Digital SAT Math - Non-linear equations in one variable - Medium Practice Questions - 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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DSAT MAth and English – full syllabus practice tests
▶️ Answer/Explanation
Answer: C
Use discriminant \( b^2 – 4ac \) (negative = no real solutions).
A) \( 3x^2 – 3 = 0 \): \( a = 3, b = 0, c = -3 \), \( 0 – 4 \cdot 3 \cdot -3 = 36 \) (real solutions).
B) \( 3x^2 + 3x = 0 \): \( a = 3, b = 3, c = 0 \), \( 9 – 4 \cdot 3 \cdot 0 = 9 \) (real solutions).
C) \( 3x^2 + 3x + 3 = 0 \): \( a = 3, b = 3, c = 3 \), \( 9 – 4 \cdot 3 \cdot 3 = -27 \) (no real solutions).
D) \( 3x^2 – 6x + 3 = 0 \): \( a = 3, b = -6, c = 3 \), \( 36 – 4 \cdot 3 \cdot 3 = 0 \) (one real solution).
▶️ Answer/Explanation
Answer: B
At peak, \( x = 4 \), \( y = 8 \).
Substitute: \( 8 = \frac{-4(4 – 8)}{k} \).
Simplify: \( 8 = \frac{-4(-4)}{k} = \frac{16}{k} \).
Solve: \( 8k = 16 \), \( k = 2 \).
▶️ Answer/Explanation
Answer: C
Vertex at \( (30, 50) \), passes through \( (0, 0) \) and \( (60, 0) \).
Form: \( y = a(x – 30)^2 + 50 \).
Substitute \( (0, 0) \): \( 0 = a(0 – 30)^2 + 50 \).
Solve: \( 0 = 900a + 50 \), \( 900a = -50 \), \( a = -\frac{1}{18} \).
Equation: \( y = -\frac{1}{18}(x – 30)^2 + 50 \).