Intermediate 2 Course Details

By Mr Vass on 25/2/2005

Intermediate 2 Mathematics Course Details
Students are required to complete three units:
 Mathematics 1, Mathematics 2 and Mathematics 3
OR
 Mathematics 1, Mathematics 2 and Applications of Mathematics
Mathematics 1 (Int 2)
1. Calculations involving percentages
• carry out calculations involving percentages in appropriate contexts:
appreciation/depreciation
2. Volumes of solids
• find the volumes of spheres, cones and prisms
• round calculations to a required number of significant figures
3. Linear relationships
• find the gradient of a straight line between two points (x1, y1) and (x2, y2)
• know that in the equation y = ax + b of a straight line, ‘a’ represents the gradient and ‘b’ represents the intercept on the y-axis and use this to sketch the line without drawing accurately
• determine the equation of a straight line in the form y = ax + b from its graph
4. Algebraic operations
• multiply algebraic expressions involving brackets
• factorise algebraic expressions:
common factor
difference of two squares
with numerical coefficients >1[A/B]
factorise trinomial expressions
5. Properties of the circle
• find the length of an arc of a circle
• find the area of a sector of a circle
• use the properties of circles:
relationship between tangent and radius
angle in a semi-circle
the interdependence of the centre, bisector of a chord and a perpendicular to a chord [A/B]
Mathematics 2 (Int 2)
1. Trigonometry
• find the sine, cosine and tangent of angles other than acute angles
• find the area of a scalene triangle using area = ½ bc sin A
• solve scalene triangles by using the Sine Rule/Cosine Rule
• use the Cosine Rule to find an angle of a triangle, given all three sides [A/B]
2. Simultaneous linear equations
• construct formulae to describe a linear relationship
• know the significance of the point of intersection of two graphs: solve simultaneous linear equations in two variables graphically
• solve simultaneous linear equations in two variables algebraically
3. Graphs, charts and tables
• extract and interpret data from bar graphs, line graphs, pie charts and stem-and-leaf diagrams construct bar graphs, line graphs and stem-and leaf diagrams
• construct and interpret a scattergraph
• add a cumulative frequency column to an ungrouped frequency table
• find the median and quartiles from a data set or ungrouped frequency table
• construct and interpret boxplots and dotplots
• construct a piechart
4. Use of simple statistics
• calculate the mean, mode and range of a data set or an ungrouped frequency table
• calculate the semi-interquartile range from a data set or ungrouped frequency table
• calculate the standard deviation of a data set
• determine the equation of a best-fitting straight line on a scattergraph and use it to estimate a y-value given the x-value
• know that probability is a measure of chance between 0 and 1
• find probability where all the outcomes are equally likely
Mathematics 3 (Int 2)
1. Algebraic operations
• reduce an algebraic fraction to its simplest form
• apply the four rules to algebraic fractions
• change the subject of formulae
• simplify surds
• express with a rational denominator [A/B]
• simplify expressions using the laws of indices
2. Quadratic functions
• recognise quadratics of the form y = kx2 and y = (x + a)2 + b; a, b, k Z from their graphs
• identify the nature and coordinates of the turning point and the equation of the axis of symmetry of a quadratic of the form y = k(x + a)2 + b; a, b Z, k =±1
• know the meaning of the term ‘roots of a quadratic equation’
• solve quadratic equations graphically
• solve quadratic equations by factorisation and by using the quadratic formula
3. Further trigonometry
• recognise the graphs of sine, cosine and tangent functions
• sketch and identify trigonometric functions involving a multiple angle
• involving a phase angle [A/B]
• solve simple trigonometric equations in degrees
• define the period of a trigonometric function either from its graph or from its equation
• simplify expressions using Trig Identities [A/B]
Applications of Mathematics (Int 2)
1. Straightforward calculations in a social context
• know the terms: gross pay, net pay, basic pay, wage, overtime, bonus, annual salary, monthly salary, commission, income tax, taxable income, tax allowances, superannuation, National Insurance
• calculate overtime payments and incentive payments such as commission
• calculate net earnings given salary, details of incentive schemes and details of deductions
• calculate tax deductions given details of earnings, allowances and rates of tax
• know the meaning of the terms: with (without)loan protection, payment protection, APR, minimum payment, credit limit
• use a loan table:
to find the monthly repayment for a given amount
to calculate the total repayments based on a set of conditions
to calculate the cost of the loan, ie, the difference between the total repayments and the loan
understand the different charges involved in using a credit card
solve problems involving the interpretation of information presented in loan repayment tables
2. Logic diagrams
• know the meaning of the terms: vertices (nodes), order of node and arcs in a network diagram
• construct and interpret a network diagram
• construct and interpret a tree diagram
• recognise statement boxes and decision boxes in a flowchart
• interpret and use a flowchart which contains at least two decision boxes
• enter given data into a spreadsheet
• enter formulae into a spreadsheet
• replicate (copy and paste) formulae in a spreadsheet
• use the SUM and AVERAGE functions in a spreadsheet
• design a spreadsheet
3. Formulae
• interpret and use formulae expressed in words in applications
• interpret and use formulae expressed in symbols in applications
4. Statistical assignment
• estimate the mean, median, mode, quartiles and semi-interquartile range for grouped or interval data in a frequency table
• estimate:
the mean by using the midpoint of each group or interval
the mode by using the previous and next frequency to the modal class
the median and quartiles from an ogive
semi-interquartile range


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