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Algebra - Writing and using formulas

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A formula is a mathematical rule expressed in symbols that shows the relationship between different quantities (variables).

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Variables are letters used to represent numbers that can change, while constants are fixed numerical values.

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Substitution involves replacing the letters in a formula with specific numbers to calculate a value.

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Writing a formula requires translating a real-life scenario or a word problem into an algebraic equation with an equals sign (=).

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The 'subject' of a formula is the variable that stands alone, usually on the left-hand side of the equals sign.

📐Formulae

P=2(l+w)P = 2(l + w) (Perimeter of a rectangle)

A=l×wA = l \times w (Area of a rectangle)

s=dts = \frac{d}{t} (Average speed = distance divided by time)

C=nxC = nx (Total cost = number of items ×\times price per item)

F=1.8C+32F = 1.8C + 32 (Converting Celsius to Fahrenheit)

💡Examples

Problem 1:

A taxi company charges a fixed 'pick-up' fee of 5andthen5 and then 2 for every kilometer (k) traveled. Write a formula for the total cost (C).

Solution:

C=2k+5C = 2k + 5

Explanation:

The total cost starts at a constant 5. For every kilometer kk, we add 2, which is expressed as 2×k2 \times k or 2k2k.

Problem 2:

Given the formula v=u+atv = u + at, find the value of vv when u=10u = 10, a=2a = 2, and t=5t = 5.

Solution:

v=20v = 20

Explanation:

Substitute the values into the formula: v=10+(2×5)v = 10 + (2 \times 5). Following the order of operations (BODMAS/BIDMAS), calculate the multiplication first: 10+10=2010 + 10 = 20.

Problem 3:

The perimeter (PP) of a regular pentagon is given by the formula P=5sP = 5s, where ss is the length of one side. Find the side length if the perimeter is 35 cm.

Solution:

s=7 cms = 7\text{ cm}

Explanation:

Substitute the known value into the formula: 35=5s35 = 5s. To find ss, divide both sides by 5: 35÷5=735 \div 5 = 7.