krit.club logo

Algebra - Using variables and constants

Grade 6IGCSE

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

🔑Concepts

•

Variable: A letter (like xx, yy, or nn) used to represent an unknown value or a value that can change.

•

Constant: A fixed value or a number that does not change (e.g., 55, −10-10, 1/21/2).

•

Term: A single part of an expression which can be a number, a variable, or a product of numbers and variables (e.g., 4x4x, 77, abab).

•

Coefficient: The numerical factor of a term containing a variable (e.g., in 5y5y, 55 is the coefficient).

•

Algebraic Expression: A mathematical phrase combining variables, constants, and operating symbols (++, −-, ×\times, ÷\div) without an equals sign.

•

Substitution: The process of replacing a variable with a specific numerical value to find the total value of the expression.

📐Formulae

Expression=(Coefficient×Variable)±Constant\text{Expression} = (\text{Coefficient} \times \text{Variable}) \pm \text{Constant}

Perimeter of a Square=4s (where s is the side length)\text{Perimeter of a Square} = 4s \text{ (where } s \text{ is the side length)}

Perimeter of a Rectangle=2l+2w (where l is length and w is width)\text{Perimeter of a Rectangle} = 2l + 2w \text{ (where } l \text{ is length and } w \text{ is width)}

Total Cost=(Price per item×n)+Fixed Charge\text{Total Cost} = (\text{Price per item} \times n) + \text{Fixed Charge}

💡Examples

Problem 1:

Write an algebraic expression for the following: 'Seven more than triple a number xx'.

Solution:

3x+73x + 7

Explanation:

'Triple a number xx' means 3×x3 \times x, and 'seven more than' means we add 77 to that result.

Problem 2:

Evaluate the expression 5a−2b5a - 2b when a=4a = 4 and b=3b = 3.

Solution:

1414

Explanation:

Substitute aa with 44 and bb with 33: (5×4)−(2×3)=20−6=14(5 \times 4) - (2 \times 3) = 20 - 6 = 14.

Problem 3:

A car rental company charges a flat fee of 5050 plus 0.200.20 per kilometer driven (kk). Write the expression for the total cost.

Solution:

50+0.2k50 + 0.2k

Explanation:

The flat fee is a constant (5050). The cost per kilometer depends on the variable kk, so it is 0.20×k0.20 \times k.

Problem 4:

Identify the terms and the coefficient of xx in the expression: 12x−912x - 9.

Solution:

Terms: 12x12x and −9-9; Coefficient of xx: 1212

Explanation:

Terms are separated by plus or minus signs. The coefficient is the number multiplied by the variable xx.