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

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

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

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

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

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