Completing the Square (A) WORKSHEET
Suitable for Year groups: Year 10, Year 11
GCSE Tier: Higher Plus
Targeting grades: 8-9
Prerequisite knowledge: Expanding and simplifying expressioms involving double brackets. Addition and subtraction of fractions.
Completing the Square (A) WORKSHEET DESCRIPTION
This worksheet is designed to develop students' understanding of quadratic expressions and how they can be manipulated in different ways.
In Section A, students are introduced to perfect squares by expanding expressions such as (x + a)2, where a is an integer, and matching equivalent expressions. This section builds their foundational knowledge and recognition of perfect squares.
Section B progresses the learning by providing students with an opportunity to expand and simplify expressions in the form (x + a)2 + b, where a and b are integers, match up equivalent expressions, and then write quadratic expressions in this form.
Section C extends this by introducing factorised expressions where a and b are fractions.
The worksheet culminates with an extension task that requires students to express a quadratic in the form a(x + b)2 + c, applying their understanding to a new level of difficulty
In Section A, students are introduced to perfect squares by expanding expressions such as (x + a)2, where a is an integer, and matching equivalent expressions. This section builds their foundational knowledge and recognition of perfect squares.
Section B progresses the learning by providing students with an opportunity to expand and simplify expressions in the form (x + a)2 + b, where a and b are integers, match up equivalent expressions, and then write quadratic expressions in this form.
Section C extends this by introducing factorised expressions where a and b are fractions.
The worksheet culminates with an extension task that requires students to express a quadratic in the form a(x + b)2 + c, applying their understanding to a new level of difficulty
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