Calculator Tips & Tricks for A-Level Maths/Further Maths ➕➖➗✖️ [fx-CG50 Graphics, fx-991EX Classwiz]

The video introduces two calculators: the Casio fx-CG50 (graphics) and the Casio fx-991EX Classwiz (scientific). The goal is to demonstrate how to use these calculators to verify answers and gain as many marks as possible in A-Level Maths and Further Maths exams, rather than providing full tutorials or direct solutions.

Using the graph section (menu option 5) to sketch functions like y = |2x - 5| - 3. The video shows how to input modulus signs (option -> numeric -> abs) and plot variables (x theta t button). It also covers setting up axes scales, using the zoom feature (factor zoom for consistent scaling), and adjusting the visible window (V-Window) for better visualization, particularly recommending 'initial' for grids with proportional axes.

Demonstrates using the 'G-Solve' function for graphical analysis. This includes finding roots (x-intercepts), minimum/maximum points (vertices), and y-intercepts. The video also shows how to find intersection points of two graphs, emphasizing that this is for verification of algebraic solutions. The process for verifying maximum points of a function within a range and calculating definite integrals graphically (integral of sin^2(x) between 0 and pi) is covered, highlighting the calculator's role in confirming manual calculations.

The 'Run Matrix' section (menu option 1) is introduced for detailed calculations. This includes verifying integral results using the math function (f4 -> integral button) and checking derivatives (d/dx from math menu). It also shows how to calculate sums of series using sigma notation (math -> sigma) and the vital technique of storing values into variables (alpha A, B, C, D) for complex, repetitive calculations, particularly useful in Further Maths for roots of polynomials.

The 'SolveN' function (option -> calc -> solveN) is highlighted as a powerful feature unique to the graphics calculator. It can solve equations, including trigonometric ones, within a specified range (e.g., 0 to 360 degrees). The video stresses that while it provides solutions, it's primarily for verifying solutions obtained through manual algebraic steps, as direct calculator answers may not grant full marks.

The 'Equation' menu (menu option A) is explored for solving simultaneous equations (e.g., 2 variables) and polynomial equations (quadratics, cubics). It demonstrates how to input coefficients to find solutions for linear systems and roots of polynomials. A practical example shows how to solve for 'a' and 'b' in an exponential model by setting up two simultaneous equations, treating e^(-2) and e^(-8) as coefficients. It also demonstrates solving pseudo-quadratics in trigonometry.

The 'Statistics' menu (menu option 2) is used for binomial distribution calculations. The video recommends consistently using 'BCD' (Binomial Cumulative Distribution) for all probability types (less than or equal to, less than, exactly equal to, greater than or equal to, and between ranges), demonstrating its versatility over the 'BPD' function by using inclusive lower and upper limits.

Exploration of the normal distribution features in the statistics menu. Specifically, how to use 'Inverse Normal' to find 'a' values given a probability, mean, and standard deviation. The calculator's ability to switch between 'left', 'right', and 'central' tails is emphasized, which is particularly useful for finding quartiles.

This section switches to the fx-991EX Classwiz. It shows how to verify integrals and derivatives, similar to the graphics calculator, but notes the Classwiz is significantly slower for complex integrals and only provides decimal answers for derivatives, requiring extra steps for verification. It also demonstrates calculating sums of series using the sigma notation button.

Explains how to store values into variables (A, B, C, D) on the Classwiz using the 'STO' button, enabling quicker computations for repeated expressions. The 'Equation and Function' menu on the Classwiz (menu option A) is demonstrated for solving simultaneous equations and polynomial equations, mirroring the graphics calculator's functionality for these types of problems.

Further use of the Classwiz's polynomial solver for cubics and pseudo-quadratics (like those involving sin x). The video shows how to find roots and turning points (min/max) of quadratics. A unique feature of the Classwiz is its ability to solve inequalities, which is demonstrated with a quadratic inequality, highlighting it as an advantage over the graphics calculator.

The video concludes by reiterating that calculators are verification tools, not substitutes for manual work. Students are advised to use them to check answers, particularly for integration and differentiation, to ensure accuracy and catch errors. Consistent practice with the calculator throughout the course is recommended to build speed and familiarity with its functions.