<p>**Procedurally generated questions on Sequences. **<br /> The skills build in complexity, and ends with a large section of mixed questions. All questions have answers.</p> <p>Designed for use by individuals or as a resource from which questions can be taken.<br /> This resource covers the following characteristics for students to use (for both Arithmetic and Geometric Sequences:</p> <ul> <li>A given term, U_n</li> <li>The sum of the first n terms, S_n</li> <li>The first term, a</li> <li>The common difference / ratio, d / r</li> </ul> <p>The sequences are all split as “simple” or “hard”. With simple, arithmetic and geometric sequences will use integer characteristics. Geometric sequences may also generate with unit-fraction ratios. With “hard” sequences, fractional terms are randomly generated.</p> <p>All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!</p> <p>Please: Do not attempt every question in one go.</p> <p>Contents: (50+ questions per section. It’s a lot.)</p> <ol> <li>Given the first 4 terms of an Arithmetic or Geometric sequence, calculate a characteristic.</li> <li>Given two terms of an arithmetic sequence, calculate a third.</li> <li>Given two characteristics for an arithmetic sequence, calculate a third.</li> <li>Given two terms of a geometric sequence, calculate a third.</li> <li>Given two characteristics for a geometric sequence, calculate a third.</li> <li>Given two characteristics and the sequence type, calculate a third.</li> </ol>

<p>**Procedurally generated questions on Linear Equations. **<br /> The skills build in complexity, and ends with a large section of mixed questions. All questions have answers.</p> <p>Designed for use by individuals or as a resource from which questions can be taken.<br /> This resource covers the following line equation forms to give students a variety of practice :</p> <ol> <li>y = mx + c</li> <li>ax + by = c (a,b,c are integers)</li> <li>x/a + y/b = 1 (where the line does not intercept the origin)</li> <li>y - a = m(x - b)</li> </ol> <p>All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!</p> <p>Please: Do not attempt every question in one go.</p> <p><strong>Contents</strong>: (~170 questions per section. It’s a lot.)</p> <ol> <li>Equations of vertical and horizontal lines</li> <li>Finding the y-intercept</li> <li>Given x or y, find the other ordinate</li> <li>Creating parallel and perpendicular line equations</li> <li>Equation of a line given the gradient and a point</li> <li>Equation of a line through two points</li> <li>Is the point on, above or below the line</li> <li>Perpendicular bisector of two points</li> <li>Mixed questions</li> </ol>

<p>Procedurally generated questions on Quadratic Expressions.<br /> The skills build in complexity, and ends with a large section of mixed questions.</p> <p>Designed for use by individuals or as a resource from which questions can be taken. All questions have answers.</p> <p>All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!</p> <p>Please: Do not attempt every question in one go.</p> <p>Contents (~100 per section):</p> <ol> <li>Expand (x + a)(x + b)</li> <li>Expand (ax + b)(cx + d)</li> <li>Factorise x^2 + ax + b</li> <li>Quadratic brackets missing a single coefficient</li> <li>Quadratic Factorisation with one bracket completed</li> <li>Factorise ax^2 + bx + c</li> <li>Mixed questions</li> </ol>

<p>Procedurally generated questions on Second Order Differential Equations.<br /> The skills build in complexity, and ends with a large section of mixed questions.</p> <p>Designed for use by individuals or as a resource from which questions can be taken. All questions have answers.</p> <p>All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!</p> <p>Please: Do not attempt every question in one go.</p> <p>Contents (~100 per section):</p> <ol> <li>Homogeneous 2nd Order DE’s with characteristic polynomials with two real solutions.</li> <li>Homogeneous 2nd Order DE’s with characteristic polynomials with a repeated solution.</li> <li>Homogeneous 2nd Order DE’s with characteristic polynomials with complex roots.</li> <li>Homogeneous 2nd Order DE’s with characteristic polynomials (MIX)</li> <li>Particular Solutions to Homogeneous 2nd Order DE’s given the initial conditions.</li> <li>Simple Non-Homogeneous 2nd Order DE’s with polynomial RHS.</li> <li>Simple Non-Homogeneous 2nd Order DE’s with exponential RHS.</li> <li>Simple Non-Homogeneous 2nd Order DE’s with trigonometric RHS.</li> <li>Non-Homogeneous 2nd Order DE’s with simple RHS.</li> <li>Complicated Non-Homogeneous 2nd Order DE’s with exponential RHS.</li> <li>Complicated Non-Homogeneous 2nd Order DE’s with trigonometric RHS.</li> <li>Non-Homogeneous 2nd Order DE’s with exponential RHS (MIX).</li> <li>Non-Homogeneous 2nd Order DE’s with combination RHSs (MIX).</li> <li>Solving Non-Homogeneous 2nd Order DE’s (Complete mix).</li> </ol>

<p>Procedurally generated questions on Complex Numbers.<br /> The skills build in complexity, and ends with a large section of mixed questions. All questions have answers.</p> <p>Designed for use by individuals or as a resource from which questions can be taken.<br /> This resource covers the following complex forms to give students a variety of practice:</p> <p>z = a + bi<br /> z = re^(ix)<br /> z = a (cos ix + i sin ix)</p> <p>All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!</p> <p>Please: Do not attempt every question in one go.</p> <p>Contents: (~100 questions per section. It’s a lot.)</p> <ol> <li>Solve z^n equals a real number.</li> <li>Solve z^n equals a complex number.</li> <li>Roots of complex cubics.</li> <li>Complex cubics with a given root missing one coefficient.</li> <li>Complex cubics with a given root and two missing coefficients.</li> <li>Arguments of Loci (Min/Max arguments such that z lies within a circle).</li> <li>Mixed Questions (double sized section).</li> </ol>

<p>Procedurally generated questions on Solving Quadratics.<br /> The skills build in complexity, and ends with a large section of mixed questions. All questions have answers, simplified where necessary.</p> <p>Designed for use by individuals or as a resource from which questions can be taken.<br /> This book starts with pre-factorised quadratics, and builds into ones that must be factorised by hand, and those needing the quadratic formula.</p> <p>All of these questions are fluency based skills which can be practiced repeatedly until they are second nature. That’s what this is for!</p> <p>Please: Do not attempt every question in one go.</p> <p>Contents: (~150 questions per section. It’s a lot.)</p> <p>Solve (x+a)(x+b)=0<br /> Solve (ax+b)(cx+d)=0<br /> Solve x^2 +ax +b = 0 (factorise)<br /> Solve ax^2 +bx +c = 0 (factorise)<br /> Using the Quadratic Formula<br /> Mixed Questions</p>