Rules and Simple Formulae

Building Rules, Writing Formulae, Substitution, and Solving for Inputs

CAPS Grade 10 Mathematical Literacy

This document explores the essential concepts of Rules and Simple Formulae. It emphasizes translating real-life situations into mathematical expressions, focusing on the "Fixed + Variable" structure, writing symbolic formulae, substitution, and solving for inputs.

1. Building a Rule from a Context

Fixed Value

Starting amount that remains constant

Example: R50 monthly fee

Variable Rate

Amount that varies based on usage

Example: R2 per minute

Word Rule Example

Total Cost = Fifty Rand plus Two Rand times the number of minutes

Fixed + Variable

3 Questions

1 Plumber: R200 call-out + R150/hour. Fixed cost?

R150

R200

R350

R50

2 Phone: R100 monthly + R1.50/min. Variable rate?

R100

R150

R1.50

R101.50

3 Taxi: R25 base + R12/km. Word rule?

Cost = R25 × km

Cost = R12 × km

Cost = R25 + R12/km

Cost = R12 + R25/km

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2. Writing Symbolic Formulae

Example

Let: C = Total Cost, m = minutes

C = 50 + 2m

Key Skill: Define what each letter stands for.

Writing Formulae

3 Questions

1 Plumber: R200 + R150/h. Formula (C=cost, h=hours)?

C = 150h

C = 200 + 150h

C = 200h

C = 150 + 200h

2 Gym: R300 monthly + R50/session. Formula?

C = 300s

C = 50 + 300s

C = 300 + 50s

C = 50s

3 Taxi: R30 base + R18/km. Formula?

C = 30k

C = 30 + 18k

C = 18k

C = 18 + 30k

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3. Substitution (Finding the Output)

Example: C = 50 + 2m, find C when m = 100

Substitute: C = 50 + 2(100)

Multiply: C = 50 + 200

Add: C = 250

Substitution Challenge

Formula: C = 100 + 5m. Find C when m = 20

Hint: Multiply first, then add fixed cost

4. Solving for the Input (Working Backwards)

Example: C = 50 + 2m, if C = 150, find m

150 = 50 + 2m

150 - 50 = 2m → 100 = 2m

m = 100 ÷ 2 = 50 minutes

Working Backwards

3 Questions

1 C = 200 + 50h. If C = 400, find h.

2 hours

4 hours

6 hours

8 hours

2 C = 100 + 2m. If C = 200, find m.

25 min

50 min

75 min

100 min

3 C = 30 + 15k. If C = 120, find k.

4 km

5 km

6 km

7 km

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5. Common Formulae Provided in Exams

Formula Type	Formula	Variables
Temperature	°C = (°F - 32) × 5/9	°C = Celsius, °F = Fahrenheit
Simple Interest	I = P × r × t	I = Interest, P = Principal, r = rate, t = time
Perimeter (Rectangle)	P = 2(l + w)	P = Perimeter, l = length, w = width
Area (Rectangle)	A = l × w	A = Area, l = length, w = width

Exam Tip: Always write down the formula first, then substitute values - this shows your method and helps earn marks even if your final answer is incorrect.

Final Assessment

8 Questions

1 Painter: R400 call-out + R180/hour. Fixed cost?

R180

R400

R580

R220

2 Formula for painter above? (C=cost, h=hours)

C = 180h

C = 400 + 180h

C = 400h

C = 180 + 400h

3 Using C = 400 + 180h, find C when h = 5.

R900

R1000

R1100

R1300

4 C = 50 + 25m. If C = 200, find m.

5 Taxi: R35 base + R14/km. Word rule?

Cost = R35 × km

Cost = R14 × km

Cost = R35 + R14/km

Cost = R14 + R35/km

6 Simple Interest formula is:

I = P × r × t

I = P × r × t ÷ 100

I = P + r + t

I = (P × r)/t

7 C = 120 + 8m, find m when C = 200.

8 Cleaner: R150 call-out + R80/hour. Cost for 4 hours?

R320

R400

R470

R600

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Conclusion

Mastering Rules and Simple Formulae is vital for Grade 10 Mathematical Literacy. By understanding how to build rules, write formulae, perform substitution, and solve for inputs, students can confidently tackle real-life mathematical problems.