# Extra maths sheets

Sometimes there seems to be a theme of the week for students I tutor.

It may be some basic facts, like multiplication tables, or special numbers, or particular ways of looking at problems, or just to read the question carefully, or even just to have fun with a particular topic.

As a result, I’m occasionally motivated to make a document or spreadsheet to provide information or assistance with the relevant theme.

See below for a selection of these. I add to this list occasionally, as I develop others.

**Click on a heading to get the corresponding file.**

## Minimum year level 6 maths

### 1. Special numbers

This document was referred to and discussed in a previous post. It lists various types of special numbers, such as squares and primes, which appear more often all over the place *because* they are special. I originally made this for upper secondary students, but even those who are younger (or older!) may benefit from a greater awareness of these numbers.

## Minimum year level 7 maths

### 2. Linear equations

This document provides examples of how to find the equation of a line from (a) a gradient of the line and a point on the line, or (b) two points on the line All such tasks reduce to one of these two possibilities.

## Minimum year level 8 maths

### 3. Angles and lines

(Added 19 Nov 2016)

This document names various types of angles and angle pairs (such as alternate and co-interior angles.

## Minimum year level 9 maths

### 4. Quadratic forms

This document outlines the various forms for presenting quadratic expressions. It also provides a summary of associated quantities e.g. intercepts of quadratic functions.

### 5. Laws of arithmetic

This document is really designed for students starting their study of matrix algebra. It outlines the laws of arithmetic, which apply both to numbers and to other quantities such as matrices. It may be easier to understand manipulation of matrix equations if the equivalent number equations are studied in parallel, an approach that not all textbooks follow.

### 6. Triangle formulas

(Added 5 March 2014)

This document covers the following triangle formulas, and where to use them: – Pythagoras Theorem – SOHCAHTOA – Cosine rule – Sine rule – Area formulas

**7. Laws of probability**

This document lists some of the basic equations for the study of probability.

### 8. Laws of **indices and logarithms**

This document lists some of the basic equations for the study of indices and logarithms.

## Minimum year level 11 maths

### 9. Base functions

(Added 1 May 2014)

This document is a single page summary of graph shapes for the main equation types covered in Victorian Year 11/12 Maths Methods.

### 10. Exponentials and logarithms

(Corrected 14 May 2014)

This document is an extension style introduction to the number *e* and some of its properties. In particular, it shows in a natural way why differentiating y=e^{x} gives dy/dx=e^{x}.

### 11. Factorising polynomials

(Updated 1 May 2014 – some rough edges smoothed out)

This document shows some special cases for factorising cubic and quartic polynomials.

### 12. Functions in turning point form

This document shows in graphical form the common features of functions y=a(x-h)^{n}+k, for n=3, 2, 0.5, -1 and -2, as well as the modulus (absolute value) function.

### 13. Graphing trigonometric functions with restricted domains

This document shows how to find the coordinates of all critical points when graphing trigonometric functions. An example graph for each of cos, sin and tan is provided. A single page summary is provided at the end.

### 14. Combining functions – addition, subtraction and multiplication of ordinates

(Added 1 May 2014)

This document shows how to graph combinations of functions. A single page summary is provided on the first page.

### 15. Function domains and ranges

(Added 27 May 2014)

This document shows how to derive implicit (maximal) domains and ranges.

### 16. Differentiability

## (Added 29 August 2014)

This document is a summary of criteria for differentiability of functions as covered in Victorian Year 11/12 Maths Methods.

## Minimum year level 12 maths

### 17. Antidifferentiation

(Added 19 Nov 2016)

This document summarises various methods of antidifferentiation.

Page 2 is designed for Specialist Maths students and is not needed by Maths Methods students.

### 18. Discrete probability distributions and probability density functions

(Added 19 Nov 2016)

This document compares formulas for discrete probability distribution and probability density functions. It can be seen that a more or less direct translation from one to the other is possible – unsurprising, as they embody eactly the same notions.

## General interest

### 19. Quadrilateral types

(for those who are fascinated by shapes)

We all know squares, kites and parallelograms, but what other quadrilaterals have names? What are their properties? How are they connected? This document is an enhancement of a diagram on the Wikipedia page for quadrilaterals. It has all the named quadrilaterals I could find.

### 20. Names of large numbers

(for those who are fascinated by large numbers)

We all know the sequence thousand, million, billion, trillion, but what comes next? This document lists the names of powers of ten up to 10^{3000}. So 10^{2562} is a tresquinquagintaoctingentillion. With these names, you can then translate, for example, 789,472,695,646,940,680,101,549,875 to seven hundred and eighty nine septillion four hundred and seventy two sextillion six hundred and ninety five quintillion six hundred and forty six quadrillion nine hundred and forty trillion six hundred and eighty billion one hundred and one million five hundred and forty nine thousand eight hundred and seventy five.

(for those who like geometric patterns)

Just a whole bunch of printable regular tessellations, using triangles, squares, hexagons, octagons and dodecagons. I have made these into a file with two sizes of each pattern. I suggest you print only the page(s) you are interested in.

### 22. Dice and card bingo

(for Y3-Y8 maths – and anyone who likes bingo)

Each sheet in this spreadsheet has grids with all the number you can get by simple arithmetic (adding, subtracting multiplying or dividing) with numbers on two or three dice or cards, that is for numbers 1 to 6 or 1 to 10. There are separate sheets for each which also include zero and negative answers. Remember that three numbers allow for the use of parentheses. An example for two dice is:

15 | 12 | 25 | 16 | 1 |

5 | 4 | 20 | 2 | 7 |

18 | 11 | 8 | 24 | 3 |

6 | 30 | 36 | 9 | 10 |

These grids can be a fun way to reinforce arithmetic operations for small numbers. You can use them like traditional bingo (first to complete a row or column wins). Or make up your own rules. I suggest that players write down the expression they use to get their chosen number in that number’s square. Use a pencil, so you can re-use the sheet more than once. There will be a new arrangement of digits each time you open the file, or if you press the <F9> key while in Excel. Also note that you need only ask to print each sheet – the parts to be printed have already been appropriately defined.

## Minimum year level 10 biology

### 23. Punnett squares

(for Y10-Y12 biology)

A Punnett square is a diagram that is used to predict an outcome of a particular cross or breeding experiment. See here for details. The essence of Gregor Mendel’s great idea displayed here is of the gene as an indivisible unit of inheritance. Those before him knew about inheritance of parents’ features by their offspring, but had thought of this process as akin to determining the sweetness of a cake mix by adding more or less sugar. There are many Punnett square diagrams on the web, but I found none showing in one place all possible combinations of simple dominant and recessive gene inheritance, making clear the expected and unexpected outcomes. This document tries to remedy that. I made this after talking about this topic to a student who had studied this (thanks Kimmy). ** **

*Note: You are free to use any file from this page for any non-commercial purpose, provided you (i) keep any copyright notice in the file intact and (ii) acknowledge this source. For other uses, please contact me: markmichell55 at gmail dot com.*

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