Grade 12 Examination Topics and Units for General Mathematics (Maths B)

Grade 12 Examination Topics and Units for General Mathematics

The General Mathematics (Maths B) topics and units are outlined in detail in the General Mathematics syllabus. The syllabus is used by teachers to teach Upper Secondary students (Grades 11 and 12) throughout Papua New Guinea. The General Mathematics syllabus is built upon concepts, skills and attitudes learnt in Lower Secondary and provides a sound foundation for further learning. Mathematics is a subject which is potentially a source of great fascination and enrichment. It is an immense, multi-faceted field of knowledge with a rich history, a dynamic present and an exciting future. It impacts upon the daily life of people everywhere and helps them to understand the world in which they live and work. Mathematics has always been and continues to be a vital component of a soundly based general education.

Grade 11 General mathematics topics and Units

There are five main topics and units taught in Grade 11 General Mathematics course. It is important that General Mathematics teachers around the country are expected to teach all the five topics and units in Grade 11. The topics and units are all examined at the end of Grade 12 in the General Mathematics National Examinations. The topics and units are outlined in details below.

11.1 Number and Application
10 weeks

Basic numeracy
Units of measurement
Ratio and proportion
Basic algebra

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Basic numeracy
Real number

discuss the historical development of real numbers
classify and relate symbols to all real numbers as
plot real numbers on a real number line
apply the properties of real numbers (Closure, Associative, Commutative and Distributive laws)

Surds

apply properties of surds
simplify and rationalise surds

Recurring and non-recurring decimals

identify decimals as recurring and non-recurring
convert recurring decimals to fractions

Significant figures

state the number of significant figures in a given number
rounding significant figures (s.f)

Estimation and error

round individual figures to 1 significant figure
state appropriate degree of accuracy; for example, to 1 d.p, 3 s. f depending on the measurement
list types of error and calculate error, absolute and relative error from any physical quantity measurements.

Standard Index form (SIF)

state numbers in the SIF (that is, a x 10n) where 1 a < 10 , nZ
convert ordinary numbers to SIF and vice versa

Indices and logarithmic laws

apply the four Indices laws in given expressions including base numbers
express index numbers in logarithmic form (such as y = ax as x = logay)
state the logarithmic laws from the four index laws
use calculator to do logarithms of base 10
Calculator
identify appropriate functions and use in all strands

Units of measurement
Metric and imperial measures

write metric measurements of length, mass and capacity
convert metric measurements to imperial or vice versa using length and mass quantities

Measuring devices and scales

use analogue and digital devices
identify scale division in each device

Ratio and proportion

apply scales on map with actual lengths on the ground
solve problems on direct and inverse variation

Basic algebra

factorise quadratic expressions
simplify algebraic fractions
solve and sketch quadratic equations
solve simultaneous equations using elimination, substitution and graphical methods
solve inequality and plot on number line or plane

11.2 Managing Money
8 weeks

Earnings and spending
Budgeting and loans

Content
Students acquire knowledge and skills through the learning and teaching of this content.

Earnings and spending

calculate salaries, wages, overtime, commission, piece work and rates as earning
calculate taxable income, goods and services tax (VAT,
GST),deductions, rebates, levies, superannuation
use foreign exchange rates to perform simple calculations

Budgeting and loans

record basic income or expenditure
estimate monthly expenses
estimate monthly income
explain basic ideas of cash flow
discuss types of loans and interest rates
calculate interest on loans

11.3 Statistics
6 weeks

Exploring data
Analysis of data

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Exploring data

construct stem and leaf plots
plot frequency polygons and histograms
tabulate and plot cumulative frequency distribution
state whether the data is skewed to the left or right of the mean
interpolate and extrapolate and/or calculate percentile, quartile and interquartile ranges

Analysis of data

calculate range, interquartile range of any given data
list and calculate the types of deviation as mean, variance and standard
Deviation

11.4 Geometry
8 weeks

Lines, angles, triangles and regular polygons
Geometric construction
Circles

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Lines, angles, triangles and regular polygons

find angle sum of interior and exterior angles of regular polygons
apply geometrical properties to find similar and congruent triangles
properties of a polygon
use properties to identify special quadrilaterals
define plane and calculate angles between a line and plane (solid trigonometry)
calculate angles between two planes
calculate the dimensions (length or width) of any given 3D

Geometric construction

use protractor and compass to construct geometric angles and shapes
draw similar triangles using scales
apply geometrical properties to prove congruency in triangles
construct scale diagrams of bearings
identify and draw common 3D shapes such as spheres, cones, pyramids and cylinders
discuss and identify planes in truncated solids in any 3D shapes

Circles

discuss circle properties and calculate the angles
draw and measure angles in a cyclic quadrilateral or polygons
apply chord and tangent properties to find the length of chord, radius, tangent and angles

11.5 Trigonometry
8 weeks

Trigonometry
Vectors

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Trigonometry

measure and calculate angles of elevation and depression
solve application problems on right-angled triangles
derive sine and cosine rule
apply sine and cosine rule to solve practical problems
discuss and measure conventional and compass bearing
discuss, illustrate and interpret contour maps
calculate average slope and distance of contour

Vectors

vector notation and position vector
use scalar multiplication to explain and apply parallel vectors

Examination Specification for General mathematics

Each unit will have 3 multiple choice questions and 1 short answer questions worth 7 marks. Note: For General mathematics, the number of questions asked per topic or unit may vary.

Grade 12 General mathematics topics and units

It is crucial that the Grade 12 General Mathematics Topics and Units be taught by General Mathematics teachers throughout the country in preparation for the grade 12 students to sit for the General Mathematics National Examinations. There are five main topics and units in Grade 12 General Mathematics. All these topics and units are examined at the end of Grade 12. The five main topics and units are outlined below.

12.1 Measurement
6 weeks of teaching and Learning

Scales and dimensions
Surveying

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Scales and dimensions
Area and scales

calculate actual area of the field given the ratios

Perimeter and area of triangles

calculate area of a triangle using Pythagoras’ theorem
calculate area of a triangle using the sine ratio
Area = ½ ab sinC
calculate area of a triangle using Heron’s formula that is, Area = S(S −a)(S −b)(S −c) where S = ½(a + b + c)

Perimeter and area of polygons

calculate area of polygon by identifying triangular shapes

Volume and surface area

calculate the surface area and volumes of pyramids, spheres and truncated solids

Surveying
Surveying on level ground without obstacles

determine pace length by measuring 100m using a tape measure or metre ruler, and trundle wheel
estimate distances and area using pace length
define survey lines, offset, and field book
sketch a survey field using field book
interpret and calculate areas and perimeter using sketch or scale diagram

Surveying around obstacles

describe offset method and triangulation
apply the methods above to survey around obstacles

12.2 Managing Money 2
8 weeks

Interest and inflation
Consumer credit
Investments
Insurance
Using simple algebraic manipulation of financial formulae

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Interest and inflation

calculate compound interest for various compounding periods
discuss and calculate inflation, appreciation and depreciation

Consumer credit

personal loans and credit cards
calculate hire-purchase
investigate flat rate interest loan
construct and investigate a housing (mortgage) loan repayment schedule
list and calculate types of service fees and charges
Investments
types of investments; calculate their profit and investment value

real estate and stock markets

calculate the dividend of chosen stocks
calculate the dividend on the sale of chosen properties

Insurance

types of insurances, policies and premium payments
calculate returns over a given time
use simple manipulation of financial formulas

12.3 Probability and Statistics
6 weeks

Probability
Correlation and regression

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Probability

calculate simple probability of events
classify and calculate events as independent and dependent
investigate and calculate events as mutually and non-mutually exclusive

Correlation and regression

plot scatter diagrams
discuss and interpret linear and non-linear relationships
calculate the regression and correlation coefficients
write equation of the regression line
interpret regression and correlation coefficient in the context of the problem

12.4 Algebra and Graphs
6 weeks

Equations
Graphs and functions

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Equations

solve linear, quadratic exponential and inequality equations
solve word problems involving linear and quadratic expressions

Graphs and functions

solve simultaneous equations graphically
graph inequalities and shade regions
sketch graphs of hyperbolic, exponential, logarithmic functions
derive equations of parabolic, hyperbolic and exponential functions
discuss and calculate asymptote in given hyperbola, exponential, logarithmic functions
applications of exponential and logarithmic functions

12.5 Applying Geometry in Papua New Guinean Arts
4 weeks

Tessellations and polyhedral

Content
Students acquire knowledge and skills through the learning and teaching of this content.
Tessellations and polyhedra

identify prisms and pyramids
construct nets of regular polygons and solids
identify shapes formed by joining squares (polyominoes) and equilateral (poliamonds)
use isometric graph paper to form tessellation patterns
use traditional arts to identify the tessellation patterns

Examination Specification

All topics and units outlined above are covered in the Grade 12 General mathematics Examination. Thus all students who are taking General mathematics must study all the units outlined above.

Atleast 3 Multiple Choice Questions 3 short answer questions with working outs for each unit in General Mathematics covers the examination layout.

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