Year 9 Higher – Number revision Use this revision list ALONGSIDE

Year 9 Higher – Number revision
Use this revision list ALONGSIDE the presumed knowledge topics…..
Recurring Decimals
Recurring decimals to fractions
Prime Factorisation
Writing a number as a product of primes
HCF and LCM from prime factorisation
Fractional and Negative Indices
Fractional Indices
Negative Indices
I can change a fraction (eg 6/11) into a recurring
decimal by using “bus-shelter” division
I know how to spot whether a fraction will
terminate or recur when written as a decimal
I can use an algebraic argument to change a
recurring decimal into a fraction (in its simplest
form)
I can write a number as a product of its prime
factors (possibly using a factor tree)
I can use prime factorisation to find the HCF of a
pair (or more) of numbers
I can use prime factorisation to find the LCM of a
pair (or more) of numbers
I understand that a fractional power represents a
“root”
I understand that a negative power represents
“one over”
I can work out complicated powers like 5 2 or

Standard Form
Standard form
Addition and subtraction
Multiplication
Division
Surds
Intro, rules and simplifying
Expanding brackets
Bounds and errors
Largest and smallest values
Reciprocals
Reciprocals
Multiplication and division of decimals
Long multiplication – traditional
Long multiplication – grid method
Multiplying decimals
Division (bus shelter)
Division of decimals
Using proportional reasoning to solve problems
Not many videos about for this – just one on
Recipes
Repeated percentage change
Multipliers
Compound Interest and depreciation
Reverse percentages
1
2
64
I understand what it means to write a number in
standard form
I can change between standard form and
“normal”
I can add and subtract numbers in standard form
I can multiply and divide numbers in standard
form
I understand what a surd is
I can simplify a surd
I can expand brackets involving surds
I understand what we mean by the upper and
lower bound for a number that has been
rounded
I can use inequality symbols to represent bounds
for a number
I can find the reciprocal of an integer, a simple
fraction, a mixed number and a decimal
I can multiply ANY two decimal numbers
together (your favourite method!)
I can divide ANY two decimal numbers
I understand what is meant by a proportional
relationship between two variables
I can solve problems involving proportional
reasoning
I understand how to use a multiplier to effect
percentage change
I can solve problems involving compound
interest and depreciation
I can solve “reverse percentage” questions
Questions
Recurring Decimals
1) Write
4
as a recurring decimal.
7
2) Determine which of the following fractions terminate and which ones recur when written as
decimals. Explain your reasoning.
5
,
8
1
,
3
11
20
2
,
7
3) Write 0.34 as a fraction in its simplest form.
4) Write 0.512 as a fraction in its simplest form.
Prime Factorisation
1) Write 300 and 252 as products of prime numbers. Use your answer to work out the Highest
Common Factor of 300 and 252.
2) Write 220 and 462 as products of prime numbers. Use your answer to work out the Lowest
Common Multiple of 220 and 462. Give your answer as a product of primes (no need to work out its
actual value).
Fractional and Negative Indices
Work out the following – give your answers as simply as possible.
1) 4-1
2) 3-2
3) 16
½
4) 8
⅓
Standard Form
1) Write the following numbers in standard form
a) 3400000
b) 25200
c) 0.023
d) 0.000045
c) 3.01 x 10-1
d) 9.876 x 10-5
2) Write the following numbers normally
a) 1.2 x 103
b) 5.62 x 105
3) If a = 1.2 x 106 and b = 6 x 104, work out the following, giving your answers in standard form
a) a + b
b) ab
c) a ÷ b
Surds
1) Simplify the following surds a)
50
2) Expand and simplify a) (1 + 2 )(3 - 2 )
b)
48
b) (3 + 3 )(5 - 3 )
Bounds and Errors
Use inequality symbols to represent the bounds of the following rounded numbers
a) w = 5 (nearest whole number)
b) x = 1.2 (1 decimal place)
c) y = 3.45 (2 decimal places)
d) z = 550 (two significant figures)
Reciprocals
Write down the reciprocal of each of the following values
a) 3
b)
1
6
c)
3
4
d) 2
1
2
e) 0.8
Multiplication and division of decimals
Showing a clear method, work out the following:
1) 23 x 576
2) 5.4 x 0.0298
3) 4505 ÷ 17
4) 151.06 ÷ 0.26
Proportional Reasoning
1) A recipe for 24 cupcakes requires 200g of flour and 150g of sugar (as well as other ingredients)
a) How much flour and sugar would be required for
(i) 12 cupcakes?
(ii) 30 cupcakes?
b) If I have 300g of flour and 200g of sugar, what is the MAXIMUM number of cupcakes that I would
be able to make?
2) It takes 4 people 3 hours to put 3000 cards into envelopes.
How long would it take…
(i)
6 people to put 6000 cards into envelopes?
(ii)
10 people to put 20000 cards into envelopes?
Write down any assumptions that you are making in your answer.
Repeated Percentage Change
1) I invest £3000 into a bank account paying COMPOUND INTEREST at 2% per annum.
(i) How much is it worth after 1 year?
(ii) How much is it worth after 5 years?
(iii) How much interest will I earn in the first 10 years of investment?
(iv) Write down an expression for how much it is worth after n years.
2) I buy a car for £6500. Every year it depreciates in value by 20%.
(i) How much is it worth after 1 year?
(ii) How much is it worth after 5 years?
(iii) Write down an expression for how much it is worth after n years.
3) In a shop sale ALL prices are reduced by 15%.
I buy a tumble dryer IN THE SALE for £136.
How much is it normally worth (ie BEFORE the sale)?