PNG Grade 12 Advance Mathematics Examination Topics and Units
Advance Mathematics Examination Topics and Units for Grade 12
Advance Mathematics course is taught at the upper secondary and national high schools throughout Papua New Guinea. The Advanced Mathematics syllabus outline learning outcomes that describe what students must know and can do at the end of Grade 11 and 12. The level of achievement of the learning outcome should improve during the two years of Upper Secondary study, (Grades 11 & 12) and it is at the end of the study that students are given a summative assessment on the level of achievement of the learning outcome. There are four units in Grade 11 and three units in Grade 12 advance mathematics which all students must complete in order to sit for the Grade 12 Advance Mathematics National Examination.
Grade 11 Advance Mathematics Topics and Units
There are four grade 11 Advance Mathematics Topics and Units that all students must complete by the end of Grade11. Advance Mathematics teachers throughout the country are expected to teach all the topics and units. Below are the topics and units of Grade 11 Advance Mathematics course.
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Unit 11. 1 Numbers and Application
10 weeks Basic Numeracy -Real number: • Discuss the historical development of real numbers • Classify and relate to all real numbers • 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 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 • 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 • State the logarithmic laws from the four index laws -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 scales • Identify scale division in each device Ratio and proportion -apply scale 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 number line or plane |
Examination Specification of Advance Mathematics
The number of Examination questions for Advance Mathematics vary every year. Through our research and experience and review of past Maths A examination papers, the education department through the measurement services division have been setting the exams in the for each unit as 3 multiple choice questions and 3 short answer questions for each unit with working outs. Unit 11.1 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs. |
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Unit 11.2 Graphs and Functions
12 weeks Algebraic expressions -forming algebraic expressions from worded problems -simplify algebraic expressions -applying the factor and remainder theorem -Simplifying exponential and logarithm expressions -expressing exponential or identical equations to logarithmic equations and vice versa Graphs and functions -solving and sketching linear and quadratic equations simultaneously -solving and writing domain and range of polynomial functions -sketching and writing quadratic, cubic and absolute value functions -solving linear inequalities and representing solutions on a plane -solving quadratic equations -sketching rational exponential and logarithmic functions -discuss linear functions or analytical geometry |
Unit 11.2 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs.
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Unit 11.3 Managing Data
10 weeks Statistics -grouped and non-grouped data -averages and standard deviation -represent data using cumulative frequency graphs -represent data using scatter graph and histogram Permutation and combination -discussing powers verses factorial -applying permutation and combination to real-life problems Probability -calculate simple probability of events -classify and calculate events as independent and dependent -investigate and calculate events as mutually exclusive |
Unit 11.3 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs.
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Unit 11.4 Geometry
8 weeks Congruence, similarity and construction -applying test for congruent triangles -constructing, investigating and proving for congruency -special and similar triangles Circles and circle properties -properties of circles -cyclic quadrilaterals -applying chord and tangent properties -constructing tangents -general equation of circles |
Unit 11.4 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs.
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Grade 12 Advance Mathematics Topics and Units
There are three grade 12 topics and units that all grade 12 Advance mathematics students must study. The topics and units are all examined in the Grade 12 Advance Maths National Examinations at the end of grade 12. Outlined below are the three main topics and units.
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Unit 12.1 Patterns and Algebra
10 weeks Sets -sets and elements -Equality of sets, subsets and Venn diagrams -applying universal set and complement of a set -discussing some algebraic laws Sequences and series -finding the nth term of an arithmetic and geometric progression -finding the sum of nth terms in arithmetic and geometric progression -finding the sum of series in AP by using sigma (∑) notation -applying rules of geometric progression to solve problems related to business and industry, compound interest, superannuation and time payments -finding the limiting sum of a geometric series Binomial Theorem -discussing and applying Pascal’s triangle in expanding binomials - discussing and applying Binomial Theorem and its properties Determinants -discussing systems of linear equations -finding solutions to the system equations -using Cramer’s rule to solve determinants of order two |
Unit 12.1 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs.
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unit 12.2 Trigonometry and Vectors
10 weeks Trigonometry -converting radian measures to degree and vice versa -discussing quadrants and applying related angles -applying right-angled triangle properties to solve real problems -applying sine and cosine rules -sketching the basic and further trigonometric functions -finding solutions of trigonometric equations -applying Pythagoras’ Theorem as the basis to form the basic trigonometric identities Vectors -identifying physical quantities as scalar and vector quantities -representing equal, opposite and multiple vectors diagrammatically -discussing unit and opposite vectors -solving vector addition problems -applying scalar products of two vectors -calculating the angles between two vectors -applying vector geometry to real life problems -solve application problems involving triangle velocities |
Unit 12.2 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs.
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unit 12.3 Calculus
10 weeks Differentiation -finding the average gradient of a curve -applying rules of differentiation -calculating tangents and normal curve -stating the nature of stationary points and sketch polynomials -solving problems on maxima and minima -finding rate of change using practical problems -differentiating trigonometric functions Integration -calculating anti-derivatives and indefinite integral -discussing the two theorems on integration -calculating definite integral -finding area under and between curves |
Unit 12.3 : Atleast 3 Multiple Choice Questions 3 short answer questions with working outs.
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