h(0)=0\)
\(h(t)=2(t—4)^2-32\)
It is given that \(h(t)=0\).
\(0=2(t-4)^2-32\)
\((t-4)^2=16\)
\(t=8\)
▶️ Answer/Explanation
Answer: 1728
For minimum value, \(x = -\frac{b}{2a}\), where \(a = 1\), \(b = -48\). So, \(x = \frac{48}{2} = 24\). Substitute \(x = 24\) into \(f(x)\): \(f(24) = 24^2 – 48 \cdot 24 + 2,304 = 576 – 1,152 + 2,304 = 1,728\).
