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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