Henry is quite confident in solving simultaneous linear equations, confidently manipulating the equations where x is the subject, even with an arbitrary variable present. He can also apply the cases of number of solutions, by following the conditions - telling apart the gradient term from the y-intercept term.

While not specifically covered in this chapter, Henry could review cancelling out terms or factors in fractions - when the numerator is divisible by the denominator, or the numerator is divisible by a factor in the denominator.

Intercept form, which we hadn’t covered previously, was handled pretty well from Henry, as he was able to independently apply the formula without needing much assistance. Application questions were attempted quite successfully too; Henry was able to apply the required formulas whenever asked or implied, albeit with more simpler questions. Regardless, Henry’s application question skills continue to improve.

Henry should be more cautious around application questions, as he tends to rush through them and omit crucial information. The harder, more extensive applications could be improved on, as it’s not obvious what’s being asked, and Henry is encouraged to tinker around to find the best course of action.

As this topic was only a recap of the content from Year 11, with a slight difficulty increase, Henry found it easier to relearn the content. Particularly, Henry does well with finding the distance, midpoints, gradient, and utilising slope-intercept form whenever required. Henry can also tell what a parallel line or perpendicular line entails - how it relates back to gradients and forms of linear equations. On a general level, Henry has gotten a lot better at independently working out worded questions, and applying the correct method, while also being more methodical with his approach instead of rushing headfirst.

Not particularly an area of improvement, but Henry may choose to practice more linear equation questions to consolidate his knowledge, and reach mastery of the content, such that he doesn’t need a formula sheet to perform linear algebra.

Piecewise functions knowledge has improved a bit. Noticeably, Henry can assign the values of arbitrary variables acting as placeholders for the piecewise functions, providing logical reason as to why those values might be correct. Initially, he struggled a bit with defining appropriate sub-functions and their domains in a piecewise function, but has greatly improved, which is really great to see.

Needs a bit more practice with differentiation, both regarding application questions that imply that differentiation is required, as well as the many methods of differentiation (product, quotient, and chain rule) and their appropriate use. Working with multiple functions could use some work too, as he sometimes applies his working out on the wrong function. Also generally needs to practice application questions, as while he has improved, still trips up with his working by making silly mistakes (dividing both sides instead of subtracting both sides, for example).