We went over questions involving a mixture of topics such as algebra, parabolas (including the use of the quadratic formula and discriminant), financial mathematics (simple interest) and bearings (which required Ray to incorporate knowledge of angle relationships). Ray correctly utilised the simple interest formula and seems to have a good understanding of financial maths.

Ray had some trouble factoring the expressions before simplifying; note, these are algebraic expressions, not equations and thus cannot be solved to determine an unknown. Ray had difficulties with the bearings question, as he needed to recall angle relationships and use them throughout these problems. Memorising the sine and cosine rules, as well as the appropriate situations in which each can be used is important for many bearings questions.

This week’s lesson involved a greater focus on factorisation and using this to find faster and alternative methods of simplifying problems instead of resorting to expanding the entire expression first. Ray correctly remembered the compound interest formula. Ray started to show more familiarity with factorising by recognising similar terms and combining these first in algebraic problems.

I wish to highlight something that Ray occasionally mixes up, and this is the different between the formulas for simple interest and compound interest. Simple interest (I = P x r x t) allows the interest to be calculated immediately whereas compound interest (A = P x (1 + r/n)^nt) produces the amount, and the principle must be subtracted from it in order to produce the interest gained. Regarding the problems involving factorisation, Ray experienced some difficulties with some of the larger expressions, and something he must take care with are the signs. When removing signs from terms, they still remain in the expression, only in a different location. Thus, the effects of its presence must still be considered. However, he must continue to revisit these problems to maintain and continually improve his ability to recognise these patterns when present. This will enable him to solve algebraic questions more quickly and accurately. Similarly, with algebraic fractions, it is important to remember the difference between the steps required when multiplying and dividing fractions in comparison to adding or subtracting fractions. Furthermore, the same simplification steps used in the earlier factorisation questions can be applied to these fraction problems. Bearings remains a topic that Ray experiences some trouble with. Practising more of these questions and revising angle relationships and the sine and cosine rules will enable him to further his understanding of these problems.

As we went over Ray’s recent exam, many of the questions were ones which he understood how to do already but may have forgotten in the moment or made a minor error completing, resulting in incorrect solutions. Finishing off the lesson with some probability questions, Ray was able to solve these correctly, remembering in some cases to take into account the objects that have already been selected for, accounting for the effect of these on the remaining probabilities. It's been an absolute pleasure to have helped Ray throughout these past few years and I wish him all the best in his future. Keep persevering through the problems; I know many great things are in store!

He should return to the questions which he incorrectly solved in his exam and retry these to fully test his comprehension of the topics following our revision session. Regarding the questions involving probability, he did overthink several of these, having the correct reasoning to start with before altering his working so that it was no longer correct. I want to stress that he must consider the context of these problems when deciding on the method of working and to trust in his abilities more.

Ray correctly remembered the vertex form of a parabola and correctly used this to quickly determine the vertex. However, all the different forms of the parabola should also be memorised, including the intercept form. This is only used when the two x-intercepts are given and can be substituted in alongside another point on the graph to quickly produce the equation of the parabola.

One of the problems involved the use of Pythagoras’ theorem and the substitution of expressions made by Ray into this before applying methods of expanding and rearranging algebraic expressions to form and solve a quadratic equation. Harder (or more involved) problems typically may require the inclusion of knowledge from several different topics which Ray should keep in mind. Ray must remember the quadratic equation and equation for the axis of symmetry as he needed to rearrange an equation and then apply the formula for the axis of symmetry. (Tips: Looking at the shape of the parabola, the axis of symmetry should be a vertical line. Hence, it must be one of the solutions given as x = some value). For financial maths, Rey remembered the compound interest formula (but it’s important to remember that the left side of the equation is not I for interest, but instead A for amount). This contrasts the simple interest formula, I = PxRxT, which immediately gives the interest without the need for the subtraction of the principal (P) from the amount (A) to obtain the interest (I), done for compound interest. Another important note is remembering to express all the terms in the same units, as the rate is given per annum for 4 years, whereas interest is compounded monthly. When dealing with questions involving parabolic motion, the object's movement can be pictured using a parabola and applying aspects of the parabola to the problem. For instance, time (t) takes the place of x and height (h) replaces y in this question. Thus, this may assist Ray in translating the question into more familiar terms (such as the maximum height being at the vertex and the time taken for the rocket to return to the group being the latter of the two values where the height is equal to 0).