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Algebra Mastery Revision

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Algebra Mastery Revision

Algebra symbols and equations

📚 Part 1: Expressions and Substitution

1. Simplify the following expressions:

a) 3x + 5x - 2x = _______________

b) 4a - 7 + 2a + 3 = _______________

c) 2(3y + 4) = _______________

2. If x = 3 and y = -2, find the value of:

a) 2x + 3y = _______________

b) x² - 4y = _______________

c) 3(x - y) + 5 = _______________

3. Expand and simplify:

a) 3(x + 4) - 2(x - 1) = _______________

b) (x + 3)(x + 2) = _______________

4. Factorise completely:

a) 6x + 9 = _______________

b) x² + 5x + 6 = _______________

c) 2x² - 8x = _______________

🔄 Part 2: Changing the Subject

5. Make x the subject of each formula:

a) y = 3x + 7

x = _______________

b) P = 2x + 5y

x = _______________

c) A = πx²

x = _______________

6. Rearrange to make the letter in brackets the subject:

a) v = u + at (make t the subject)

t = _______________

b) A = ½bh (make h the subject)

h = _______________

c) E = mc² (make m the subject)

m = _______________

🌟 Part 3: Real-World Applications

7. A mobile phone plan costs $25 per month plus $0.20 per text message.

a) Write a formula for the total cost (C) in terms of the number of text messages (t):

C = _______________

b) Calculate the cost if 150 text messages are sent: $_______________

c) Rearrange your formula to find the number of texts in terms of cost:

t = _______________

8. The temperature in Celsius (C) can be converted to Fahrenheit (F) using: F = 1.8C + 32

a) Find the Fahrenheit temperature when C = 25°C:

F = _______________°F

b) Rearrange the formula to make C the subject:

C = _______________

c) Use your rearranged formula to find the Celsius temperature when F = 86°F:

C = _______________°C

9. Challenge Problem: The area of a trapezium is given by A = ½(a + b)h, where a and b are the parallel sides and h is the height.

a) Make b the subject of the formula:

b = _______________

b) If A = 60 cm², a = 8 cm, and h = 6 cm, find the length of side b:

b = _______________ cm

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