Resources by Casio

Sketching an Exponential Function and Solving an Exponential Equation

The mathematical solution explains how to sketch the graph of an exponential function. Explanation of the graph being an increasing exponential is given and the fact that y=0 is an asymptote is discussed. The intersection point with the y axis is found and, using the information given, the graph is sketched....

Sketching the Graph of a Cubic and Transformations Thereof

The mathematical solution explains how to sketch the graph of a quadratic function given one of the roots of the equation. The factor theorem is used to express the function as a product of three linear factors and hence find all three roots. The general shape of the graph can then be determined. The...

Solving a Quadratic Equation in Sin(x)

The mathematical solution explains how to solve the equation: 6 cos²x +7sinx = 8 for x between 0 and 4π radians. The equation is rearranged to make the equation 6 cos²x +7sinx - 8 = 0 then the identity sin² x + cos...

Solving a Quadratic Inequality

The mathematical solution explains how to solve the quadratic inequality 3x[sup]2[/sup] – 10x ≥ 8 by forming, and finding the roots of, the quadratic equation 3x[sup]2[/sup] – 10x - 8 = 0. This equation is solved by factorisation. The curve y = 3x[sup]2[/sup] – 10x - 8 is then sketched and the regions of x for...

Solving Equations Involving the Modulus function, Composite Functions and Examining the Range of a Function

This question is made up of four parts. Students are required to sketch the graph of a modular function, find where this function intersect a line, find the value of a composite function and find the range of a quadratic function.

The mathematical solution explains how to sketch the modular function...

Using Partial Fractions to Evaluate the Definite Integral of an Algebraic Fraction Example One

The first part of the mathematical solution explains how to express an algebraic fraction in partial fractions. The fraction used is a straight forward example solves by equating coefficients to obtain two simultaneous equations. The second part of the video uses the result of the first part of question in...

Using Partial Fractions to Evaluate the Definite Integral of an Algebraic Fraction Example Two

The mathematical solution explains how to express a function in partial fractions where the three denominators are linear. The result is used to find the definite integral of the original function, the solution given in terms of natural logarithms in its simplest form before calculating the decimal value.

Using Rcos(x + α) to Find the Maximum and Minimum Values of a Function and to Solve a Trigonometric Equation

The mathematical solution initially explains how to find the maximum and minimum values of f(x) = 5sin x + 2cos x and how to find, in radians to 2 decimal places, the smallest positive values of x at which they occur. f(x) is written in the form Rcos(x + α). Explanation is then given as to how the maximum and...

Using Trig Identities to Solve a Quadratic in Sin x

The mathematical solution explains how to use the identity sin2x + cos2x≡ 1 to form a quadratic equation which can then be solved in a given range. The method of 'splitting the middle term' is used in order to help factorise the resulting quadratic in sin2x. The two resulting equations are then considered...