Download 2 - Castle Manor Academy

GCSE Mathematics
Revision
A Guide for
Parents
GCSE Mathematics Information
GCSE taken at CastleManor Academy
1.
GCSE Mathematics
Edexcel
Higher Tier (A* - D)
Foundation Tier (C – G)
Two exams equally weighted, one non-calculator and one calculator.
No coursework
Student’s revision
This should consist of these elements:
Past Exam Papers: All students will receive past exam papers. These will be completed in a
combination of class work and homework. It is imperative that students work through these thoroughly.
Mymaths.co.uk: This website contains help and support for students on all aspects of the course.
Your child will have been enrolled with a logon and password.
Revision guides: We recommend CGP revision guides for students to use.
Supporting your child: Useful things to do with your child include reviewing their revision progress
on mymaths.co.uk. We have also included a “Key Concepts” sheet containing maths facts that can be
used as a discussion point with your child during a coffee break.
NOTE: If your child says that they have no maths to complete, this will not be true. They
can always work on the next exam paper or practice on mymaths.co.uk.
Year 11 Revision Topics - Foundation
Use your textbook to revise and practice questions from at least one of
these topics every evening:
Number and Algebra
1. Times tables (1 to 12)
2. Indices
3. Standard form
4. Algebra/ multiplying out brackets/common factor
5. Highest common factor & Lowest common multiple
6. Prime, square and cube numbers
7. Addition, subtraction, multiplication and division including decimals
8. Long multiplication and division and estimation of answers.
9. Simplifying algebra
10.Substitution into formula
11.Constructing and solving equations
12.Trial and Improvement
13.Inequalities
14.Draw graphs of linear equations
15.Place numbers in order
16.Find a percentage, increase or decrease a number by that percent.
17.Decimal places and significant figures
18.Conversions metric to imperial, metric to metric.
19.Ratio: Simplify and divide over a ratio
20.Negative numbers
21.Adding/Subtracting fractions
22.Shading fractions
23.Compound Measures (Speed and density)
Shape, space and Measure
1. Area and perimeter of shapes
(triangle, parallelogram, square, etc)
2. Circumference and area of circle
3. Nets of shapes
4. Find the volume of shapes
5. Angles : classify and measure
6. Identify shapes and names
7. Clocks and TV times/ bus times/ AM & PM
8. Pythagoras theorem.
9. Transformations : Reflection, Rotation, Enlargement & Translation
10. Loci
11. Bearings
Handling Data
1. Mean, mode, median and Range
2. Pictograms, pie charts, frequency graphs
3. Scatter graphs and line of best fit
4. Probability and relative frequency
5. Sample space
6. Composite and multiple bar charts
7. Line graphs
8. Stem and leaf diagrams
9. Sampling types
10. Questionnaires
FOUNDATION
Castle Manor Academy
Mathematics Revision
Key Concepts – Why? How? Explain.
To help your child remember some of the Key Concepts for their GCSE Mathematics Examinations, here are
a list of Fact and Questions that you can review regularly with them.
These questions are broken down into the four sections: Number, Algebra, Shape Space and Measure and
Handling Data.
Ideally spend 15 minutes 2 or 3 times per week asking your child about these key concepts.
If they cannot explain any to you they should use one of the following resources and then you should retest
them the following night:
•
•
•
www.mymaths.co.uk
Their Maths Exercise book
Their Maths teacher
Number
Fact/Question
What your child should be able to tell/show you
A prime number has exactly 2 factors
25 is a square number because 5² = 25
3
4
7
B xB =B
10
2
B divided by B does not equal B
35% of 800 is 280
5
A Shirt costs £60 in a sale. If the sale price
includes a 20% reduction, what would the pre sale
price be?
3/5 = 6/10
2/3 of 60 is 40
-3 – 5 = -8
-6 + 10 = 4
-3 x -4 = 12
3 + 2 x 5 = 13
Estimate 12.35 x 2.76
3(x - 4) = 3x – 12
The cube of 5 is 125
0
7 =1
-5 is bigger than -7
0.4 x 0.2 = 0.08
3 out of 25 is the same as 12%
3
-6
5000 = 5 x 10
0.000006 = 6 x 10
3
4
8
4 x 10 multiplied by 3 x 10 = 1.2 x 10
5
4
3x10 + 2x10 = 3.2 x 10
5
A good estimation of 39.76 x 0.5103 is 20
I travel 7miles in 20min. My average speed is21mph
If a car depreciates at a rate of 10% per year its
value will drop by 19% in the first two years.
Name the first 12 prime numbers
Name the first 12 square numbers.
Explain why this is the case. Can you give another example?
What is the answer? Why? What is the rule you have to
remember?
How do you work this out without a calculator? How
would you do it with a calculator?
Explain why you would divide 60 by 80 and then multiply
by 100 to find the presale price.
Why?
Can you give some other equivalent fraction?
How do you calculate 2/3 of 60?
Explain why
Explain why
Why is it a positive answer?
Why is it 13 and not 25?? (BIDMAS)
Why do I use 10 x 3 to estimate this ?
Explain why
How do you calculate the cube of a number?
0
Explain why 7 is equal to 1
Explain why.
Why is the answer 0.08 and not 0.8
How would you calculate this without a calculator?
How do you write a number in standard form?
How would you calculate this?
How do you add numbers that are given in Standard form?
How would you do this estimation?
Explain why this is.
Why does it drop by 19% and not 20%??
3 2
(2 ) = 64
How did I calculate this?
What is the square root of 36?
The prime numbers between 10 and 20 are 11, 13,
17, 19
Explain why there are two answers.
Why are these prime numbers?
What is the only even prime number?
Explain why 1 is not a prime number
What is meant by the Highest common factor.
How do I calculate the lowest common multiple?
Why do I just multiply these two numbers together to
calculate the lowest common multiple?
How do I share £360 in the ratio of 1:2:3?
The highest common factor of 24 and 30 is 6
The lowest common multiple of 20 and 25 is 100
To work out the lowest common multiple of 11 and
50 I multiply 11 by 50 and get 550
If I share 360 pounds in the ratio of 1:2:3. One
person will get £60, one will get £120 and the third
will get £180
A ring is for sale for £420 plus VAT at 17.5%
Express 60 as a percentage of 96
Algebra
Fact/Question
3,5,7,9 The nth term is 2n + 1
5,11,17,23
If I had y boxes of eggs with six eggs in each box I
would have 6y eggs in total?
When x = -5, 3x + 7 = -8
3x – 2 = 10 has a solution x = 4
5x + 3 = 3x + 13 has the solution x = 5
Expand and simplify (x-4)(x+5)
Solve the equation 5(2x – 3) = 50
List all the integers that satisfy the following
inequality
-6 < 2x < 5
2pq + pq = 3pq
Factorise 3t+12
Expand and simplify
3(x-4) -2(x-10)
A line with equation y = 3x + 4 crosses the y axis at
the point (0,4) and has a slope of 3.
T = 3c + p
Shape and Measure
Fact/Question
How would I enlarge a shape by a scale factor of
2?
If a rectangle has length 5cm and width 10cm it has
2
an area of 50cm . If I enlarge it by a scale factor of
2
2 the area is then 200cm
The area of a circle is pie x radius squared.
Types of triangles are scalene, equilateral,
isosceles and right angles.
What is the full cost of the ring?
The answer is 62.5. How do I use my calculator to work
this out?
What your child should be able to tell/show
you
How do you work out the nth term of a sequence?
What is the nth term of this sequence?
Explain why.
How many eggs would I have left if I ate 4 of the eggs?
How do you calculate this?
How do you calculate this?
How do you calculate this?
What do I mean by expand and simplify?
2
The answer is x +x-20. How do you calculate this?
What do I mean by Solve? How would you solve this
equation?
What do I mean by an integer?
What are all the solutions? (There are 5 in total)
Explain why.
Why is the answer 3(t+4)?
Can you factorise 6t + 15?
2
Can you factorise x + 5x
Why is the answer x + 8
How do you know this?
Can you write the equation of a line that is parallel to y =
3x + 4?
T is the subject of this equation. What does “the subject”
of an equation mean?
Can you rearrange this equation so that c is the subject?
What your child should be able to tell/show
you
2
Why is the new area 200cm and not 100cm
2
What is the area of a circle with a) radius 10cm b)
diameter 15cm.
What are the properties of each of these triangles
Triangles, quadrilaterals and pentagons are all
polygons
A triangle with base length 6cm and height 10cm
2
has an area of 30cm
The area of a circle of radius 5cm is approx
2
78.5cm
0
The external angle of a regular pentagon is 72 .
There are two angles on a straight line. If one of
0
0
them is 30 the other must be 150 .
0
0
If two angles in a triangle are 70 and 50 then
0
the third angle must be 60 .
The order of rotation for a square is 4.
25 miles = 40km
8kg = 17.6lbs
Squares tessellate
2
There are 100mm in one cm
2
2
2
3m = 30000cm
0
If the bearing of A from B is 070 then the bearing
0
of b from a will be 250 .
Handling Data
Fact/Question
2,2,3,4,5,5,5,6
23, 34,34,35,12,13,17,5,36,27,29,30,40
If the probability of winning a match was 0.4. I
would expect to win 60 matches if I played 150
times.
If the probability of winning a match was 0.7 and
the probability of losing a match was 0.23. What is
the probability of drawing the match?
The temperature and the number of ice creams
sold have a positive correlation.
What is a polygon?
How do you calculate this?
What formula did I use to calculate this area?
How did I work this out?
What is the external angle always the same as?
Explain why this is the case.
0
Why must the third one be 60 ?
Why does a square have order of rotation 4?
What is the order of rotation of a rectangle?
How do you convert from miles to Km?
How do you convert Kg to pounds?
What is meant by tessellation?
She how you would tessellate an equilateral triangle.
Explain why this is the case even though there are only
10mm in one cm.
How does this work?
Explain why this is the case.
What your child should be able to tell/show
you
This sequence has a range of 5. Explain why
This sequence has a mean of 4. Explain why
The sequence has a mode of 5. Explain why
The sequence has a median of 4.5. Explain why
How would you display this info in a stem and leaf
diagram?
How do you calculate this?
Why is the answer not 0.7?
Why is it 0.07
What is meant by a positive correlation?
What is meant by a negative correlation and how would
you recognise one on a scatter graph?
Area
Area rectangle = length x width
L
W
H
Area triangle = (base x height) ÷2
B
H
Area of parallelogram = base x height
B
D
R
Area of circle = Π x r x r
OR Π x r2
Circumference of circle = 2 x Π x r OR
Πxd
Volume
Volume of a cylinder = Πr2h
Pythagoras theorem
c
b
Speed and Density
2
2
a +b
= c
2
Speed = Distance
Time
D
S
T
a
Density = Mass
Volume
M
D
Polygons
For an n sided polygon sum of interior angles = 180(n – 2)
Sum of exterior angles for any polygon = 360o
Interior
angle
Exterior
angle
V
Conversions to Learn
Metric
Length
10mm
100cm
1000m
=
=
=
1cm
1m
1km
Mass
1000mg
1000g
1000kg
=
=
=
1g
1kg
1tonnes
Volume
1000ml
1ml
=
=
1litre
1cm³
Imperial
12 inches
3 feet
1760 yards
16 ounces
14 pounds
2240 pounds
8 pints
=
=
=
=
=
=
=
1foot
1yard
1mile
1 pound
1 stone
1 ton
1 gallon
Metric/Imperial
1 foot
2.5cm
8km
1 kg
1 gallon
≈
≈
≈
≈
≈
30 cm
1 inches
5 miles
2.2pounds
4.5 litres
Year 11 Revision Topics - Higher
Use your textbook to revise and practice questions from at least one of these topics
every evening:
Number
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
and Algebra
Fractions and decimals
Squares, cubes and index laws
Checking solutions to calculations
Change the subject of a formulae
Formulae
Linear equations
Ratio
Expand quadratic expressions
Proportion
Graphs of quadratic equations
Linear inequalities
Prime factors, HCF and LCM
Percentages
Trial and improvement
Linear sequences
3-D coordinates and midpoints
Percentage increase and decrease
Use and generate formula
Repeated percentage change
Expand and solve quadratics
Standard form
Fractions
Simultaneous equations
Cubic and reciprocal graphs
Equation of a straight line
Upper and lower bounds
Rearrange formulae
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Quadratic expressions and equations
Equations of straight lines
Proportional relationships
Exponential growth and decay
Algebraic manipulation
Rational and irrational numbers/ surds
Quadratic equations, completing the square and quadratic
formula
Algebraic proof
Standard transformations of functions
Graphs of trigonometrical functions
Graphs of exponential functions and circles
Vectors
Shape, Space and Measure
Loci and constructions
Angles on parallel lines, in polygons and tangents
Pythagoras
Area and circumference of circles
Surface area and volume of prisms
Speed, density
Formulae for area, perimeter and volume
Transformations
Trigonometry
Similar triangles
Measures
Circle theorems
Sector area, arc length and volumes of 3D shapes
Length and angle. Problems in 3 -D shapes
Length, area and volume scale factors
Congruence
Sine and cosine rules
Handling Data
1.
Probability and relative frequency
2.
Mean from grouped data
3.
Scatter diagrams
4.
Tree Diagrams
5.
Cumulative frequency diagrams and box plots
6.
Compare distributions
7.
Sampling including stratified
8.
Histograms
9.
Probability
10.
11.
Interpret real life graphs
Compare data
HIGHER:
Castle Manor Academy
Mathematics Revision
Key Concepts – Why? How? Explain.
To help your child remember some of the Key Concepts for their GCSE Mathematics Examinations, here are
a list of Fact and Questions that you can review regularly with them.
These questions are broken down into the four sections: Number, Algebra, Shape Space and Measure and
Handling Data.
Ideally spend 15 minutes 2 or 3 times per week asking your child about these key concepts.
If they cannot explain any to you they should use one of the following resources and then you should retest
them the following night:
•
•
•
www.mymaths.co.uk
Their Maths Exercise book
Their Maths teacher
Number
Fact/Question
What your child should be able to tell/show you
A prime number has exactly 2 factors
25 is a square number because 5² = 25
3
4
7
B xB =B
10
2
B divided by B does not equal B
35% of 800 is 280
5
A Shirt costs £60 in a sale. If the sale price
includes a 20% reduction, what would the pre sale
price be?
3/5 = 6/10
2/3 of 60 is 40
-3 – 5 = -8
-6 + 10 = 4
-3 x -4 = 12
3 + 2 x 5 = 13
Estimate 12.35 x 2.76
3(x - 4) = 3x – 12
The cube of 5 is 125
0
7 =1
-5 is bigger than -7
0.4 x 0.2 = 0.08
3 out of 25 is the same as 12%
3
-6
5000 = 5 x 10
0.000006 = 6 x 10
3
4
8
4 x 10 multiplied by 3 x 10 = 1.2 x 10
5
4
3x10 + 2x10 = 3.2 x 10
5
A good estimation of 39.76 x 0.5103 is 20
I travel 7miles in 20min. My average speed is21mph
If a car depreciates at a rate of 10% per year its
value will drop by 19% in the first two years.
Name the first 12 prime numbers
Name the first 12 square numbers.
Explain why this is the case. Can you give another example?
What is the answer? Why? What is the rule you have to
remember?
How do you work this out without a calculator? How
would you do it with a calculator?
Explain why you would divide 60 by 80 and then multiply
by 100 to find the presale price.
Why?
Can you give some other equivalent fraction?
How do you calculate 2/3 of 60?
Explain why
Explain why
Why is it a positive answer?
Why is it 13 and not 25?? (BIDMAS)
Why do I use 10 x 3 to estimate this ?
Explain why
How do you calculate the cube of a number?
0
Explain why 7 is equal to 1
Explain why.
Why is the answer 0.08 and not 0.8
How would you calculate this without a calculator?
How do you write a number in standard form?
How would you calculate this?
How do you add numbers that are given in Standard form?
How would you do this estimation?
Explain why this is.
Why does it drop by 19% and not 20%??
3 2
(2 ) = 64
How did I calculate this?
What is the square root of 36?
The prime numbers between 10 and 20 are 11, 13,
17, 19
Explain why there are two answers.
Why are these prime numbers?
What is the only even prime number?
Explain why 1 is not a prime number
What is meant by the Highest common factor.
How do I calculate the lowest common multiple?
Why do I just multiply these two numbers together to
calculate the lowest common multiple?
How do I share £360 in the ratio of 1:2:3?
The highest common factor of 24 and 30 is 6
The lowest common multiple of 20 and 25 is 100
To work out the lowest common multiple of 11 and
50 I multiply 11 by 50 and get 550
If I share 360 pounds in the ratio of 1:2:3. One
person will get £60, one will get £120 and the third
will get £180
A ring is for sale for £420 plus VAT at 17.5%
Express 60 as a percentage of 96
Express 48 as a product of its primes
The cost of ribbon is directly proportional to its
length. If 2.5m = £1.35, what is the cost of 6m?
What is the upper and lower bound of 48 (2 s.f.)?
If I put £25 into a savings account with an interest
rate of 5% per year. How much would I have after 6
years?
Algebra
Fact/Question
3,5,7,9 The nth term is 2n + 1
5,11,17,23
If I had y boxes of eggs with six eggs in each box I
would have 6y eggs in total?
When x = -5, 3x + 7 = -8
3x – 2 = 10 has a solution x = 4
5x + 3 = 3x + 13 has the solution x = 5
Expand and simplify (x-4)(x+5)
Solve the equation 5(2x – 3) = 50
List all the integers that satisfy the following
inequality
-6 < 2x < 5
2pq + pq = 3pq
Factorise 3t+12
Expand and simplify
3(x-4) -2(x-10)
A line with equation y = 3x + 4 crosses the y axis at
the point (0,4) and has a slope of 3.
T = 3c + p
Show that the equation x3 – 2x has a solution
between 2 and 3
What is the full cost of the ring?
The answer is 62.5. How do I use my calculator to work
this out?
How do you express a number as a product?
Do we need to simplify the answer?
How do I find the cost of 1m?
How do I round to significant figures?
What is the formula for repeated percentage increase?
Why can I not just find 5% and then multiply by 6?
What your child should be able to tell/show
you
How do you work out the nth term of a sequence?
What is the nth term of this sequence?
Explain why.
How many eggs would I have left if I ate 4 of the eggs?
How do you calculate this?
How do you calculate this?
How do you calculate this?
What do I mean by expand and simplify?
2
The answer is x +x-20. How do you calculate this?
What do I mean by Solve? How would you solve this
equation?
What do I mean by an integer?
What are all the solutions? (There are 5 in total)
Explain why.
Why is the answer 3(t+4)?
Can you factorise 6t + 15?
2
Can you factorise x + 5x
Why is the answer x + 8
How do you know this?
Can you write the equation of a line that is parallel to y =
3x + 4?
T is the subject of this equation. What does “the subject”
of an equation mean?
Can you rearrange this equation so that c is the subject?
How do I show this using trial and improvement?
Solve x2 + 4x – 10 = 0
How do I complete the square?
Solve x2 – 5x + 3 = 0
What is the quadratic formula? How do I use it to solve
this?
What is the gradient and y intercept of the following What do m and c stand for in y = mx + c
straight line graph: y = 3x + 6 ?
What would be the gradient of a line perpendicular
to y = 2x – 2 ?
How do you know if a line is parallel or perpendicular?
Solve
How do you solve simultaneous equations?
3x + y = 5
5y + 4x = 14
Shape and Measure
Fact/Question
How would I enlarge a shape by a scale factor of
2?
If a rectangle has length 5cm and width 10cm it has
2
an area of 50cm . If I enlarge it by a scale factor of
2
2 the area is then 200cm
The area of a circle is pie x radius squared.
Types of triangles are scalene, equilateral,
isosceles and right angles.
What your child should be able to tell/show
you
2
Why is the new area 200cm and not 100cm
2
What is the area of a circle with a) radius 10cm b)
diameter 15cm.
What are the properties of each of these triangles
A 10m long ladder is lent against a wall at
an angle of 720. How far will the ladder be
from the bottom of the wall?
Work out the size of each interior angle in
a regular decagon.
What is SOH CAH TOA?
Construct a 300 angle.
How do I construct an angle of 600?
Calculate the volume of a cylinder with a
radius of 4cm and a height of 6cm.
How do I calculate the cross sectional area of a cylinder?
What does congruence mean?
What are the features of congruent shapes?
Find the missing
angles n, o and p.
Triangle ABC is such that a = 6cm, b= 9
cm and C = 250. Work out the area of
triangle ABC.
What do the exterior angles of a shape add up to?
What are the different circle theorems?
How do you use the formula
1 ab sin C ?
2
Triangles, quadrilaterals and pentagons are all
polygons
A triangle with base length 6cm and height 10cm
2
has an area of 30cm
The area of a circle of radius 5cm is approx
2
78.5cm
0
The external angle of a regular pentagon is 72 .
There are two angles on a straight line. If one of
0
0
them is 30 the other must be 150 .
0
0
If two angles in a triangle are 70 and 50 then
0
the third angle must be 60 .
The order of rotation for a square is 4.
25 miles = 40km
8kg = 17.6lbs
Squares tessellate
2
There are 100mm in one cm
2
2
2
3m = 30000cm
0
If the bearing of A from B is 070 then the bearing
0
of b from a will be 250 .
Handling Data
Fact/Question
2,2,3,4,5,5,5,6
23, 34,34,35,12,13,17,5,36,27,29,30,40
If the probability of winning a match was 0.4, I
would expect to win 60 matches if I played 150
times.
If the probability of winning a match was 0.7 and
the probability of losing a match was 0.23. What is
the probability of drawing the match?
The temperature and the number of ice creams
sold have a positive correlation.
What is a polygon?
How do you calculate this?
What formula did I use to calculate this area?
How did I work this out?
What is the external angle always the same as?
Explain why this is the case.
0
Why must the third one be 60 ?
Why does a square have order of rotation 4?
What is the order of rotation of a rectangle?
How do you convert from miles to Km?
How do you convert Kg to pounds?
What is meant by tessellation?
She how you would tessellate an equilateral triangle.
Explain why this is the case even though there are only
10mm in one cm.
How does this work?
Explain why this is the case.
What your child should be able to tell/show
you
This sequence has a range of 5. Explain why
This sequence has a mean of 4. Explain why
The sequence has a mode of 5. Explain why
The sequence has a median of 4.5. Explain why
How would you display this info in a stem and leaf
diagram?
How do you calculate this?
Why is the answer not 0.7?
Why is it 0.07
How do you draw a histogram?
What is meant by a positive correlation?
What is meant by a negative correlation and how would
you recognise one on a scatter graph?
What do the bars represent?
How do you calculate the mean from a
frequency table with grouped data?
Mark decided to carry out a questionnaire to
find out how many DVDs people buy.
What extra columns do you need to add to the table?
Which columns do you total?
What are the key guidelines you need to remember when
writing questionnaires?
He uses this question on his questionnaire:
How many DVDs do you buy?
1–5
5 – 10
10 – 15
15 – 20
Write two different things that are wrong with
this question.
A teacher takes a stratified sample of 50
pupils. There are 276 boys and 324 girls in the
group. How many boys and girls would be
sampled?
What is the definition of a stratified sample?
What is the definition of a random sample?
Three ordinary coins are flipped.
Draw a tree diagram to show the possible
outcomes.
Work out the probability of getting:
i) 3 heads ii) 2 heads and a tail (in any order)
What values do you multiply and which do you add when
using tree diagrams?
How do you draw a pie chart?
How do you calculate the angles from the frequencies?