x² = 49 gives x = 7 or x = −7 and x = 2 is a root of x² − 5x + 6 = 0, so this Year 10 sheet opens by square-rooting and by testing roots in a quadratic. The answers add x = 3 or x = −5 from a factorised equation.
Key Takeaways
x² = 49 has solutions x = 7 and x = −7 (Q1).
x = 2 is a root of x² − 5x + 6 = 0 (Q2).
Q5 records x = 3 or x = −5 as solutions.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.Solve x² = 49.
(a) x = 7 only(b) x = -7 only(c) x = 7 or x = -7(d) x = 49 or x = -49
2.Which of these is a root of x² - 5x + 6 = 0?
(a) 2(b) 6(c) -1(d) 5
3.Solve x² - 4 = 0.
(a) x = 2 only(b) x = -2 only(c) x = 2 or x = -2(d) x = 4 or x = -4
4.The discriminant of x² - 6x + 9 is zero. What does this tell us about the roots?
(a) There is one repeated root(b) There are two distinct roots(c) There are no real roots(d) There are infinitely many roots
5.Solve (x - 3)(x + 5) = 0.
(a) x = 3 or x = -5(b) x = -3 or x = 5(c) x = 3 or x = 5(d) x = -3 or x = -5
6.Which of these is a quadratic equation?
(a) y = 2x + 1(b) y = x³ - 2(c) y = x² - 3x + 2(d) y = 1 ÷ x
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Solve x² - 9x = 0.
8.Solve x² + 7x + 12 = 0 by factorising.
9.Write x² + 6x + 5 in completed square form.
10.Solve x² = 36.
11.Factorise x² - 2x - 8.
12.Solve x² + 5x + 6 = 0.
13.Solve x² - 6x + 8 = 0.
14.Solve (2x - 1)(x + 3) = 0.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The product of a number and the number increased by 2 is 24. Find the positive value of the number.
16.A rectangle has length (x + 3) cm and width (x - 1) cm. Its area is 21 cm². Find x.
17.A ball is thrown so its height in metres is h = 20t - 5t². After how many seconds does it return to the ground?
18.The square of a number is 16 more than 6 times the number. Find the positive value of the number.
19.A rectangular garden is 2 m longer than it is wide and has area 15 m². Find its width.
20.Solve x² - 10x + 21 = 0, given that both roots are positive integers.
Answer Key
1. c) x = 7 or x = -7
2. a) 2
3. c) x = 2 or x = -2
4. a) There is one repeated root
5. a) x = 3 or x = -5
6. c) y = x² - 3x + 2
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 solves x² = 49?
x = 7 or x = −7, option (c) in this worksheet (Q1).
Which is a root of x² − 5x + 6 = 0?
x = 2, option (a) in this worksheet (Q2).
What are the solutions of x² + 2x − 15 = 0?
x = 3 or x = −5, option (a) in this worksheet (Q5).
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