MCR 3U1 Unit 1: Algebraic Skills Review

A set of vocabulary flashcards covering Grade 10 algebraic skills, polynomial definitions, factoring methods, systems of equations, and quadratic properties as reviewed in MCR 3U1 Unit 1.

Variable

A letter whose value can vary.

Numerical Coefficient

The numerical (number) value in front of the variables in a term.

Literal Coefficient

The variable (letter) part of a term including the letters’ exponents.

Constant Term

A term without variables; it is a number without a letter.

Polynomial

An expression which has terms added or subtracted.

Monomial

An expression with one term where multiplication joins all parts.

Binomial

An expression with two terms that are separated by addition or subtraction signs.

Trinomial

An expression with three terms that are separated by addition or subtraction signs.

Degree of a Term

The sum of all the exponents on the variables within a term.

Degree of a Polynomial

The degree equal to the highest degree term within the expression.

Descending Order

When terms in an expression are written from highest degree to lowest degree, with constant terms written last.

Like Terms

Terms that have the exact same literal coefficient, meaning the exact same variables with the exact same exponents.

Distributive Law (Property)

Rule stating that every term in the first bracket must be multiplied by every term in the second bracket; in general: $(a + b)(c + d) = ac + ad + bc + bd$.

Method of Substitution

An algebraic method for solving a linear system that replaces one variable with an expression in terms of the other to result in one equation with one unknown.

Method of Elimination

An algebraic method for solving a linear system by adding or subtracting equations to eliminate a variable.

Common Factoring

The process of identifying the greatest common factor (GCF) and dividing the expression by that factor.

Difference of Squares

A factoring pattern for expressions in the form $a^2 - b^2$, resulting in $(a - b)(a + b)$.

Simple Trinomial

A trinomial in the form $x^2 + bx + c$ where factors are written as $(x + m)(x + n)$ such that $m + n = b$ and $m \times n = c$.

Complex Trinomial

A trinomial in the form $ax^2 + bx + c$ where the lead coefficient $a \neq 1$.

Perfect Square Trinomial

A trinomial where the linear term is double the product of the square roots of the quadratic and constant terms, such as $4x^2 - 12x + 9 = (2x - 3)^2$.

Factoring by Grouping

A method used when terms share common factors in pairs, allowing for the extraction of a binomial common factor.

t-Substitution

A method for factoring quadratic-type expressions by substituting a simple variable ($t$) for a multi-variable or higher-degree algebraic expression.

Standard Form

The quadratic equation form $y = ax^2 + bx + c$.

Factored Form

The quadratic equation form $y = a(x - s)(x - t)$, which identifies the x-intercepts as $(s, 0)$ and $(t, 0)$.

Vertex Form

The quadratic equation form $y = a(x - h)^2 + k$, identifying the vertex as $(h, k)$.

Roots

The values of x where the parabola touches or crosses the x-axis, also referred to as zeros, solutions, or x-intercepts.

The Discriminant

The expression $b^2 - 4ac$ found under the square root in the quadratic formula, used to determine the nature of the roots.

Two Distinct Real Roots

The nature of the roots of a quadratic equation when the discriminant $b^2 - 4ac > 0$.

One Real Root (Two Equal Roots)

The nature of the roots of a quadratic equation when the discriminant $b^2 - 4ac = 0$.

No Real Solutions

The nature of the roots of a quadratic equation when the discriminant $b^2 - 4ac < 0$.

Completing the Square

A method used to convert a quadratic equation from Standard Form to Vertex Form to find the maximum or minimum.

Partial Factoring

A procedure to find the axis of symmetry by setting $y$ equal to the y-intercept ($c$) and finding two x-values with the same y-value.

Optimization

The process of finding the maximum or minimum value of a quadratic function by determining the y-value of the vertex.