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
What is the graph of the equation \(y=x^2-2\) ?
▶️Answer/Explanation
Ans: B
The equation \(y = x^2 – 2\) represents a quadratic function, which graphs as a parabola. Let’s analyze its properties:
The vertex of the parabola represented by the equation \(y = x^2 – 2\) is the point where the graph reaches its minimum or maximum value. Since the coefficient of \(x^2\) is positive, the parabola opens upwards, and the vertex represents the minimum point of the graph.
To find the vertex, we can use the formula:
\[ x_{\text{vertex}} = -\frac{b}{2a} \]
\[ y_{\text{vertex}} = f(x_{\text{vertex}}) \]
For the given equation \(y = x^2 – 2\):
\[ a = 1, \quad b = 0, \quad c = -2 \]
\[ x_{\text{vertex}} = -\frac{0}{2 \cdot 1} = 0 \]
\[ y_{\text{vertex}} = (0)^2 – 2 = -2 \]
So, the vertex is at \((0, -2)\).
Intercepts:
1. y-intercept: To find the y-intercept, let \(x = 0\):
\[ y = (0)^2 – 2 = -2 \]
So, the y-intercept is at \((0, -2)\).
2. x-intercepts: To find the x-intercepts, let \(y = 0\), then solve for \(x\):
\[ 0 = x^2 – 2 \]
\[ x^2 = 2 \]
\[ x = \pm \sqrt{2} \]
So, the x-intercepts are at \((- \sqrt{2}, 0)\) and \((\sqrt{2}, 0)\).
[Calc] Question Easy
For the polynomial function f, the table shows some values of x and their corresponding values of 𝑓(𝑥). Which of the following could be the graph of y equals 𝑓(𝑥)?
▶️Answer/Explanation
Ans: B
To determine which graph corresponds to the given values of \(f(x)\) for specific \(x\) values, we can compare the given points to the points on each graph.
The table provides the points:
- \((-4,0)\)
- \((-1,3)\)
- \((1,5)\)
At x=-1 and x=1 value of y is positive which is only in case -B
[Calc] Question Easy
The function k is defined by k(x) =\(\frac{3x-5}{2x+3}\) the value of k(1) ?
A) \(\frac{5}{2}\)
B) \(\frac{8}{5}\)
C) \(\frac{-2}{5}\)
D) \(\frac{-3}{2}\)
▶️Answer/Explanation
C) \(\frac{-2}{5}\)
To find the value of \(k(1)\) for the function \(k(x) = \frac{3x – 5}{2x + 3}\):
Substitute \(x = 1\) into the function:
\[
k(1) = \frac{3(1) – 5}{2(1) + 3}
\]
\[
k(1) = \frac{3 – 5}{2 + 3}
\]
\[
k(1) = \frac{-2}{5}
\]
Answer: C) \(-\frac{2}{5}\)
[No-Calc] Question Easy
\(g(x)=\frac{2+x}{x}\)
For the given function g, what is the value of g(8)?
▶️Answer/Explanation
1.25
Given the function \(g(x) = \frac{2 + x}{x}\), we need to find the value of \(g(8)\).
Substitute \(x = 8\) into the function:
\[g(8) = \frac{2 + 8}{8} = \frac{10}{8} = \frac{5}{4}\]
So, \(g(8) = \frac{5}{4}\).
[Calc] Question Easy
Which polynomial is equivalent to
$$
\left(12 x^4-5 x+18\right)+\left(6 x^4+13 x^2+7 x-9\right) ?
$$
A) $\left(18 x^8+13 x^3+2 x+9\right)$
B) $\left(18 x^8+8 x^3+25 x-9\right)$
C) $\left(18 x^4+13 x^2+2 x+9\right)$
D) $\left(18 x^4+8 x^2+25 x-9\right)$
▶️Answer/Explanation
C
[Calc] Question Easy
The function $f$ is defined by $f(x)=x^2-5 x+6$. What is the value of $f(4)$ ?
A) 0
B) 2
C) 12
D) 30
▶️Answer/Explanation
B
Questions
In the $x y$-plane, which of the following changes to the graph of the equation $y=x^2+3$ will result in the graph of the equation $y=\left(x^2+3\right)-6$ ?
A. A shift 6 units to the left
B. A shift 6 units to the right
C. A shift 6 units upward
D. A shift 6 units downward
▶️Answer/Explanation
Ans: D
Questions
The functions $f$ and $g$ are defined by $f(x)=4 x$ and $g(x)=x^2$. For what value of $x$ does $f(x)-g(x)=4$ ?
A. -2
B. -1
C. 1
D. 2
▶️Answer/Explanation
Ans: D
Question
Which of the following equations has a graph in the $x y$-plane with no $x$-intercepts?
A. $y=x^2+3 x+4$
B. $y=x^2-5 x-6$
C. $y=3 x^2$
D. $y=2 x-5$
▶️Answer/Explanation
Ans: A