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Year 10 Algebra Rubric

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Year 10 Algebra Rubric

Use this self-assessment to show what you can do. For each task, write your working, then circle a level: Getting started, Secure, or Stretch. Use a calculator or graphing tool only where the task says you may.

Mountain hike challenge

Grace, Lachlan and Dylan are planning a mountain hike. Complete the tasks and use the rubric at the end to reflect on your algebra.

1.A route-planning app stores a distance expression as (3a²b)(2ab³). Simplify it fully. Then state which exponent laws you used.

2.The area of a rectangular lookout platform is represented by (x + 4)(x + 2). Expand the expression, then factorise x² + 7x + 12.

3.A simplified model for a hiker’s height above a valley floor is h(t) = −t² + 6t, where t is time in hours after departure. At what times is the hiker at valley-floor height? Show an algebraic method.

4.For the function y = (x − 2)² − 3, give the vertex, axis of symmetry, direction of opening and y-intercept. Sketch the graph on the axes.

5.Two trail-marker packs contain a total of 18 markers. One pack has twice as many markers as the other, plus 3. If the smaller pack contains x markers and the larger contains y, solve x + y = 18 and y = 2x + 3.

6.The distance in kilometres remaining after t hours is modelled by r(t) = 24 − 3t. Find r(4), and explain what the result means in the hike context.

7.A student solves x² − 5x + 6 = 0 by factorising. Write the factorised equation and both solutions. How could a graph confirm the solutions?

8.A shuttle to the trailhead costs $8 per person plus a fixed $12 booking fee. Write a function C(n) for the cost for n hikers. Find the cost for 5 hikers and explain why the model is linear.

9.A lookout platform has area x² + 2x − 15 square metres. Factorise the expression. If the platform’s side lengths are x + 5 and x − 3, explain what values of x make both lengths positive.

Self-assessment rubric

After completing the tasks, circle one description in each row. Use your working above as evidence.

Algebraic operations and exponent laws: Getting started — I need prompts to simplify. | Secure — I simplify accurately and explain exponent rules. | Stretch — I choose efficient methods for complex expressions.

Quadratics: Getting started — I can expand or factorise simple expressions with support. | Secure — I expand, factorise and solve quadratics accurately. | Stretch — I recognise efficient methods and justify solutions.

Graphs, functions and modelling: Getting started — I identify some features or substitute into a rule. | Secure — I connect a rule to its graph and interpret results in context. | Stretch — I evaluate a model’s assumptions and explain its limitations.

Next step: Which task best shows your strongest algebra skill? What will you practise next, and what evidence tells you that?