Mathematico | Mathematico

Skip to content

Main Navigation

Problems Past papers

Appearance

Sidebar Navigation

Quadratics

Factorising I

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Factorising II

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Parabolas

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Completing the square

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Finding the vertex

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

The quadratic formula

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

The discriminant

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Points of intersection

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Quadratic inequalities

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Quadratics in disguise

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Coordinate Geometry

Distance between points

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Midpoints

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Gradient

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Equation of a straight line

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Parallel and perpendicular

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Equation of a circle

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Tangent and normal to a circle

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Polynomials

Function notation

Cubic functions

Problem 1

Problem 2

Problem 3

Long division

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Long division

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

The factor and remainder theorems

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Partial Fractions

Problem 1

Problem 2

Inequalities

Functions

Modulus equations I

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Translation of graphs

Problem 1

Problem 2

Problem 3

Problem 4

Enlargement of graphs

Problem 1

Problem 2

Problem 3

Sequences

Explicit sequences

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Recursive sequences

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Increasing/decreasing sequences

Problem 1

Problem 2

Problem 3

Periodic sequences

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Partial sums

Problem 1

Sigma notation

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Arithmetic Sequences

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Arithmetic Series

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Geometric sequences

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Geometric series

Problem 1

Problem 2

Problem 3

Problem 4

Sum to infinity

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Binomial expansion

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Generalised expansion

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Trigonometry

Basic trigonometry

Sin, cos and tan

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Trigonometric identites

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Using identities

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Transformed equations

The cosine rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

The sine rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Area of a triangle

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Radians

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Arcs and sectors

Problem 1

Problem 2

Problem 3

Problem 4

Addition formulae

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Double angle formulae

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Harmonic Form

Problem 1

Problem 2

Problem 3

Problem 4

Reciprocal functions

Problem 1

Problem 2

Problem 3

Small angle approximations

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Exponentials and Logarithms

Exponential functions

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Logarithms

Problem 1

Problem 2

Problem 3

Logarithms II

Problem 1

Problem 2

Problem 3

Problem 4

Laws of logarithms I

Problem 1

Problem 2

Laws of logarithms II

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Logarithm equations

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Equations with $e$

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Differentiation

Estimating Change

Estimating Gradients

First principles

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Differentiating Polynomials (and beyond)

Problem 1

Problem 2

Tangents and Normals

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Turning points

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Optimisation

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Differentiation of sin and cos

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Differentiating $e^{kx}$

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

The Product Rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

The Chain Rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

The quotient rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Implicit differentiation

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Parametric curves

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Related rates of change

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Convexity and concavity

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Numerical Methods

Change of sign rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Iteration

Problem 1

Problem 2

Problem 3

Problem 4

Newton-Raphson

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

The trapezium rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Riemann sums

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Integration

Geometric area

Integrating $\sin^2$ and $\cos^2$

Integration by parts

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Integration by substitution (indefinite)

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Integration by substitution (definite)

Parametric integration

Problem 1

Problem 2

Problem 3

On this page

Table of Contents for current page

The sequence defined by

u_{n} = n^{2} - 19 n + 18

contains a pair of consecutive terms which are equal. What is the value of these terms and where in the sequence do they appear?

If the $n^{th}$ term is $u_{n},$ then the next term is $u_{n + 1} .$ We are looking for a pair where

u_{n} = u_{n + 1}

u_{n + 1} = (n + 1)^{2} - 19 (n + 1) + 18

Previous pageProblem 5

Next pageProblem 7