• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4

# Borders Maths Coursework

Extracts from this document...

Introduction

## Borders Maths Coursework

Here we are look at what happens when you put a (square) border on each side of the original shape.

Me starting point will have no borders

When I add the borders I put them on each side of the first square and there are 4 borders

Middle

Number of black squares

Number of white squares

1

4

5

8

13

12

25

16

41

20

61

24

Using this I can guess what the next number of white squares will be 20.

A you can see there are 20 white cubes.

This shape has 24 borders

Now

Conclusion

shape I will times 4 by 10 and the number of borders will be 40

Now I will work out the nth term for all the squares in the pictures.

 Number of square 5 13 25 41

1st      2nd        3rd        4th

5    13     25    41

1st8      12      16

2nd    4        4

The nth term for all the cubes is 22n-1.

The 10th number will be worked out by 4 times 10 minus 1 which is 39.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Mathematics Coursework: problem solving tasks

3 star(s)

676 tile spacers are needed in total. Say I want to tile a room that is not exactly square; I will not be able to use these formulas. But I can refer back to page 4. Page 4 illustrates how many spacers of each kind are needed starting with a straight line of tiles, then by looking at two rows of tiles then three, etc.

2. ## GCSE Maths Sequences Coursework

Therefore; Nth term for shaded = 6N Total If you take stage 1 and divide it into columns as I have here, we find that there are two columns of 2 and one of 3 which means that: 2x2=4 1x3=3 4+3 =3+3+1 =3x1�+3x1+1 =3N�+3N+1 2 3 2 3 3 4

1. ## algebra coursework

- (Z� + 11XZ - 11Z) = 10X� - 20X + 10 10X� - 20X + 10 = 10 (X-1)� 10X� - 20X + 10 � 10 = X�- 2X + 1 X� - 2X + 1 = (X-1) (X+1)

2. ## Number Stairs

Total for algebraic staircase= n+n+1+n+2+n+3+n+8+n+9+n+10+n+16+n+17+n+24 = 10n + 90 We can also evaluate that Stair number (n) = 5 By substitution stair total= 5+5+1+5+2+5+3+5+8+5+9+5+10+5+16+5+17+5+24= 10(5) + 90=140 Here is another example by using the algebraic stair case substitution: As we can see here n=stair number, and the 4x4 stair case

1. ## Mathematics Borders

+ d 3 5 = 8+ 4b + 2c + d 3 = 4b + 2c + d = 7 [equation 2] 3 * If n=3 U3 = 1 (3)3 + b(3)2 + c(3) + d 3 14 = 9 + 9b + 3c + d = 9b + 3c

2. ## Mathematical Coursework: 3-step stairs

77 78 79 80 81 64 65 66 67 68 69 70 71 72 55 56 57 58 59 60 61 62 63 46 47 48 49 50 51 52 53 54 37 38 39 40 41 42 43 44 45 28 29 30 31 32 33 34 35 36

1. ## Staircase Coursework

So the formula works 3 step stair on a 6x6 grid ( 2 ) I will now try to find a formula for a 3 step stair on a 6x6 grid 3 step stairs on a 6x6 grid 19 20 21 22 23 24 13 14 15 16 17 18

2. ## Investigate Borders - a fencing problem.

Experiment I will try to find the number of squares needed for border number 6 using the formula, I found out, above: nth term = 4 x 6 = 24 Common Difference nth Term Results My prediction was 24 which is the correct answer, for the number of squares needed

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to