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.

Prepare for the Year 10 Mathematics Core assessment focusing on simultaneous equations, quadratic equations, and both linear and non-linear relationships. This quiz will help you practice key concepts and improve your problem-solving skills before the assessment date on 30 August 2024.