IMIS FO2 Arithmetic

FO2 ARITHMETIC

Prerequisites

None

Assessment

By a single 21/2 hour externally set examination paper.

Aims

At the conclusion of the course the student should be able to:

• Perform calculations using the fundamental processes of arithmetic, using terms and alternative number bases that are common within the commercial context.
• Use basic algebraic notation and demonstrate competence with elementary algebraic processes.
• Perform calculations utilising functional notation and use this in plotting and interpreting graphs of linear functions.
• Draw and interpret graphs of quadratic equations and other related functions.
• Demonstrate an understanding of sets and of elementary operations upon them.
• Demonstrate an understanding of elementary statistics

Objectives

1 Perform calculations using the fundamental processes of arithmetic, using terms and alternative number bases that are common within the commercial context.

• Apply the four rules of arithmetic to decimals, signed integers and vulgar fractions and apply the processes of conversion between each.
• Apply the concept of place value and its relationship with the denary, octal and hexadecimal number systems
• Convert between binary, octal and denary numbers in the context of positive integral values.
• Describe percentages and their relationship to fractions and convert between percentages, fractions and decimals.
• Express one quantity as a percentage of another, calculate percentages of given quantities, together with percentage increase and decrease as applied to problems involving discounts, loans, hire purchase and depreciation.
• Perform calculations using ratios involving two or more quantities including their application to map scales.
• Perform calculations involving currency conversions, commission, wages, piecework, rate of pay local taxes and insurance and percentage profit/loss
• Perform calculations involving the use of indices.
• Express two or more quantities in order of magnitude using the rules of precedence to evaluate expressions involving the use of +, -, x, - , ( ) and indices.

1.2 Use the terms Principal, Rate and Amount and be able to calculate simple interest and apply this to inverse problems involving simple interest.

• Calculate compound interest and to appreciate the differences between simple and compound interest.
• Evaluate problems to an appropriate order of magnitude using significant figures and decimal places.

2.0 Use basic algebraic notation and demonstrate competence with elementary algebraic processes.

• Use the terminology of variables, constants and the use of subscripted variables.
• Evaluate algebraic expressions for given values of the variables, applying the rules of precedence.
• Manipulate linear algebraic equations to make any given variable the subject.
• Solve commercial problems using linear algebraic equations in a single variable.
• Factorise algebraic expressions by extracting a single term.

3.0 Perform calculations utilising functional notation and use this in plotting and interpreting graphs of linear functions.

• Solve a pair of linear simultaneous equations in two variables and check the result by graphical and algebraic means.
• Factorise algebraic expressions by extracting a linear factor, including recognition and use of the difference of two squares and of perfect squares.
• Solve quadratic equations exactly by the use of factors.
• Solve commercial problems using quadratic equations by graphical means and the use of formula.

4.0 Draw and interpret graphs of quadratic equations and other related functions.

• Use functional notation to define functions of the form f(x) = ax + b and calculate the image f(x) for a variety of values of x.
• Use rectangular Cartesian co-ordinates to plot linear functions using tables of values of f(x) against x.
• Plot and interpret the graphs of linear and quadratic functions using tables of values of f(x) against x, with particular regard to slope (gradients) and intercepts; including the recognition of turning values in the quadratic function.
• Apply the processes of translation, reflection (in the Cartesian axes or in lines parallel to them), rotation (through 90º, 180º, 270º, or 360º) and enlargement to points, straight line segments and plane figures.
• Plot and interpret the graphs of:
• The cubic function f(x) = ax3.
• The function f(x) = ______ (x / - b/a) ax + b

5.0 Demonstrate an understanding of sets and of elementary operations upon them

• Use the terminology of sets, in particular Universal Set, element, subset, empty set and complement.
• Represent sets and their interrelationships by the use of Venn diagrams.
• Define the Union and the Intersection of two or three sets.
• Use the notation n(A) for the number of elements in set A and apply this notation in problems concerning the Union and the Intersection of sets.

6.0 Demonstrate an understanding of elementary statistics

• Describe the difference between quantitative & qualitative data and between discrete & continuous data.
• Construct a frequency distribution table from raw data.
• Represent data by pictorial/graphical means using: Bar Charts, Histograms, Pie Charts and Pictograms.
• Calculate summary measures of central tendency, median, mode and arithmetic means for ungrouped data.