PLP-for-Higher Maths
... I can find the area between a curve and the x-axis I know that there are no negative areas I can find the area between two curves I can solve differential equations ...
... I can find the area between a curve and the x-axis I know that there are no negative areas I can find the area between two curves I can solve differential equations ...
Bridging the gap notes
... 5) The algebra techniques- they practise collecting like termsi.e. 4(2L) + 4L + 4 x 8 = 12L + 32 for total edge-length The associative law 2L x L x 8 = 16L2 for volume Both of the above for surface area 6)More subtly, it helps unconsciously with the substitution problem (Q1) as stated earlier (i.e. ...
... 5) The algebra techniques- they practise collecting like termsi.e. 4(2L) + 4L + 4 x 8 = 12L + 32 for total edge-length The associative law 2L x L x 8 = 16L2 for volume Both of the above for surface area 6)More subtly, it helps unconsciously with the substitution problem (Q1) as stated earlier (i.e. ...
PELL’S EQUATION, I 1. Introduction − dy For d in Z
... reducing both sides mod 5 to get x2 ≡ 6 mod 5, since that congruence has a solution so there is no contradiction. Reduce mod 3 instead: the equation becomes x2 − 5y 2 ≡ 0 mod 3, or x2 ≡ 5y 2 ≡ 2y 2 mod 3. This too has a solution, namely (0, 0), so it doesn’t seem like progress has been made. But thi ...
... reducing both sides mod 5 to get x2 ≡ 6 mod 5, since that congruence has a solution so there is no contradiction. Reduce mod 3 instead: the equation becomes x2 − 5y 2 ≡ 0 mod 3, or x2 ≡ 5y 2 ≡ 2y 2 mod 3. This too has a solution, namely (0, 0), so it doesn’t seem like progress has been made. But thi ...
