Junior Cert Ordinary Level Paper 1

Transcription

1 Sets Junior Cert Ordinary Level Paper 1 Write down the elements of a set Is something an element/not an element of a set Null Set Equal sets are these sets equal Subsets Be able to draw a Venn diagram The Universal set A B - All of A Union (And) all of B A B - A Intersection B A B - In A but not in B U - Universal Set A - A Compliment (Everything not in A) # - Cardinal Number of a Set (The number of elements in a set) Arithmetic Use and apply the laws of indices Write ratios in their simplest form Cancel down Divide amounts into a ratio - Add ratio numbers together - Divide this number into the amount - Multiply each ratio by this amount Equivalent ratios ratios that are equal Direct proportion Inverse proportion Factors a factor of a number is any number that divides exactly into it Divisors numbers that divide into a number exactly Multiples the numbers in that numbers times tables. E.G. The multiples of 3 are: 3, 6, 9, 12, Write a number as a product of its prime factors Wages - Find the tax on the 1 st amount - Take the 1 st amount from the annual wage and find the tax on this amount - Add the two tax amounts together to find the gross tax - Take the tax credit from the gross tax to find out the tax payable Distance, Speed & Time - Distance = Speed Time - Speed = Distance Time - Time = Distance Speed Percentages - To find a percentage of a number divide by 100 and multiply by the number given - To find one number as a percentage of the other put the first number over the second and multiply by 100 Solve percentage profit & loss problems Percentage discount Calculate Compound Interest for 1, 2 or 3 years Covered in Class Revised

2 Algebra VAT - Adding vat on: Divide by 100, multiply by the vat rate & add onto the original price Currency - Look at the exchange rate and work out if amount of money goes up or down Estimation & Rounding - 5 and higher round up; 4 and lower round down Subbing in numbers for letters Collecting like terms only add/subtract same letters Multiplying out brackets Multiplying x by x Simplifying Solve simple equations with letters on one side & numbers on the other Solving equations with letters on both sides Removing brackets & then solving equations multiply the brackets by what s outside them Making your own equations & finding x Taking out the Highest Common Factor - Taking out the highest number/letter & putting it outside the brackets Factorising by grouping split the expression into 2 & factorise both parts Factorise quadratic Equations Difference of Two Squares Solve inequalities & be able to graph them on a number line. Dots for Natural numbers & Integers, Thick line for Real numbers Adding/subtracting algebraic Fractions Find the lowest common denominator Solving equations with fractions only cross multiply if there s only one thing on either side of the = if there s 2 things on one side of the equals simplify that first to a single fraction Simplifying algebraic fractions Solving quadratic equations. Factorise and then let both brackets equal 0 Making written equations with x 2 and solve to find x Simultaneous Equations. Eliminate the x s or the y s and then sub in your answer for x or y, which ever you ve found first Make your own simultaneous equation & solve Sequences & Patterns List the next 3,4 or 5 terms in a linear sequence Find the common difference between each term in a linear sequence Describe the rule for a sequence in your own words Draw the next pattern in a sequence Write the first 5 or 6 terms of a sequence when given the nth term (T n ) Find the general term (T n ) of a sequence Use a table to represent a pattern/sequence Graph a linear sequence Recognise a non-linear sequence (Quadratic or Exponential) Generate a Quadratic sequence from its nth term (T n ) Find the first & second difference of a quadratic sequence Recognise the graph of a quadratic sequence Recognise an exponential sequence (a sequence that is doubling or trebling)

3 Functions Know what the domain & range are Be able to sub into a function Be able to plot coordinates Be able to graph lines on graph paper Be able to recognise the point of intersection Be able to recognise lines parallel to the axes Draw a quadratic graph Find the maximum & minimum points of a quadratic function from its graph The Metric System Convert lengths and weights Find the length of time on a timetable Find the distance, speed and time Perimeter, Area & Volume Junior Cert Ordinary Level Paper 2 Find the perimeter of a square/rectangle (2 length + 2 width) Find the area of a square/perimeter (length x width) Find the missing side of a rectangle when given the area divide the area by the side you re given. To find the missing side when given the perimeter take away the side you re given 2 times & divide your answer by 2 Find the area of a triangle( ½ base x height) Find the base or perpendicular height of a triangle when given the area - sub what you re given into ½ base x height Remember to include units in your answer Find the area of a compound shape by breaking it into smaller shapes Find the area of a border find the area of the outside shape and then the area of the inside shape & then take the inside from the outside Find the volume of a rectangular solid using l x w x h Find the length of a missing side in a rectangular solid when given 2 sides and the volume Find the surface area of a rectangular prism using 2lb + 2lh + 2bh Volume: Rectangular Solid: l w h Cube: l 3 Cylinder: πr 2 h Sphere: 4 3 πr3 Hemisphere: 2 3 πr3 Units: cm 3, mm 3, m 3, km 3 Total Surface Area: Cuboid: 2lb + 2lh + 2bh Cube: 6l 2 Cylinder: 2πrh + 2πr 2 Sphere: 4πr 2 Hemisphere: 2πr 2 + πr 2 Units: cm 2, mm 2, m 2, km 2 Covered in Class Revised

4 Statistics Probability Combined Solids Break up the shape into manageable pieces i.e. into a cone, a cylinder and a hemisphere and find the volume of the separate parts & then add them together. Draw a bar chart Read information from a bar chart Draw a pie chart Read information from a pie chart Construct a Stem & Leaf Diagram Find the median & mode of a Stem & Leaf Diagram Find the mode. Mode is most common Mean or average add all the numbers and divide by the number of numbers Find the range the difference between the smallest & the biggest Find the median the middle value Find the mean of a frequency distribution table Find the mode of a frequency distribution table Place events on the probability scale, 0 = impossible; 1 = certain Find the probability of an event occurring Calculate the probability of an event not occurring Know the Fundamental Principle of Counting List all the possible outcomes of an experiment Use a sample space to list the outcomes of 2 events Use a tree diagram to list the outcomes of 2 events Find the relative frequency of an event Find the expected frequency of an event Coordinate Geometry Be able to plot coordinates Find the distance between two points using the formula Find the midpoint between two points using the formula Translate a point Find the slope of a line using the formula Reflect a point through the axes & through the origin Find the equation of a line when given the slope and a point on the line Be able to figure out where a lines crosses the y axis from looking at the equation of that line Be able to write down the slope of a line by looking at the equation of that line slope is the number in front of the x Verify a point is on a line by subbing the point into the equation. Find the point where a line crosses the y axis by subbing in x=0 Find the point where a line crosses the x axis by subbing in y=0 Find the point of intersection of 2 lines using simultaneous equations Trigonometry Know what a Right Angled Triangle is Use Pythagoras to find missing sides when there s ONE missing side & it s a RIGHT ANGLED TRIANGLE! Use SOH CAH TOA to write down the value of angles as fractions Use SOH CAH TOA to find missing angles & sides of a Right Angled Triangle Know when to use Sin 1, Tan 1, Cos 1 Angle of depression, Angle of Elevation

5 Solve Real life problems using trigonometry Transformation Geometry List the number of lines of symmetry a shape has Find the image of a point, line, triangle, square through axial symmetry Find the image of a point, line, triangle, square through central symmetry Translate a point or a shape from one position to another Geometry Know what acute/obtuse/reflex angles are The sum of the angles on a straight line is 180 The sum of the angles at a point is 360 Find the missing angles on a straight line/ at a point Use a protractor to measure the size of an angle Vertically opposite angles are equal Corresponding angles are equal (parallel lines) Alternate angles are equal in size (parallel lines) Fill in the missing angles on a set of parallel lines Know the sum of the angles in a triangle is 180 Find the missing angles in a triangle Know that the exterior angle of a triangle is equal to the two interior angles added together Prove two triangles are congruent using SSS, SAS, ASA, RHS In isosceles triangle two sides and two angles are equal Angles and sides in a equilateral triangle are all equal The biggest angle in a triangle is opposite the longest side Know the properties of a square and a rectangle Opposite sides and opposite angles in a parallelogram are equal A diagonal bisects the area of a parallelogram Use Pythagoras theorem to find a missing side in a right angled triangle Angle in a semicircle standing on a diameter is a right angle In a cyclic quadrilateral opposite angles add up to 180 Construction 1: Construct the bisector of an angle Construction 2: Construct the perpendicular bisector of a line Construction 4: Construct a line perpendicular to a given line l, passing through a given point Construction 5: Construct a line parallel to a given line, through a given point Construction 6: Divide a line segment into 2 or 3 equal parts Construction 8: Construct a line segment of a given length on a given ray Construction 9: Construct an angle of a given number of degrees Construction 10: Construct a triangle when given the lengths of all 3 sides Construction 11: Construct a triangle when given the lengths of 2 sides and 1 angle (SAS) Construction 12: Construct a triangle when given the size of 2angles and the length of 1 side (ASA) Construction 13: Construct a Right-Angled triangle, given the length of the hypotenuse and one other side Construction 14: Construct a Right-Angled triangle, given one side and one other angles Construction 15: Construct a rectangle, given the side lengths