Home › Worksheets › IGCSE Year 9 Math › Formulae and Factorising Prepared by Mohsim Digital Education
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x² + 5x factorises to x(x + 5) and making a the subject of F = ma gives a = F ÷ m, so this Year 9 sheet opens with a common factor and a rearragned formula. The key also expands 3(x − 4) to 3x − 12 and factors x² − 9.
Key Takeaways
x² + 5x = x(x + 5) (Q1).
a = F ÷ m makes a the subject of F = ma (Q2).
Q3 records 3x − 12 as an expansion.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
Factorise x² + 5x.
(a) x(x + 5) (b) x(x + 1) (c) x²(1 + 5) (d) x(x + 5x)
2.
Make a the subject of F = ma.
(a) a = mF (b) a = F ÷ m (c) a = m ÷ F (d) a = F - m
3.
Expand 3(x - 4).
(a) 3x + 12 (b) 3x - 7 (c) 3x - 12 (d) 3x - 4
4.
Factorise x² - 9.
(a) (x - 3)(x - 3) (b) (x + 3)(x + 9) (c) x(x - 9) (d) (x - 3)(x + 3)
5.
Make t the subject of v = u + at.
(a) t = (v + u) ÷ a (b) t = v - u + a (c) t = (v - u) ÷ a (d) t = (u - v) ÷ a
6.
Factorise 6x² + 9x.
(a) 3(2x² + 3x) (b) 3x(2x + 3) (c) 6x(x + 9) (d) 3x(2x + 9)
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Expand 2(x + 5).
8.
Factorise 12a - 18.
9.
Make r the subject of C = 2πr.
10.
Expand (x + 3)(x + 2).
11.
Factorise x² + 7x + 12.
12.
Make y the subject of 3x + y = 9.
13.
Expand and simplify 4(2x - 1) - 3(x + 2).
14.
Factorise x² - 100.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
The area of a rectangle is A = lw. If A = 48 cm² and l = 8 cm, find the width w.
16.
A car travels a distance d = vt. If v = 60 km/h and t = 2.5 hours, find d.
17.
The perimeter of a square is P = 4s. If P = 36 cm, find the side length s.
18.
A number n satisfies n² - 25 = 0. Find the two possible values of n.
19.
The area of a triangle is A = ½bh. If A = 20 cm² and b = 8 cm, find the height h.
20.
Make x the subject of y = mx + c, then find x when y = 19, m = 3 and c = 4.
Answer Key
1. a) x(x + 5)
2. b) a = F ÷ m
3. c) 3x - 12
4. d) (x - 3)(x + 3)
5. c) t = (v - u) ÷ a
6. b) 3x(2x + 3)
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
How is x² + 5x factorised?
x(x + 5), option (a) in this worksheet (Q1).
What is a when F = ma?
a = F ÷ m, option (b) in this worksheet (Q2).
What does 3(x − 4) expand to?
3x − 12, option (c) in this worksheet (Q3).