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Quadratic equations - MYP Questionbank | RevisionDojo

Practice Quadratic equations with authentic MYP MYP Standard Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

If the discriminant $\Delta$ of the quadratic equation $ax^2 + bx + c = 0$ is exactly equal to $b^2$ , which of the following is a necessary conclusion about the solutions of the equation?

Question 2

Find the values of $k$ such that the equation $x^2 - kx + 9 = 0$ has exactly one real solution.

Question 3

Find the exact solutions for the quadratic equation $2m^2-14m+23=0$ using the quadratic formula.

Question 4

What are the roots of the quadratic equation $3(x - 4)(2x + 1) = 0$ ?

Question 5

Fill in the blank: To solve $x^2 + 12x = 5$ by completing the square, you must add ________ to both sides of the equation to create a perfect square trinomial on the left side.

Question 6

Find the discriminant $\Delta$ for the quadratic equation $-2x^2 + 4x - 5 = 0$ .

Question 7

A projectile's height in meters is modeled by $h = -5t^2 + 20t + 2$ . To find the time $t$ when the projectile returns to its initial height of 2 meters, we solve $-5t^2 + 20t = 0$ . Using factorization, what is the non-zero solution for $t$ ?

Question 8

True or False: The quadratic formula can be used to solve the equation ${x^2 - 9 = 0}$ by substituting ${a = 1, b = 0,}$ and ${c = -9}$ .

Question 9

Find the value of $k$ such that the equation $x^2 + kx + 25 = 0$ has exactly one real solution.

Question 10

When the equation $x(x - 4) = 2x + 3$ is written in the standard form $ax^2 + bx + c = 0$ , what is the value of the coefficient $b$ ?

Type

Difficulty

Question 1

If the discriminant $\Delta$ of the quadratic equation $ax^2 + bx + c = 0$ is exactly equal to $b^2$ , which of the following is a necessary conclusion about the solutions of the equation?

Question 2

Find the values of $k$ such that the equation $x^2 - kx + 9 = 0$ has exactly one real solution.

Question 3

Find the exact solutions for the quadratic equation $2m^2-14m+23=0$ using the quadratic formula.

Question 4

What are the roots of the quadratic equation $3(x - 4)(2x + 1) = 0$ ?

Question 5

Fill in the blank: To solve $x^2 + 12x = 5$ by completing the square, you must add ________ to both sides of the equation to create a perfect square trinomial on the left side.

Question 6

Find the discriminant $\Delta$ for the quadratic equation $-2x^2 + 4x - 5 = 0$ .

Question 7

Question 8

True or False: The quadratic formula can be used to solve the equation ${x^2 - 9 = 0}$ by substituting ${a = 1, b = 0,}$ and ${c = -9}$ .

Question 9

Find the value of $k$ such that the equation $x^2 + kx + 25 = 0$ has exactly one real solution.

Question 10

When the equation $x(x - 4) = 2x + 3$ is written in the standard form $ax^2 + bx + c = 0$ , what is the value of the coefficient $b$ ?

Type

Difficulty

Question 1

If the discriminant $\Delta$ of the quadratic equation $ax^2 + bx + c = 0$ is exactly equal to $b^2$ , which of the following is a necessary conclusion about the solutions of the equation?

Question 2

Find the values of $k$ such that the equation $x^2 - kx + 9 = 0$ has exactly one real solution.

Question 3

Find the exact solutions for the quadratic equation $2m^2-14m+23=0$ using the quadratic formula.

Question 4

What are the roots of the quadratic equation $3(x - 4)(2x + 1) = 0$ ?

Question 5

Fill in the blank: To solve $x^2 + 12x = 5$ by completing the square, you must add ________ to both sides of the equation to create a perfect square trinomial on the left side.

Question 6

Find the discriminant $\Delta$ for the quadratic equation $-2x^2 + 4x - 5 = 0$ .

Question 7

Question 8

True or False: The quadratic formula can be used to solve the equation ${x^2 - 9 = 0}$ by substituting ${a = 1, b = 0,}$ and ${c = -9}$ .

Question 9

Find the value of $k$ such that the equation $x^2 + kx + 25 = 0$ has exactly one real solution.

Question 10

When the equation $x(x - 4) = 2x + 3$ is written in the standard form $ax^2 + bx + c = 0$ , what is the value of the coefficient $b$ ?

Quadratic equations Questionbank