P5 Explain the Charasteristics of the Local Business Environment

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  • Topic: Expression, Factorization, Multiplication
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Homework Sheet - Basic Algebra

1. John and Sarah are simplifying this expression.

3a + 8b + 7a – 6b

John says the answer is 2a + 2b and Sarah says the answer is 10a + 14b. What is the correct answer?
Sarah

2. Simplify these expressions.

a) 4d + 6e – 2d – 3e = 2d-3e
b) 12g – 3h – 8g + h = 4g-4h
c) k + 2k + 3k – m – 2m – 3m = 6k-3m
d) 7c + 4d – 10c + 5d = -3c+9d

3. Multiply out these brackets.

a) 3(2a + 7) = 6a+21 b) 5(3x – 2y) = 15x-10c) 2(4g2 – 3g) = 8g2-6

4. Expand the brackets and then simplify the expression.

a) 2(x + 8) + 3(x + 1) = 2x+16+3x+3 = 5x+19
b) 3(2x + 3) + 2(2x – 3) = 6x+9+4x-6 = 10x+15
c) 4(2a – 5) + 3(a – 1) = 8a-20+3a-3 = 11a-23
d) 2(4a + 1) – 2(a – 1)= 8a+2-2a-2 = 6a

5. Factorise these expressions by removing a common factor.

a) 4a + 6 = 2(2a+3)b) 9x – 6 = 3(3x-2)c) 7g2 – 2g = g(7g-2) d) 4b2 + 6b = b (4b+6)e) 12x2 + 3x = 6x(2x f) 6ab – 9a = 3a(2b-3)

6. The formula for working out the perimeter of a rectangle is P = 2(b + h) where b is the base length and h is the height. The formula for the perimeter of a square is P = 4s where s is the length of each side of the square.

h
s

b

Chloe says the rectangle will have a longer perimeter than the square. Find two examples to show that she is sometimes correct and sometimes wrong.

Example (Chloe correct)Example (Chloe wrong)

7. The cost of hiring a wallpaper stripper at two shops is shown (C is the cost in £, d is the number of days hired).

“Hire is Us” “Low-Hire” uses the formulauses the formula
C = 5d + 3C = 4d + 6

Junade is not sure how many days he will need to hire the machine. Use different values for d to explain which shop he might choose.

8. A formula can approximately predict a boy’s expected adult height (h) by first adding together his mother’s height (m) and father’s height (f) (in cm), to 12.5cm...
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