DSAT Math Practice Questions - Advanced : Systems of Non linear equations in one and 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
DSAT MAth and English – full syllabus practice tests
Question Hard
\(
\begin{aligned}
x – y &= 1 \\
x + y &= x^2 – 3
\end{aligned}
\)
Which ordered pair is a solution to the system of equations above?
A. $(1 + \sqrt{3}, \sqrt{3})$
B. $(\sqrt{3}, -\sqrt{3})$
C. $(1 + \sqrt{5}, \sqrt{5})$
D. $(\sqrt{5}, -1 + \sqrt{5})$
▶️Answer/Explanation
Answer: A
Question Hard
\(
\frac{1}{x^2 + 10x + 25} = 4
\)
If \( x \) is a solution to the given equation, which of the following is a possible value of \( x + 5 \)?
\[
A.\(\frac{1}{2}\)
B. \(\frac{5}{2}\)
C. \(\frac{9}{2}\)
D. \(\frac{11}{2}\)
▶️Answer/Explanation
Answer: A
Question Hard
\(
57x^2 + (57b + a)x + ab = 0
\)
In the given equation, \( a \) and \( b \) are positive constants. The product of the solutions to the given equation is \( kab \), where \( k \) is a constant. What is the value of \( k \)?
\(
\begin{array}{ll}
\text{A. } \frac{1}{57} \\
\text{B. } \frac{1}{19} \\
\text{C. } 1 \\
\text{D. } 57
\end{array}
\)
▶️Answer/Explanation
Answer: A
Product of roots: \(\frac{c}{a}\)
Here, $c=ab$ and $a=57$
The product of the solutions to the given equation is \( kab \), where \( k \) is a constant.
\(kab=\frac{ab}{57}\)
\(k=\frac{1}{57}\)
Question Hard
The graph of the function \( f \), defined by
$
f(x) = -\frac{1}{2} (x – 4)^2 + 10,
$
is shown in the \( xy \)-plane above. If the function \( g \) (not shown) is defined by
$
g(x) = -x + 10,
$
what is one possible value of \( a \) such that \( f(a) = g(a) \)?
▶️Answer/Explanation
Ans: 2 or 8
