Home / Digital SAT Math: Practice Questions-Passport to advanced mathematics-Operations with polynomials

# Digital SAT Math: Practice Questions-Passport to advanced mathematics-Operations with polynomials

## 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 $$y=x^2-2$$ ?

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)?

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) $$\frac{-3}{2}$$

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)?

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) $\left(18 x^4+8 x^2+25 x-9\right)$

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

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

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

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. $y=2 x-5$