Home / Digital SAT Math Practice Questions – Medium : Systems of Non linear equations in two variables

Digital SAT Math Practice Questions – Medium : Systems of Non linear equations in two variables

Digital SAT Math Practice Questions - Medium : Systems of Non linear equations in two variables - New Syllabus

DSAT 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

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Question Medium


A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the xy-plane above. How many solutions does this system have?

A) 0

B) 1

C) 2

D) 3

▶️ Answer/Explanation
Solution

Answer: C

Graph shows a parabola and a line intersecting at two points.

Count intersections: 2 solutions.

Question Medium

Quadrant graph

In the xy-plane shown, the quadrants are labeled I, II, III, and IV. The graph of \( y = -{(x + h)}^2 + k \), where \( h \) and \( k \) are positive constants, is a parabola. In which quadrant is the vertex of this parabola?

A) Quadrant I

B) Quadrant II

C) Quadrant III

D) Quadrant IV

▶️ Answer/Explanation
Solution

Answer: B

Equation: \( y = -{(x + h)}^2 + k \), \( h > 0 \), \( k > 0 \).

Rewrite: \( y = -{(x – (-h))}^2 + k \), vertex at \( (-h, k) \).

\( -h < 0 \), \( k > 0 \), so vertex is in Quadrant II.

Question  Medium

What is the graph of the equation \(y=2(3)^{x}\) ?

▶️Answer/Explanation

Ans: A

For $x=0\Rightarrow =2(3)^{0}=2$

For $x=1\Rightarrow =2(3)^{1}=6$

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