Download Higher GCSE Key Facts to learn 203.78KB 2017

De La Salle College Mathematics Department
Useful Resources

Student Shared Area resources: See detail in table below of available resources
www.dls-jersey.co.uk /
Folder Title
Maths Help
Booklet for
students
10 Ticks
Practice
worksheets
Past Papers
login / Remote Access / RM Shared Docs / Secondary pupils / Maths
Description
Guidance for use
Available in the main ‘Maths’
folder; this provides a summary of
each of the main topics at GCSE. A
hard copy of the booklet can be
obtained from the Maths
Department.
Huge number of worksheets
arranged by National Curriculum
Level. Students will benefit from
practising worksheet designated
from level 5 to levels 7_8 (targeting
D grade to B grade content). Not all
of the levels 7_8 content is relevant
to the Foundation tier of entry and
much relates to Higher tier.
Past papers dating back to 2011 for
a range of examination boards.
Students at De La Salle are prepared
for the AQA examination board
papers and will be double-entered
for both AQA and WJEC papers in
June of Year 11. Past papers are
accompanied by mark schemes.
Use the contents page at the front of the booklet to look up
key topics. These are sorted by ‘Number’, ‘Algebra’,
‘Statistics’ and ‘Shape and Space’. The booklet summarises
the methods taught throughout secondary school and provides
a tool for students to complete independent research when
stuck.
Open excel document entitled; “A Topic reference” and use
the ‘Find and select’ option on the tool bar to ‘Find’ specific
topics by key word search.
Homework
papers
This folder contains copies of all of
the KS4 homework papers which
are designed to provide ongoing
revision towards the final
examinations.
Schemes of
learning
This contains folders showing our
teaching methodology which
explains how to understand topics
within each of the main areas of
‘Arithmetic’ (Number and Algebra),
‘Statistics’ and ‘Shape, Space and
Measure’.
1
Note the ‘Ref.’ Including level of pack, pack number and
page number
Select the pack and print off / view relevant pages. Answers
are included in separate folders.
Use the ‘Recommended Foundation examination practice’
column in the Study Plan to complete a past paper each week,
alternating between Non-Calculator and Calculator papers.
Check solutions using the mark schemes and highlight areas
of miscomprehension or weakness. Attend the weekly Maths
clubs to address these areas.
Use the ‘Maths Help Booklet for students’ in the student
shared area (or obtain a hard copy from the Maths
department) to help with independent study and to look up
topics while completing the past papers.
While students will continue to be set homework papers on a
weekly basis and all students are expected to complete these
or correct these to a minimum C grade pass (see grading in
footnotes on each paper), students can revisit old assignments,
or access future assignments through this folder. Staff in the
department are happy to mark completed papers and support
students with areas of weakness.
Identify an area of weakness, or focus on a recommended
topic focus as shown in the Study Plan, and target a relevant
worksheet in the ‘Topic Revision worksheets’ folder within
the ‘Schemes of Learning’ folder.
Use the learning plans to review the methods taught in class.
These learning plans provide more detail than each of the
summary pages in the student ‘Maths Help Booklet for
students’.
De La Salle College Mathematics Department
FOUNDATION GCSE MATHEMATICS:
STUDENTS MUST MEMORISE THE FOLLOWING:
N
Not to scale:
N
Bearings are measured from north in a clockwise
direction and are written with 3 figures
eg Bearing of B from A is 048o Bearing of A from B is 312o
48
B
312o
o
A
Interior angles of a triangle add up to 180 degrees
Interior angles of a quadrilateral add up to 360 degrees
Interior angles of a pentagon add up to 540 degrees etc
Exterior angles of any shape add up to 360 degrees
a
b
d
c
f
e
g
b
h
Parallel Lines and Transversals
Opposite angles are the same (a & d , b & c , e & h , f & g)
Corresponding angles are the same (a & e , b & f , c & g , d & h)
Alternate angles are the same (c & f , d & e)
and all angles on a straight line are supplementary meaning they
add up to 180 degrees
Perimeter = length around the outside edge of a closed shape
Area of a rectangle = length × width cm2
Area of a triangle = ½ base × height cm2
cm
(area is equivalent to counting how many squares)
(complete the triangle into a rectangle then halve the area)
l1
h
Area of trapezium = (average of length 1 and length 2) × height
l2
Volume of a prism = Area of cross section × length of prism
tangent
radius
chord
i.e.
l1  l 2
 h cm2
2
cm3
Parts of a circle,
circumference and area
diameter
sector
C = πd
“Cherry pie’s delicious,
Apple pies are too!
circumference
Circumference of circle = п × diameter (where п ≈ 3.14)
Area of circle = п × radius2
Pythagoras’ Theorem: for any right-angled triangle: a2 + b2 = c2
Remember: always label the length opposite the right angle: “c”
2
A = πr2
c
b
a
b
De La Salle College Mathematics Department
Imperial to metric conversions
2.2 pounds (lbs) ≈ 1 kilogram
5 miles ≈ 8 kilometres
1 gallon ≈ 4.5 litres
1 inch ≈ 2.5 centimetres
1.75 pints ≈ 1 litre
1 foot ≈ 30 centimetres
Metric equivalences
10 millimetres = 1 centimetre
100 centimetres = 1 metre
1000 millimetres = 1 metre
1000 metres = 1 kilometre
1000 milligrams = 1 gram
1000 grams = 1 kilogram
1000 kilograms = 1 (metric) tonne
Compound measures:
Speed =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
Imperial equivalences
12 inches = 1 foot
14 pounds = 1 stone
𝑀𝑎𝑠𝑠
Density = 𝑉𝑜𝑙𝑢𝑚𝑒
𝑇𝑖𝑚𝑒
Naming some common shapes and properties of shapes
2D
3D
Equilateral triangle (all sides same length)
Triangular-based pyramid (tetrahedron)
Isosceles triangle (2 sides same length)
Square-based pyramid
Scalene triangle (all sides different length)
Cone
Square
Cube
Rectangle
Cuboid
Rhombus (like a diamond … diagonals perpendicularly bisect)
Triangular prism (understand the word prism!)
Parallelogram (2 pairs of parallel sides)
Cylinder
Kite (one diagonal perpendicularly bisects the other)
Trapezium (just one pair of parallel sides eg:
)
Equivalent fractions, decimals and percentages:
1
2
 0.5  50%
1
3
 0.3333...  33.333...%
1
8
 0.125  12.5%
1
9
 0.1111...  11.11...%
1
4
 0.25  25%
3
8
2
3
3
4
 0.75  75%
 0.2  20%
2
5
 0.4  40%
3
5
 0.6  60%
 0.6666...  66.666...%
 0.375  37.5%
2
9
1
5
5
8
 0.625  62.5%
7
8
 0.875  87.5%
 0.2222...  22.222...% etc
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 … etc
Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … etc
Cube numbers: 1, 8, 27, 64, 125 … etc
Triangular numbers: 1, 3, 6, 10, 15, 21, 28, … etc
Equation of a straight line:
or
y = mx + c
…
y=…x+…
(where m is the gradient and c is the y-intercept)
Averages and spread:
f = frequency (this means “how many”)
x = the variable
Mean: Sum of values ÷ number of values
(this involves “making all piles the same size”)
Median: Middle value when written in size order
Mode: Most common value
Range: Largest value – smallest value
3
De La Salle College Mathematics Department
HIGHER GCSE MATHEMATICS:
STUDENTS MUST MEMORISE THE FOLLOWING:
Indices:
ax a ∗ 𝑏𝑥 𝑏 = 𝑎𝑏𝑥 𝑎+𝑏
𝑥𝑎
= 𝑥 𝑎−𝑏
(𝑥 𝑎 )𝑏 = 𝑥 𝑎𝑏
1
𝑥 −𝑎 = 𝑥 𝑎
𝑥𝑏
1
𝑎
𝑥 𝑎 = √𝑥
𝑥0 = 1
Surds: √ab = √𝑎√𝑏
√𝑎 + √𝑎 = 2√𝑎
√𝑎
√𝑏
𝑎
= √𝑏
Eg.
2𝑥 3 ∗ 4𝑥 5 = 2 ∗ 4 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥 = 8𝑥 8
𝑥4
𝑥∗𝑥∗𝑥∗𝑥
Eg.
Eg.
Eg.
= 𝑥∗𝑥 =
2 3
(𝑥 ) = 𝑥 6
1
1
8−2 = 82 = 64
Eg.
Eg.
92 = √9 = 3
1000 = 1
𝑥2
1
Eg.
Eg.
Eg.
𝑥2
1
= 𝑥2
2
√40 = √4√10 = 2√10
√5 + √5 = 2√5
√20
√5
20
= √ 5 = √4 = 2
Circle Theorems:
Angle in a semi-circle
Angles in the same
The angle in the centre
The angle between
Is 90°
segment are equal
is double the angle at the circum. Radius and tangent
Is 90°
Opposite angles in a
cyclic quadrilateral
add up to 180°
Alternate segment
theorem
Tangents which meet at a point
are equal in length
Types of Graph:
…
Linear: y = … x + …
(one solution for x)
4
Quadratic: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
(up to two solutions for x)
Cubic: : 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑
(up to three solutions for x)
De La Salle College Mathematics Department
Pythagoras Theorem:
Trigonometry:
c
a
h
o
a² + b² = c²
Sin 𝜃 = ℎ𝑜 Cos 𝜃 = 𝑎ℎ Tan 𝜃 = 𝑎𝑜
𝜃
b
a
Formulae:
a
Area of a Triangle:
h
Area of a Trapezium:
A=½hxb
h
A = ½ (a+b) x h
b
b
Volume of a Sphere:
Volume of a Cone:
4
1
V = 3 𝜋𝑟 2 ℎ
V = 3 𝜋𝑟³
B
Sine Rule:
a
a
C
a
A
a
b
a
Cosine Rule:
𝟏
Area of any triangle = 𝟐 𝒃𝒄 𝑺𝒊𝒏𝑨
B
a
a
C
a
c
a
b
a
Quadratic Formula:
To solve 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
5
𝒂
𝒃
𝒄
=
=
𝑺𝒊𝒏 𝑨
𝑺𝒊𝒏 𝑩
𝑺𝒊𝒏 𝑪
c
a
𝒂² = 𝒃𝟐 + 𝒄𝟐 − 𝟐𝒃𝒄 𝒄𝒐𝒔 𝑨
A
a
x=
−𝑏 ± √𝑏2 −4𝑎𝑐
2𝑎