Home › Worksheets › IB Year 12 Math › Quadratics and Inequalities Prepared by Mohsim Digital Education
Name: _________________________
Date: _________________________
Score: _______ / 40
The quadratic formula reads x = (−b ± √(b² − 4ac)) ÷ 2a and the discriminant is b² − 4ac, so this IB sheet opens with the solving formula and its deciding number. The answers record no real roots and a parabola for the graph shape.
Key Takeaways
The quadratic solutions use x = (−b ± √(b² − 4ac)) ÷ 2a (Q1).
The discriminant is b² − 4ac (Q2).
Q4 records a parabola as the graph shape.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The solutions of the quadratic equation ax² + bx + c = 0 are given by
(a) x = (−b ± √(b² − 4ac)) ÷ 2a (b) x = (−b ± √(b² − 4ac)) ÷ a (c) x = (−b ± √(b² − 4ac)) × 2a (d) x = (b ± √(b² − 4ac)) ÷ 2a
2.
The discriminant of a quadratic equation is
(a) b² − 4ac (b) b² + 4ac (c) √(b² − 4ac) (d) 4ac − b²
3.
If the discriminant is negative, the quadratic equation has
(a) no real roots (b) two real roots (c) one real root (d) a repeated root
4.
The graph of a quadratic function is a
(a) parabola (b) straight line (c) circle (d) hyperbola
5.
If a > 0 in y = ax² + bx + c, the parabola
(a) opens upwards (b) opens downwards (c) has no vertex (d) is a straight line
6.
The axis of symmetry of a parabola y = ax² + bx + c is given by
(a) x = −b ÷ 2a (b) x = b ÷ 2a (c) x = −b × 2a (d) x = −b ÷ a
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
State the quadratic formula.
8.
Define the discriminant.
9.
If the discriminant is zero, how many distinct real roots does the equation have?
10.
Write the completed square form of a quadratic expression.
11.
How do you find the axis of symmetry of a parabola?
12.
If a < 0, does the parabola open upwards or downwards?
13.
Give one real-life application of a quadratic model.
14.
Solve x² − 9 = 0 by factorising.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
Solve x² − 5x + 6 = 0 by factorising.
16.
Using the quadratic formula, solve x² + 6x + 8 = 0.
17.
Find the discriminant of x² + 4x + 5 = 0 and state the number of real roots.
18.
Find the discriminant of 2x² − 4x + 2 = 0 and state the number of real roots.
19.
Write x² + 6x + 10 in completed square form.
20.
The height of a ball is modelled by h = −5t² + 20t. Using the axis of symmetry t = −b ÷ 2a, find the time at which the height is maximum.
Answer Key
1. a) x = (−b ± √(b² − 4ac)) ÷ 2a
2. a) b² − 4ac
3. a) no real roots
4. a) parabola
5. a) opens upwards
6. a) x = −b ÷ 2a
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What are the solutions of ax² + bx + c = 0?
x = (−b ± √(b² − 4ac)) ÷ 2a, option (a) in this worksheet (Q1).
What is the discriminant?
b² − 4ac, option (a) in this worksheet (Q2).
What happens when the discriminant is negative?
There are no real roots, option (a) in this worksheet (Q3).