Mathematics: Paper 1 - Guidelines for 2025 GEC Tests

Subject Guidelines for the 2025 GEC Tests

Mathematics: Paper 1

Content Area: Numbers, Operations and Relationships
Whole Numbers

  • Properties of Numbers: Describe the real number system by recognizing, defining, and distinguishing properties of the following types:

    • Natural Numbers: Counting numbers starting from 1 (e.g., 1, 2, 3, …).
    • Whole Numbers: Natural numbers including zero (0, 1, 2, 3, …).
    • Integers: Whole numbers that can be positive, negative, or zero (…, -2, -1, 0, 1, 2, …).
    • Rational Numbers: Numbers that can be expressed as the fraction of two integers (e.g., $ rac{1}{2}$, 0.75).
    • Irrational Numbers: Numbers that cannot be expressed as the fraction of two integers (e.g., $ rac{ ext{√2}}{1}$, $ ext{π}$).

  • Multiples and Factors: Use prime factorization of numbers to find the Least Common Multiple (LCM) and Highest Common Factor (HCF).

  • Solving Problems: Solve problems in contexts involving:

    • Ratio
    • Rate
    • Direct Proportion
    • Indirect Proportion
    • Finance
Integers

  • Properties of Integers: Apply commutative, associative, and distributive properties of addition and multiplication for integers.

    • Additive Inverses: For any integer $a$, its additive inverse is $-a$ such that $a + (-a) = 0$.
    • Multiplicative Inverses: For any integer $a
      eq 0$, its multiplicative inverse is $ rac{1}{a}$ such that $a imes rac{1}{a} = 1$.

  • Calculations with Integers: Perform calculations involving all four operations (addition, subtraction, multiplication, and division) with integers, including operations that involve:

    • Squares: $a^2$
    • Cubes: $a^3$
    • Square Roots: $ ext{√}a$
    • Cube Roots: $ ext{∛}a$
Exponents

  • Calculations Using Exponential Form: Apply the following general laws of exponents:

    • Multiplication: $ a^m imes a^n = a^{m+n} $
    • Division: $ a^m ÷ a^n = a^{m-n}, ext{ if } m > n $
    • Power of a Power: $ (a^m)^n = a^{m imes n} $
    • Power of a Product: $ (a imes b)^n = a^n imes b^n $
    • Zero Exponent: $ a^0 = 1 $
    • Negative Exponent: $ a^{-m} = rac{1}{a^m} $

  • Perform Calculations: Perform calculations involving all four operations using numbers in exponential form.

Patterns, Functions and Algebra
Numeric and Geometric Patterns

  • Investigate and Extend Patterns: Investigate and extend numeric patterns looking for relationships between numbers, including patterns represented in:

    • Physical or Diagram Form: Exploring tangible forms of patterns.
    • Tables: Tabular representation of numeric relationships.
    • Algebraically: Pattern relationships demonstrated with algebraic expressions.
    • Geometric Patterns: Identify geometric relationships similar to numeric patterns.

  • General Rules for Relationships: Describe and justify the general rules for observed relationships between numbers using:

    • Own words.
    • Algebraic language.
Algebraic Expressions

  • Algebraic Language: Identify and classify like and unlike terms in algebraic expressions and recognize:

    • Coefficients: The numerical factor in terms.
    • Exponents: The power to which a number or variable is raised.
    • Types of Expressions: Recognize and differentiate between monomials, binomials, and trinomials.

  • Expand and Simplify Expressions: Apply commutative, associative, and distributive laws for rational numbers to simplify algebraic expressions involving operations. This includes:

    • Determining squares and cubes of single algebraic terms.
    • Finding the product of two binomials or the square of a binomial.
    • Determining numerical values of algebraic expressions by substitution.

  • Factorization: Factorize algebraic expressions, considering:

    • Difference of Two Squares.
    • Trinomials of the Form: $ x^2 + bx + c $ and $ ax^2 + bx + c $, where $ a $ is a common factor.

  • Simplifying Expressions: Simplify algebraic expressions that involve the above factorization processes and also simplify algebraic fractions using factorization.

Algebraic Equations
  • Setting Up Equations: Set up equations to describe problem situations.
  • Analyzing Equations: Analyze and interpret equations describing a situation.
  • Solving Equations: Solve equations by:
    • Inspection.
    • Using additive and multiplicative inverses.
    • Employing laws of exponents.
    • Substitution.
    • Generating tables of ordered pairs.
    • Factorization.
    • Form: A product of factors = 0.
Functions and Relationships
Input and Output Values
  • Determine Values: Determine input values, output values, or rules for patterns and relationships using:
    • Flow Diagrams
    • Tables
    • Formulae
    • Equations
Equivalent Forms
  • Check Equivalence: Determine, interpret, and justify the equivalence of different descriptions of the same relationship or rule presented:
    • Verbally
    • In flow diagrams
    • In tables
    • By formulae
    • By equations
    • By graphs on a Cartesian plane
Graphs

  • Interpreting Graphs: Focus on features of graphs, specifically:

    • x-intercept: The point where the graph crosses the x-axis.
    • y-intercept: The point where the graph crosses the y-axis.
    • Gradient: The slope of the line, indicating its steepness.

  • Drawing Graphs: Use tables of ordered pairs to plot points on the Cartesian plane and draw graphs, with a focus on:

    • Drawing linear graphs from given equations.
    • Determining equations from given linear graphs.