Cell Structure and Microscopy Overview
Understanding the structure of cells including plant, animal, and bacterial cells. Learn about the differences between eukaryotic and prokaryotic cells, organelles, and key functions. Explore the importance of microscopy in studying cells and how magnification and resolution are crucial for detailed observations. Practice useful conversions and solve microscopy-related problems for a comprehensive understanding.
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Presentation Transcript
Expand the following to create 2 quadratic identities: (x + 3)(x - 3) (2n + 1)(2n - 1) (2n + 1)(2n - 1) 4n2 - 1 (x + 3)(x - 3) x2 - 9 What do you notice?
(2n + 1)(2n - 1) 4n2 - 1 (x + 3)(x - 3) x2 - 9 When expanded, the middle terms cancelled out. This is a special case called the Difference of two squares that allows us to expand and factorise certain expressions very quickly. Can you think why its called the difference of two squares? x2 32 (2n)2 12
(2n + 1)(2n - 1) 4n2 - 1 (x + 3)(x - 3) x2 - 9 When expanded, the middle terms cancelled out. This is a special case called the Difference of two squares that allows us to expand and factorise certain expressions very quickly. What will these expressions need to have in order for us to apply this case? We must have a subtraction, for the difference and we must have square numbers
Consider x2 4 x2 + 0x 4 +2 -2 (x 2)(x + 2) x2 25 +5 -5 x2 + 0x 25 (x 5)(x + 5)
Consider this square b a How can we find the area of the coloured shape? Total Area White Area
Consider this square b a How can we find the area of the coloured shape? a2 White Area
Consider this square b a How can we find the area of the coloured shape? a2 - b2
Consider this square b a What if we rearrange the shape? a2 - b2
Consider this square Why? a - b b a a b What are the dimensions now? a2 - b2
Consider this square a - b b a a b What is the area of the rearranged shape? (a + b)(a b) a2 - b2
Consider this square a - b b a a b What do you know about the 2 areas? (a + b)(a b) a2 - b2
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 Extension: Factorise x2 - 84
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3)
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3) (a + 10)(a - 10)
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3) (a + 10)(a - 10) (2h + 6)(2h - 6)
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3) (a + 10)(a - 10) (2h + 6)(2h - 6) (4v + 7)(4v - 7)
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3) (a + 10)(a - 10) (2h + 6)(2h - 6) (4v + 7)(4v - 7) (5x + 9)(5x - 9)
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3) (a + 10)(a - 10) (2h + 6)(2h - 6) (4v + 7)(4v - 7) (5x + 9)(5x - 9) (x + 8)(x - 8)
Factorise the following: 1 2 3 4 5 6 x2 - 9 a2 100 4h2 - 36 16v2 49 25x2 81 x2 64 (x + 3)(x - 3) (a + 10)(a - 10) (2h + 6)(2h - 6) (4v + 7)(4v - 7) (5x + 9)(5x - 9) (x + 8)(x - 8) Extension: (x + 84)(x - 84)
Thinking about the difference of two squares can you find the value of the following without using a calculator! 132 32 262 242 (13 - 3)(13 + 3) (26 - 24)(26 + 24) 10 X 16 2 X 50 160 100
