Fundamental Concepts (Algebra)
ICSE Class 6 · Mathematics · Chapter 18
What this chapter covers
- Constants, variables and unknowns
- Literal numbers
- Terms and expressions
- Factors and coefficients
- Like and unlike terms
- Polynomials and degree
Key points
- Algebra uses letters to stand for numbers and follows the same rules as arithmetic.
- A pattern that works in every case can be written as one general rule with a letter, such as "the sum of the first n odd numbers is n × n".
- A constant has a fixed value; a variable can take different values; an unknown is one particular number still to be found.
- Literal numbers are letters used for numbers. Write 3 × a as 3a, a × a as a2, and x ÷ 4 as (x)/(4).
- An algebraic expression is made of terms joined by + or - signs. The sign in front of a term belongs to it.
- A monomial has one term, a binomial two terms and a trinomial three terms.
- The factors of a term are the things multiplied to make it. The numerical coefficient is the number factor with its sign.
- Like terms have the same letters with the same powers; unlike terms do not.
- A polynomial has only whole-number powers of its letters and no letter in a denominator.
- The degree of a term is the sum of the powers of its letters; the degree of a polynomial is the highest degree of its terms.
Questions answered
In the rule "the perimeter of a square is 4s", which is the constant and which is the variable?
4 is the constant and s, the side of the square, is the variable.
Riya thinks of a number, adds 9 and gets 20. Write this using a letter for the unknown, and find the number.
If the number is x, then x + 9 = 20. The number is 11, because 11 + 9 = 20.
Write in short form: y × y × 3 × y.
3y3.
Write the terms of 7a2 - 4ab + b - 2 and name its constant term.
The terms are 7a2, -4ab, b and -2. The constant term is -2.
Is 5pqr a monomial, a binomial or a trinomial?
A monomial, because p, q and r are only multiplied, so it has just one term.
In -8x2y, write the numerical coefficient and the coefficient of y.
The numerical coefficient is -8. The coefficient of y is -8x2.
Pick out the like terms: 3mn, 3m, -mn, 5nm, m2n.
3mn, -mn and 5nm are like terms. 3m and m2n are unlike all of these.
Find the degree of 2x2y + 5xy - 3y4 + 1.
The terms have degrees 3, 2, 4 and 0. The highest is 4, so the degree is 4.