Check list for Int 2 Mathematics

Intermediate 2 Checklist

Unit 1 Outcome 1 – Percentages  round numbers and calculations to up to 3 significant figures.  increase by a given percentage by multiplying by a number > 1  decrease by a given percentage by multiplying by a number < 1  perform calculations involving appreciation and depreciation  calculate compound interest  find an original amount given the value after a specific

percentage increase or decrease

Outcome 2 - Volumes  use a formula to calculate the volume of a sphere given its

radius or diameter  use a formula to calculate the volume of a cone given the radius or diameter of its base, and its height  use a formula to calculate the volume of a cylinder given the radius or diameter of its end face, and its height  identify prisms and calculate the volume of a cylinder given the area of the end face, and the height of the prism

Outcome 3 – Linear Relationships  know and use the gradient formula to find the gradient of a

line joining 2 points on a coordinate grid  know that parallel lines have the same gradient  know that horizontal lines have zero gradient and vertical lines have infinite gradient  sketch a straight line given its equation in form y = mx + c  find the gradient and y-intercept of a straight line from its equation in the form y = mx + c  determine the equation of a straight line from its graph  use other forms of y = mx + c, such as C = aD + n  know that equations like ax + by + c = 0 also represent straight lines and rearrange into form y = mx + c

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Done?

Unit 1 (cont’d) Outcome 4 – Perform Algebraic Operations  multiply out more than one bracket and simplify more complex

expressions, such as 3(x – 2) – 4(x + 9)  multiply out pairs of brackets, such as (x + 3)(6x -5)  factorise expressions with algebraic common factors, such as x2 + x = x(x + 1)  factorise expressions with combinations of numerical and algebraic common factors, such as 12x2 + 6x = 6x(2x + 1)  factorise expressions which have the difference of two squares  factorise expressions which have the difference of two squares after having been factorised with a common factor  factorise trinomial expressions  factorise trinomial expressions where the coefficient of the x2 term is > 1  solve mathematical problems that require factorisation skills

Outcome 5 – Circles  find the length of an arc of a circle given the angle at the

centre  find the area of a sector of a circle given the angle at the centre  know that the angle in a semi-circle is 90 degrees  define a tangent to a circle  know that the angle between a tangent and a radius is 90 degrees  know the bisector of a chord of a circle makes a right angle with the centre of the circle  use all the above rules to solve problems involving circles, semi-circles, chords and tangents

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Done?

Unit 2 Outcome 1 – Trigonometry  find the sine, cosine and tangent values of angles > 90

degrees, including whether they are positive and negative values  find the area of a triangle using ½ bcsinA  find the length of a side of a triangle using the sine rule  find an angle of a triangle using the sine rule  find the length of a side of a triangle using the cosine rule  find an angle of a triangle using the cosine rule  know when to use sine and cosine rules

Outcome 2 – Simultaneous Equations  solve simultaneous equations using graphs of straight lines  solve simultaneous equations algebraically (using elimination)  use simultaneous equations to solve problems involving two

variables

Outcome 3 – Use Graphs, Charts and Tables  construct and interpret tables, graphs, pie charts, and stem &

leaf  find the mean, median, mode and range of a data set  construct pie charts from raw data using relative frequencies  construct and interpret dot plots  construct and interpret a cumulative frequency column for an ungrouped frequency table  calculate the quartiles and semi-interquartile range from a data set  construct and interpret box plots

Outcome 4 – Statistics  construct a scatter graph, and use the equation of the line of

best fit to calculate the value of one variable given the other  calculate the quartiles and semi-interquartile range from an ungrouped frequency table  calculate the standard deviation of a data set  calculate probability as a measure of chance between 0 and 1  calculate probability using relative frequency

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Done?

Unit 3 Outcome 1 – Algebraic Operations  reduce an algebraic fraction to its simplest form  work with algebraic fractions

o o o o

add subtract multiply divide

 change the subject of a formula  simplify surds  use laws of indices to simplify expressions

Outcome 2 – Quadratic Functions  determine equations of quadratics from their graphs

o Form y = (x+a)2 + b o Form y = kx2  identify nature and coordinates of turning point, and axis of symmetry from form y = k(x+a)2 + b  solve quadratic equations o graphically o by factorising o using quadratic formula

Outcome 3 – Use Further Trigonometry  sketch graphs of trigonometric functions

such as y= 5sin30o + 2  identify trigonometric functions from their graphs  solve simple trigonometric equations using degrees

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Done?