Educational math worksheet combining memory and literacy skills with algebraic problems and real-world examples.

Let's go through the image and solve each section step by step. The worksheet is divided into Memory, Simplify expressions, Literacy, Skill 1, 2, 3, and Stretch sections.

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🔹 Memory Section: Substitution

> "To substitute, replace the variable with its corresponding value."

Example given:
Let $ a = 5 $
Then $ 4a = 4 \times a = 4 \times 5 = 20 $

This shows how to substitute a number for a variable in an expression.

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🔹 Simplify the following expressions (ROK)

We are asked to simplify these:

1) $ 3 \times a $ → This is simply $ 3a $

2) $ b + b + b + b $ → There are four $ b $'s → $ 4b $

3) $ a + b $ → Already simplified → $ a + b $

4) $ a \times a $ → $ a^2 $

5) What is the formula for the perimeter of this regular shape?

The shape shown is a regular pentagon (5 equal sides), with side length labeled $ h $.
Perimeter = sum of all sides → $ 5h $

✔ So, the formula is: $ P = 5h $

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🔹 Literacy: Explain the links between substitution and football. Use examples.

Explanation:

Substitution in math means replacing variables with actual values — just like in football, where players take positions or roles on the field.

For example:
- In football, a player might be assigned a role like “striker” or “defender.” When the team substitutes a player during a match, they replace one player with another who fills that same role.
- Similarly, in algebra, if we have an expression like $ 3x + 2 $, and we know $ x = 4 $, we substitute 4 for $ x $:
$ 3(4) + 2 = 12 + 2 = 14 $

So, substitution is like replacing a placeholder (variable) with a real value — just as a football player is replaced by another who takes over their role.

Another example:
- A team’s formation is like a formula. If the formation is 4-4-2 (4 defenders, 4 midfielders, 2 forwards), and one midfielder gets injured, you substitute them with another midfielder. That’s like substituting a variable in a formula with a new value.

✔ So, substitution is about replacing parts with equivalents — whether it's numbers in math or players in football.

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🔹 Skill 1: Let $ x = 4 $ and $ y = -3 $

Evaluate each expression:

1) $ 3x + 6 = 3(4) + 6 = 12 + 6 = 18 $
2) $ 3x - 15 = 3(4) - 15 = 12 - 15 = -3 $
3) $ 2y - 2 = 2(-3) - 2 = -6 - 2 = -8 $
4) $ 4x + 9 = 4(4) + 9 = 16 + 9 = 25 $
5) $ 3 - x = 3 - 4 = -1 $
6) $ 3 - y = 3 - (-3) = 3 + 3 = 6 $
7) $ 5 - 2x = 5 - 2(4) = 5 - 8 = -3 $
8) $ 7 + y = 7 + (-3) = 4 $

✔ Skill 1 Answers:
1) 18
2) -3
3) -8
4) 25
5) -1
6) 6
7) -3
8) 4

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🔹 Skill 2: Let $ x = 2 $ and $ z = 5 $

1) $ x^2 + 5 = (2)^2 + 5 = 4 + 5 = 9 $
2) $ x^2 - 3 = 4 - 3 = 1 $
3) $ 2x^2 + 3 = 2(4) + 3 = 8 + 3 = 11 $
4) $ 6x^2 - 7 = 6(4) - 7 = 24 - 7 = 17 $
5) $ x^3 - 7 = (8) - 7 = 1 $
6) $ z^2 + 3 = 25 + 3 = 28 $
7) $ 3z^2 - 80 = 3(25) - 80 = 75 - 80 = -5 $

✔ Skill 2 Answers:
1) 9
2) 1
3) 11
4) 17
5) 1
6) 28
7) -5

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🔹 Skill 3: Let $ s = -2 $ and $ t = -4 $

1) $ s^2 + 4 = (-2)^2 + 4 = 4 + 4 = 8 $
2) $ s^2 - 7 = 4 - 7 = -3 $
3) $ 2s^2 + 5 = 2(4) + 5 = 8 + 5 = 13 $
4) $ 6s^2 - 2 = 6(4) - 2 = 24 - 2 = 22 $
5) $ t^2 + 7 = (-4)^2 + 7 = 16 + 7 = 23 $
6) $ t^2 - 20 = 16 - 20 = -4 $
7) $ t^3 + 1 = (-4)^3 + 1 = -64 + 1 = -63 $

✔ Skill 3 Answers:
1) 8
2) -3
3) 13
4) 22
5) 23
6) -4
7) -63

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🔹 Stretch Questions

#### 1) Given expressions:
$$
10 - 2x,\quad 3x + 10,\quad x^2,\quad -3x,\quad x^{-1},\quad x^0
$$
Let $ x = 5 $

Evaluate each:

- $ 10 - 2x = 10 - 10 = 0 $
- $ 3x + 10 = 15 + 10 = 25 $
- $ x^2 = 25 $
- $ -3x = -15 $
- $ x^{-1} = \frac{1}{x} = \frac{1}{5} = 0.2 $
- $ x^0 = 1 $ (Any non-zero number to power 0 is 1)

Now list them in ascending order:

- $ -15 $, $ 0 $, $ 0.2 $, $ 1 $, $ 25 $, $ 25 $

So ascending order:
→ $ -3x $, $ 10 - 2x $, $ x^{-1} $, $ x^0 $, $ 3x + 10 $, $ x^2 $

But note: $ 3x+10 = 25 $, $ x^2 = 25 $ → both equal

So final ascending order:
$$
-3x < 10 - 2x < x^{-1} < x^0 < 3x + 10 = x^2
$$

a) Ascending order:
1. $ -3x $ → -15
2. $ 10 - 2x $ → 0
3. $ x^{-1} $ → 0.2
4. $ x^0 $ → 1
5. $ 3x + 10 $ → 25
6. $ x^2 $ → 25

✔ Order: $ -3x,\ 10 - 2x,\ x^{-1},\ x^0,\ 3x+10,\ x^2 $

b) Can you reverse the order?
Yes, but only if you start from largest to smallest.
Descending order: $ x^2 = 3x+10 $, $ x^0 $, $ x^{-1} $, $ 10 - 2x $, $ -3x $

But since $ x^2 $ and $ 3x+10 $ are equal, they can be swapped.

✔ Yes, reversing is possible.

c) Could you make every expression have the same value?

Try to find $ x $ such that all expressions are equal.

Let’s suppose:
- $ x^0 = 1 $ always (for $ x \ne 0 $)
- $ x^{-1} = \frac{1}{x} $
- We want $ \frac{1}{x} = 1 $ → $ x = 1 $

Check if all expressions equal when $ x = 1 $:

- $ 10 - 2x = 10 - 2 = 8 $
- $ 3x + 10 = 3 + 10 = 13 $
- $ x^2 = 1 $
- $ -3x = -3 $
- $ x^{-1} = 1 $
- $ x^0 = 1 $

Values: 8, 13, 1, -3, 1, 1 → Not equal.

Try to make them equal?

Suppose we want $ x^2 = x^{-1} $ → $ x^2 = \frac{1}{x} $ → $ x^3 = 1 $ → $ x = 1 $

At $ x=1 $, still not equal.

Is there any $ x $ where all are equal? Unlikely because:
- $ x^0 = 1 $
- $ x^{-1} = 1/x $
- $ x^2 $ grows fast
- Linear terms vary

Only way all could be equal is if all expressions evaluate to same number.

But $ x^0 = 1 $ always → so all must be 1.

Set $ x^0 = 1 $, then need:
- $ 10 - 2x = 1 $ → $ 2x = 9 $ → $ x = 4.5 $
- $ 3x + 10 = 1 $ → $ 3x = -9 $ → $ x = -3 $
- Contradiction

So no single $ x $ makes all expressions equal.

✔ No, you cannot make all expressions have the same value.

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#### 2) Find values of $ a $ and $ b $ when $ p = 10 $

Given:
- $ a = \dfrac{3p^3}{2} $
- $ b = \dfrac{2p^2(p - 3)}{7p} $

Plug in $ p = 10 $:

Find $ a $:
$$
a = \frac{3(10)^3}{2} = \frac{3(1000)}{2} = \frac{3000}{2} = 1500
$$

Find $ b $:
$$
b = \frac{2(10)^2(10 - 3)}{7(10)} = \frac{2(100)(7)}{70} = \frac{1400}{70} = 20
$$

✔ So:
- $ a = 1500 $
- $ b = 20 $

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✔ Final Summary of Answers

#### ROK – Simplify:
1) $ 3a $
2) $ 4b $
3) $ a + b $
4) $ a^2 $
5) $ P = 5h $

#### Literacy:
Substitution is like replacing a player in football — e.g., a midfielder substituted with another who plays the same role. In math, we replace variables with values.

#### Skill 1 (x=4, y=-3):
1) 18
2) -3
3) -8
4) 25
5) -1
6) 6
7) -3
8) 4

#### Skill 2 (x=2, z=5):
1) 9
2) 1
3) 11
4) 17
5) 1
6) 28
7) -5

#### Skill 3 (s=-2, t=-4):
1) 8
2) -3
3) 13
4) 22
5) 23
6) -4
7) -63

#### Stretch:
1a) Ascending: $ -3x,\ 10 - 2x,\ x^{-1},\ x^0,\ 3x+10,\ x^2 $
1b) Yes, descending order possible
1c) No, cannot make all values equal
2) $ a = 1500 $, $ b = 20 $

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