Year 10 Mathematics Core Assessment Task 3

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%

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.

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.

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.

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.

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.

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.

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.