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Junior Cert Maths

Junior Cert Maths. Crash Course. What you need on the day:. Pen Pencil Calculator Compass Set squares Protractor Ruler. Key Terms. Common Mistakes to Avoid:. Be careful with minus signs – the single most common source of error

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Junior Cert Maths

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  1. Junior Cert Maths Crash Course

  2. What you need on the day: Pen Pencil Calculator Compass Set squares Protractor Ruler

  3. Key Terms

  4. Common Mistakes to Avoid: Be careful with minus signs – the single most common source of error Don’t try to do too much in one step – break it down into smaller steps. If your workings become overly-complicated, check back in case you’ve made a slip. Always feel free to check any calculation using your calculator. In many questions, especially algebra, you can do checks on your answer to make sure you have got it right before moving on. Attempt everything!!!!!! Ask yourself, using estimates and common sense – does this answer look right? If not, then re-check your work. Give answers to the correct degree of accuracy as requested e.g. to 2 decimal places. Make sure you answer the question you’ve been asked – check this before moving on. If you have enough time, recheck all steps and your final answer (at the end of exam)

  5. Paper Breakdown by Topic: Paper 1 Paper 2 Statistics Probability All the Geometries Co-ordinate Transformation Area Volume Axioms and Proofs Constructions • Number Systems • Applied Arithmetic • Sets • Algebra • Functions

  6. Number systems • Natural Numbers (N) 1 2 3… • Integers (Z) -3 -2 -1 0 1 2 3 • Rational Numbers: Anything a/b • Irrational: Anything not a/b • Real Numbers: Anything with a number • Prime Factors, LCM, HCF and BIMDAS • Number lines and graphing • Inequalities < > • Ratio and proportion • Index Laws • Scientific Notation • Surds and reciprocals

  7. Applied Arithmetic • 24 Hour Clock • VAT • Speed Distance Time • Bills • Percentage Profit/Loss • Percentage Increase/decrease • Income Tax • Compound Interest • Currency Exchange • Timetables

  8. Sets • Operations • Union • Intersection • Subset • Element • Complement ‘ • Null Set • Cardinal Numbers # • Less A\B • Associative Property • Distributive Property • Read and Write Venn Diagrams

  9. Algebra • Simplifying Expressions • Solving equations • Rearrangement of formula • Form equation from paragraph • Simultaneous equations • Use tables and graphs to represent and analyse patterns • Quadratic Equations and formula • Equations with fractions • Algebraic division • Factorise • Taking out HCF • Factoring by grouping • Quadratics • Difference of two squares

  10. Functions • Domain • Co-domain • Range • Shape of graphs • Min Max from graph • Points of intersection

  11. Statistics • Bias • Methods of Collecting Data • Types of data • Appropriate graph for a data set • Bar Chart • Histogram • Pie chart • Stem and Leaf • Line plot • Mean, Mode, Median, & Range • Interquartile Range

  12. Probability • Familiarise with dice, deck of cards and coin odds. • Probability Scale, 0 – Impossible 1 – Certain • Estimate probability from given info • Sample Spaces • List possible outcomes • Fundamental Principal of Counting

  13. Area Volume • Find lengths, area, and volumes from given information using formula from log tables • Scale diagrams • Draw Nets of 3D shapes

  14. Log Tables p10 p11

  15. Co-Ordinate Geo

  16. Constructions • Measuring a length on a line segment • Measuring an angle on a line segment • Bisecting an Angle • Bisecting a Line • Constructing a Perpendicular bisector through a point • Dividing a Line into Equal Parts • Construct a triangle given the lengths of three sides • Construct a triangle given the length of two sides and one angle • Construct a triangle given the length of one side and two angles • Construct a right angled triangle given the length of two sides • Construct a right angled triangle given the length of one side and one angle • Construct an equilateral triangle • Constructing a rectangle PRACTISE PRACTISE PRACTISE

  17. Axioms and Proofs Axioms Formal Proofs Angles in a triangle add to 180 Exterior angle = sum of 2 interior opposite angles In parallelogram, opposite angle are equal and opposite sides are equal Theorem of Pythagoras The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc • One line through any 2 points • Distance is never negative • AB = BA • If C is between A and B then AB = AC +CB • Triangle Congruence • SSS, ASA, SAS, RHS • A null angle = 0, right angle = 90, straight angle = 180 • Given any line l and point p, there is exactly one line which is perpendicular to l through p

  18. Trigonometry • Pythagoras • Use Sin Cos or Tan to find missing angle or side • Howto find the sin, cos and tan of an angle less than 90° • Howto find the measurement of an angle if given the sin, cos or tan of that angle • Work with trigonometric ratios in surd form for angles of 30°, 45° and 60° • Be able to work with angles in degrees, minutes and seconds and in decimal form • How to solve right-angled triangles using Pythagoras’s theorem or using sin, cos or tan This Photo by Unknown Author is licensed under CC BY-SA

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