Year 10 Mathematics Core Assessment Task 3

Assessment Overview

• Year 10 Mathematics Core assessment: Task no 3
• Focus areas: Simultaneous Equations, Quadratic Equations, Linear and Non-Linear Relationships
• Assessment date: Issued on 23 July 2024, conducted on 30 August 2024
• Total weight of task: 20%

Outcomes Assessed

• MA5-EQU-P-01: Solving monic quadratic, linear inequalities, and cubic equations.
• MA5-EQU-P-02: Solving linear equations with multiple steps, including quadratic and simultaneous equations.
• MA5-LIN-C-01: Finding midpoint, gradient, length of intervals, and graphing linear relationships.
• MA5-LIN-C-02: Interpreting linear relationships using gradient/slope-intercept form.
• MA5-LIN-P-01: Applying transformations and solving problems in line equations.
• MA5-NLI-C-01: Connecting algebraic and graphical representations of quadratic and exponential relationships.
• MA5-NLI-C-02: Comparing features of parabolas in diverse contexts.
• MA5-NLI-P-02: Interpreting non-linear relationships and transformations both algebraically and graphically.
• MAO-WM-01: Enhancing understanding and fluency in mathematics through problem-solving techniques.

Test Structure

• Format: In-class examination with various question types.
• Types of questions include:
  • Multiple Choice
  • Short Response
  • Working Mathematically
• Duration: 50 minutes + 5 minutes reading time.

Equipment Required

• Writing instruments: Pen, pencil.
• Calculating device: Calculator.
• Measuring tool: Ruler.

Feedback and Marking Criteria

• Marking criteria to be discussed in class; includes model answers.
• Key evaluation elements:
  • Correct solutions for questions asked.
  • Logical presentation of working and proofs.
  • Valid reasoning and acceptable format for proofs.
  • Clear explanations when necessary.
  • Appropriate mathematical terminology.
  • Neat diagrams/graphs with correct labeling.
  • Use of proper units and rounding with indicated extent.

Absences and Penalties

• In case of absence, complete SMSM Medical Form and Illness/Misadventure form must be submitted on the first return to school.
• Late submission penalty: 20% deduction per day, maximum of 5 days.
• Assessment malpractice or plagiarism leads to a zero mark; resubmission required.

Simultaneous Equations

• Definition: A collection of equations with multiple variables solved simultaneously for their values.
• Types:
  • Linear Simultaneous Equations: Formulated as ax + by = c, where a, b, and c are constants.
  • Non-linear Simultaneous Equations: Includes at least one equation that is not linear, such as quadratics.
• Methods of Solving:
  • Substitution: Isolate a variable in one equation and substitute it into another.
  • Elimination: Combine equations to eliminate one variable and solve for the other.
  • Graphical Method: Graph each equation to find intersection points, representing solutions.

Quadratic Equations

• Standard Form: Expressed as ax² + bx + c = 0, where a is non-zero.
• Key Features:
  • Roots: Quadratic equations can have real or complex solutions.
  • Discriminant (D): Calculated as D = b² - 4ac; it determines the nature of the roots:
    • D > 0: Two distinct real roots exist.
    • D = 0: One real root, repeated.
    • D < 0: Two complex roots are present.
• Methods of Solving:
  • Factoring: Breaking down into the form (px + q)(rx + s) = 0.
  • Quadratic Formula: Used to find roots as x = [-b ± √(b² - 4ac)] / (2a).
  • Completing the Square: Rearranging the equation to form a perfect square trinomial.

Linear Relationships

• Definition: A relationship characterized by a straight line on a graph.
• Equation Form: Represented as y = mx + b, where:
  • m: Slope, indicating the rate of change of y with respect to x.
  • b: Y-intercept, the value of y when x equals zero.
• Characteristics:
  • Slope signifies the direction (positive for upward, negative for downward) and steepness of the line.
  • Maintains a consistent rate of change between the variables.
• Graphing: Creating a straight line by plotting points derived from values of x and their corresponding y values.

Non-Linear Relationships

• Definition: Relationships that create curves or complex patterns on a graph rather than straight lines.
• Types:
  • Quadratic Relationships: Represented by parabolic curves (example: y = ax² + bx + c).
  • Exponential Relationships: Express growth or decay patterns (example: y = ab^x).
  • Logarithmic Relationships: Involves logarithmic functions (example: y = log(x)).
• Characteristics:
  • Exhibit varying rates of change and can form cycles or curves.
• Graphing: Involves plotting discrete points and connecting them to reveal the underlying relationship.