If sin2x + cos2x = 1...

If sin²x + cos²x = 1, tan²x + 1 = sec²x, what is

1. 16 – 4sin²x
2. 4 + 2tan²x
3. 16 – x²
4. 1 + 2x²

Factorise, Differentiate, Evaluate

Factorise in 10 seconds

1. m² + 10m + 21
2. 2x² – x – 15
3. 5m² - 21m + 4
4. x² + 10x + 24
5. 3m² - 22m - 45
6. 2x² – 12x + 18

Differentiate in 10 seconds

1. 5m² - 21m + 4
2. x⁸ + 10x⁵ + 24x
3. 3m⁵ - 2m⁴
4. (5m² - 21m + 4)⁷
5. (X⁸ + 10x⁵ + 24x)³
6. (3m⁵ - 2m⁴)³
7. (7x³ – 5)⁸
8. (2x⁵  + 3)⁶
9. (5x³ + 4)³
10. (7 – 3x⁵)⁹

Evaluate

1. 4mht – 3h² when h = 3, m= 5 t = 2
2. 7h² – 5m when h = 3, m= 5 
3. (4mht – 3h²) / (7h² – 5m) when h = 3, m= 5 t = 2
4. (4mht – 3h²) / (7h² – 5m)     when h = 3, m= 5 t = 2  
5. 2/3 (2x² - 3)^2/3           when x = 8
6. 2/3 (1 + 2x²)^2/3 when x = 0
7. 2/3 (1 + 2x²)^2/3 when x = 2
8. 2/3 (2x² - 3)^2/3         when x = -8
9. 2/3 (1 + 2x²)^2/3 when x = 8
10. 16x – 8/3x³ + x⁵/5 when x = 2
11. 16x – 8/3x³ + x⁵/5 when x = 0
12. 16x – 8/3x³ + x⁵/5 when x = 1
13. 16x – 8/3x³ + x⁵/5 when x = -2

Representing the Number 16

Give 10 ways to represent the number 16 using known numbers only

1. 28 -12 
2. (400/100)  + (20 – 6)
3. (3 x 2) + (100/20) + (2 + 5) -2
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Give 10 ways to represent the number 16 using unknown numbers and give value of unknowns at the end

1. mh + p m=5, h=3, p=1
2. 3g – 2 g = 6 
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Give 10 ways to represent the number 16 using unknown numbers and determine the value of unknowns 

1. h²
2. kl – 5
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