2 Nov/Dec Flashcards
Percentages, Sequences, Transformations
Name the four transformations.
Translation
Reflection
Rotation
Enlargement
Vector notation
(x) = right
(y) = up
What are invariant points?
Points that don’t change under a transformation.
Draw the following lines:
1) y=1
2) x=2
3) x=0
4) y=0
5) y=x
6) y=-x
Are they all right?
Is the following equation right? If not correct it.
x=-y
Wrong
y=-x
What is the nth term for this sequence:
3, 7, 11, 15
3→7 = +4, 7→11 = +4 } 4n
4*1 =4
4→3 = -1 } -1
= 4n-1
3n+2 is the nth term for a sequence. Will 61 be in the sequence? Explain.
61 = 3n+2 59 = 3n 59/3 = n 19.67 = n n is not an integer so 61 can't have a place in the sequence.
What is the nth term for this sequence?
3+2a, 3+4a, 3+6a
What is the 5th term?
+2a each time } 2an
2a→2a+3 } +3
= 2an+3
(2a*5)+3 = 10a +3
What is the nth term for this sequence?
-3, 1, 5, 9, 13
-3→1 = +4, 1→5 = +4 } 4n
4*1 = 4
4→-3 = -7 } -7
4n-7
What is the nth term for this sequence?
3, 8, 15, 24, 35
1) Find the 1ˢᵗ and 2ᶮᵈ difference.
3→8 = +5, 8→15 = +7, 15→24 = +9
5→7 = +2, 7→9 = +2 } 2/2 = 1 } n²
2) Subtract n² from the sequence and find the difference between the new sequence (if needed).
= +2 } 2n
3) n² + 2n
The formula for a geometric sequence (where…)
T(n) = ar ⁿ¯¹
a = first term r = common ratio
Find the nth term for the following sequence:
2, 8, 32, 128
T(n) = 2*4 ⁿ¯¹
Rule for finding percentages
New / Original
N/O
Calculation for repeated percentage change.
Initial amount * Percentage multiplier ^x
x = time frame
Calculation for compound interest.
A = P(1 + r/100)ⁿ
A = Total amount after n years P = Original value r = Interest per annum n = Number of years the money is invested
