What is geometric change?
Percentage
82%
I can …
H2.1 I can use recurrence formulae
Prove it!
The second term of a geometric sequence is 4 and
the 4th term is 8. Find the values of a) the common
ratio b) first term and c) the 10th term.
Hint:
H3.2 I can find the nth term for
sequences with ratios that are surds
Calculate the following, leave as a fraction where
appropriate:
78%
H1.3 I calculate with fractional
indices
a.
b.
c.
d.
e.
f.
g.
Which rectangle has a larger area?
76%
C1.3 I can solve area problems with
surds
H1.2 I can rationalise denominators
72%
C1.2 I can simplify surds
Multiplying and dividing
1.
√2 x √3
2.
√5 x √2
Taking a number out
1.
√18
3.
2.
√24
4.
Combining simplification
1.
2√2 x 2√7
2.
2√5 x 3√2
3.
2√5 x 3√3
1.
3.
4.
√8
√200
√12 ÷ √3
√30 ÷ √3
5.
6.
4.
5.
6.
√12
√75
12√40 ÷ 3√8
14√6 ÷ 2√2
4√21 ÷ 2√3
Change the following recurring decimals to fractions
Hint: Find 100x each time
a.
68%
H1.1 I can change recurring decimals
into fractions
b.
2. Change the following recurring decimals to fractions
Hint: You may need to find 1000x or more!
5.
a.
b.
c.
Change the following recurring decimals to fractions
Hint: You will need to work out two multiples of x
a.
b.
What is geometric change?
Percentage
64%
I can …
H3.1 I can find the nth term of a
quadratic sequence
Prove it!
Work out the nth terms of these sequences:
a.
2, 5, 10, 17, 26
b.
2, 8, 18, 32, 50
c.
0, 3, 8, 15, 24
What is the nth term of the sequence below?
Find the nth term of the sequence below:
60%
C3.3 I can find the nth term of a
geometric sequence
C3.4 I can explain whether a term is
in a given sequence
3, 6, 12, 24
Explain whether 100 will appear in this
sequence.
Miss Boothman bought a new car over the holidays.
The depreciation rate of the car is 20% each year
she has it. If she bought the car for £50,000, how
much will the car be worth in 5 years’ time?
58%
C2.3 I can calculate depreciation
C2.4 I can solve problems involving
growth and decay
56%
C2.2 I can calculate compound
interest
A bouncy ball is dropped from the top
of the Shard, which is 306 m tall.
After each bounce it reaches a height
that is 10% less than its previous
height.
What is the height of the ball after 14 bounces?
Mr Holmes has £450 to put in a savings account, if
he is going to leave the money in the bank for 5
years calculate how much interest he would receive
from the following banks:
Natwest: 1% compound interest
Barclays: 1.2% simple interest
What is geometric change?
Percentage
52%
48%
I can …
C1.6 I can calculate using numbers in
standard form
C1.5 I can express numbers in
standard form
Prove it!
Complete the following questions:
1.
(3 x 104) x (2 x 108)
2.
(4 x 105) x (8 x 10-3)
3.
(7 x 10-3) x (3 x 10-2)
4.
(6 x 10³)²
Complete the following questions:
1.
(8 x 109) ÷ (2 x 103)
2.
(3.9 x 105) ÷ (1.3 x 108)
3.
(2.2 x 106) ÷ (4.4 x 102)
4.
1 ÷ (2 x 108)
A: Write the following numbers in standard
form
1. 0.0064
3.
50000
5.
0.4
2. 3403000
4.
0.00873
6.
89
B: Change the following numbers so that they
are written in standard form
Hint: Start by changing from the question
into a normal number then change this into
standard form. Think carefully – is there a
quicker way of doing this?
1.
23 x 10³
2.
0.01 x 10
5.
-4
6*.
3.
123 x 103
0.009 x 1010
4.
33.3 x 10-8
7.89 x 1003
1. Simplify the following
a.
b.
c.
d.
44%
C1.4 I can apply laws of indices
e.
f.
g.
h.
i.
2. Calculate the following:
a..
b.
c.
What is geometric change?
Percentage
I can …
Prove it!
1. Find the nth term of the following sequences.
2. Find the 50th term in the sequence
40%
36%
30%
C3.1 I can generate terms of sequence
given the nth term rule
C3.2 I can find the nth term of a
linear sequence
a)
b)
c)
d)
e)
2, 4, 6, 8, 10
7, 14, 21, 28
-2, -1, 0, 1, 2
4, 7, 10, 13
4, 9, 14, 19
Match the decimal multiplier with the
statement
“Increase by 20%”
x1.05
“Decrease by 2%”
x1.02
C2.1 I can use decimal multipliers to
“Increase by 5%”
x0.98
increase and decrease by a percentage
“Decrease by 12%”
x1.2
“Increase by 2%”
x0.88
C1.1 I can calculate with powers and
roots
Identify the square numbers from the list
below:
45, 100, 1, 80, 64, 10, 8, 4
Calculate:
82 =
52 + 23 =
√49 - √100 =
Key Words:
Rational
Irrational
Surd
Indices
Compound interest
Depreciation
Standard Form
Recurring
Geometric
Arithmetic
Linear
Nth term