algebra
Syllabus Context
1. Use tables to represent a repeating-pattern situation
2. generalise and explain patterns and relationships in words and numbers 3. write arithmetic expressions for particular terms in a sequence 4. use tables, diagrams and graphs as tools for representing and analysing linear, quadratic and exponential patterns and relations (exponential relations limited to doubling and tripling) 5. develop and use their own generalising strategies and ideas and consider those of others 6. present and interpret solutions, explaining and justifying methods, inferences and reasoning 7. find the underlying formula written in words from which the data is derived (linear relations) 8. find the underlying formula algebraically from which the data is derived (linear, quadratic relations) 9. show that relations have features that can be represented in a variety of ways 10. distinguish those features that are especially useful to identify and point out how those features appear in different representations: in tables, graphs, physical models, and formulas expressed in words, and algebraically 11. use the representations to reason about the situation from which the relationship is derived and communicate their thinking to others 12. recognise that a distinguishing feature of quadratic relations is the way change varies 13. discuss rate of change and the y-intercept, consider how these relate to the context from which the relationship is derived, and identify how they can appear in a table, in a graph and in a formula 14. decide if two linear relations have a common value (decide if two lines intersect and where the intersection occurs) 15. investigate relations of the form y=mx and y=mx +c 16. recognise problems involving direct proportion and identify the necessary information to solve them 17. explore graphs of motion 18. make sense of quantitative graphs and draw conclusions from them 19. make connections between the shape of a graph and the story of a phenomenon 20. describe both quantity and change of quantity on a graph 21. evaluate expressions of the form • ax + by • a (x + y) • x2+ bx + c • axy, • ax2+ bx + c • x3 + bx2 + cx + d 22. add and subtract simple algebraic expressions of forms such as: • (ax + by + c) ± (dx + ey + f) • (ax2 + bx +c) ± (dx2 + ex + f) • (ax + by + c) ±… ± (dx + ey + f) • (ax2 + bx + c) ±… ± (dx2 + ex + f) 23. use the associative and distributive property to simplify such expressions as: • a(bx + cy + d) + e(fx + gy + h) • a(bx + cy + d) + … + e(fx + gy + h) • a(bx2 + cx + d) • ax(bx2+ c) • (x+y)(x+y) • (x-y)(x-y) 24. multiply expressions of the form: • (ax + b)( cx + d) • (ax + b) (cx2 + dx + e) 25. divide expressions of the form: • ax2 + bx + c ÷ dx + e • ax3+ bx2+ cx + d ÷ ex + f 26. factorise expressions such as • ax, axy • abxy + ay, • sx - ty + tx - sy, • ax2 + bx, • x2 + bx + cx2 – a2 • ax2+ bx + c, difference of two squares a2x2 – b2y2 27. rearrange formulae 28. solve first degree equations in one or two variables, with coefficients elements of Z and solutions also elements of Z 29. solve first degree equations in one or two variables with coefficients elements of Q and solutions also in Q 30. solve quadratic equations of the form x2 + bx + c = 0 and x2 + bx + c is factorisable 31. form quadratic equations given whole number roots 32. solve simple problems leading to quadratic equations 33. solve equations of the form 34. solve linear inequalities 35. explore patterns and formulate conjectures 36. explain findings 37. justify conclusions 38. communicate mathematics verbally and in written form 39. apply their knowledge and skills to solve problems in familiar and unfamiliar contexts 40. analyse information presented verbally and translate it into mathematical form 41. devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions. |
Exam Conext
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Revision Resources & HomeWork Assignments
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