Mathematics 9 - Diagnostic Test

In a small town, a gardener named Abigail is trying to determine the shape of a flower bed she wants to create. She knows that the area of the flower bed can be represented by a quadratic equation. Which of the following equations could represent the area of the flower bed?

• x³ + 2x = 0

• x² + 3x – 5 = 0

• 2x + 1 = 0

• 5x – 3 = 7

Sophia is studying different types of equations in her math class. She learns that one specific type of equation has a unique characteristic. What makes an equation quadratic?

• The variable is in the denominator

• The highest exponent of the variable is 2

• The equation contains only integers

• The equation is factorable

In a small town, a gardener is trying to design a parabolic garden bed. He knows that the shape of the garden bed can be represented by a quadratic equation. Which of the following equations does NOT represent a standard form of a quadratic equation?

• ax² + bx + c = 0

• x² = 4x + 5

• x² + 6 = 3x

• 1/x + 2 = 3

Noah is trying to find the length of a side of a square garden. He knows that the area of the garden is 25 square meters. To find the length of one side, he uses the equation x² = 25. What are the possible lengths of one side of the garden?

• ±5

• 5 only

• ±25

• No solution

Ava has a rectangular garden area represented by the equation x² - 5x + 6 = 0. She wants to find the dimensions of the garden by factoring the equation. What are the possible lengths of the sides of her garden?

• 2 and 3

• -2 and -3

• 5 and 6

• -5 and -6

Arjun is trying to find the length of a side of a square garden, and he knows that the area of the garden is 10 square meters. What is the first step in solving the equation x² - 10 = 0 to find the length of the side using square roots?

• Add 10 to both sides

• Factor the equation

• Take the square root of 10

• Subtract 10 from both sides

Elijah is trying to find the dimensions of a rectangular garden. The area of the garden can be represented by the equation x² + 2x - 35 = 0, where x represents one dimension of the garden. Which of the following equations is best solved using factoring?

• x² + 2x - 35 = 0

• x² - 7x + 1 = 0

• 2x² + 5 = 0

• x² = 4x - 7

Emma is trying to determine the best method to solve the equation representing the trajectory of a ball thrown into the air, given by x² + x + 1 = 0. What method should she use?

• Factoring

• Extracting roots

• Completing the square or quadratic formula

• Graphing

Elijah is trying to determine the nature of the roots of a quadratic equation that represents the area of a square garden he wants to build. The equation is x² + 6x + 9 = 0. What is the discriminant of this equation?

• 0

• 36

• 4

• -12

Grace is trying to find the values of x that satisfy the equation x² + 1 < 0. Which of the following best describes the solution set of her equation?

• All real numbers

• All complex numbers

• No real solution

• One solution