Number 19 continued
Algebra 12
What all should know
Solve more complex problems by breaking them into smaller steps or tasks, choosing and using efficient techniques for calculation.
What most should know
Check results using appropriate methods.
Use a calculator efficiently and appropriately to perform complex calculations with numbers of any size, knowing not to round during intermediate steps of a calculation; use the constant, and sign change keys, function keys for powers, roots and fractions, brackets and the memory.
Enter numbers into a calculator and interpret the display in context (negative numbers, fractions, decimals, percentages, money, metric measures, time).
Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT; use trial and improvement where a more efficient method is not obvious.
What some should know
Use the reciprocal key of a calculator.
Enter numbers in standard form into a calculator and interpret the display.
Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes.
Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.
Recognise that equations of the form y = mx + c correspond to straight-line graphs.
Use the prime factor decomposition of a number.
Use ICT to estimate square roots and cube roots.
Use index notation for integer powers and simple instances of the index laws.
Given values for m and c, find the gradient of lines given by equations of the form y = mx + c.
Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations, including distancetime graphs.
Represent problems and synthesise information in algebraic, geometric or graphical form; move from one form to another to gain a different perspective on the problem.
Know and use the index laws (including in generalised form) for multiplication and division of positive integer powers; begin to extend understanding of index notation to negative and fractional powers, recognising that the index laws can be applied to these as well.
Investigate the gradients of parallel lines and lines perpendicular to these lines.
Plot graphs of simple quadratic and cubic functions, e.g. y = x2, y = 3x2 + 4, y = x3.
