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100+ Free SACE Stage 2 General Mathematics Practice Questions

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Key Facts: SACE Stage 2 General Mathematics Exam

30%

Weighting of the external written examination in final subject grade

SACE Board of South Australia

70%

Weighting of school-based assessment (Skills Tasks & Investigation)

SACE Board of South Australia

2 hours

Working time for the external written examination (+ 10 min reading)

SACE Board of South Australia

4 topics

Core syllabus topics assessed across the Stage 2 curriculum

SACE General Mathematics Subject Outline

SACE Stage 2 General Mathematics is the Year 12 general mathematics course in South Australia, evaluated via 70% school-based tasks and a 30% 2-hour external examination. Key topics comprise matrix modeling, networks & decision math, statistical analysis, and financial mathematics. This 100-question practice set provides thorough MCQ preparation with complete step-by-step calculations and distractor breakdowns.

Sample SACE Stage 2 General Mathematics Practice Questions

Try these sample questions to test your SACE Stage 2 General Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Given the 2x2 matrix A = [[3, -2], [5, 4]], calculate the scalar multiplication 2A.
A.[[6, -4], [10, 8]]
B.[[5, 0], [7, 6]]
C.[[6, -2], [5, 8]]
D.[[9, -4], [25, 16]]
Explanation: Scalar multiplication requires multiplying every element inside matrix A by 2: 2*3=6, 2*(-2)=-4, 2*5=10, 2*4=8.
2Calculate the matrix sum A + B for A = [[4, 1], [-3, 2]] and B = [[2, 5], [1, -4]].
A.[[8, 5], [-3, -8]]
B.[[6, 6], [-2, -2]]
C.[[2, -4], [-4, 6]]
D.[[6, 4], [-4, -2]]
Explanation: Matrix addition is performed entrywise: (4+2=6), (1+5=6), (-3+1=-2), (2+(-4)=-2), resulting in [[6, 6], [-2, -2]].
3In a directed network represented by an adjacency matrix A, what does an entry of a_ij = 2 signify?
A.Vertex i and vertex j both have a vertex degree of 2 in the graph.
B.There are 2 indirect paths of length 2 connecting vertex i and vertex j.
C.There are 2 direct one-step directed edges pointing from vertex i to vertex j.
D.The shortest distance between vertex i and vertex j is equal to 2 units.
Explanation: In a standard adjacency matrix A, entry a_ij records the number of direct 1-step directed edges leading from vertex i to vertex j. Therefore a_ij = 2 means 2 direct edges point from i to j.
4Matrix M has dimensions 2x3 and matrix N has dimensions 3x4. What are the dimensions of the product matrix M x N?
A.Matrix multiplication is undefined for these dimensions
B.3x3
C.4x2
D.2x4
Explanation: For matrix multiplication M_{p x q} x N_{q x r}, the inner dimensions must match (q = 3), and the resulting product matrix has outer dimensions p x r = 2x4.
5Given A = [[1, 3], [2, 4]] and B = [[5, 0], [1, 2]], calculate entry (1,1) of the product matrix A x B.
A.8
B.5
C.11
D.14
Explanation: Entry (1,1) of A x B is obtained by taking the dot product of row 1 of A [1, 3] and column 1 of B [5, 1]^T: (1 * 5) + (3 * 1) = 5 + 3 = 8.
6Adjacency matrix A = [[0, 1, 1], [1, 0, 1], [0, 1, 0]]. Calculate entry (1,2) of A^2 representing 2-step paths from vertex 1 to vertex 2.
A.0
B.1
C.2
D.3
Explanation: Entry (1,2) of A^2 is dot product of row 1 of A [0, 1, 1] and col 2 of A [1, 0, 1]^T: (0*1) + (1*0) + (1*1) = 0 + 0 + 1 = 1.
7In a state transition matrix T where column vectors represent state transitions, what must each column sum equal?
A.Total population size
B.0.0
C.1.0
D.Determinant of T
Explanation: In a stochastic transition matrix using column-state convention, each column represents the complete set of transition probabilities from a given state, which must sum to 1.0 (100%).
8Transition matrix T = [[0.8, 0.3], [0.2, 0.7]] and initial state vector S_0 = [100, 200]^T. Calculate S_1 = T x S_0.
A.[80, 140]^T
B.[110, 190]^T
C.[150, 150]^T
D.[140, 160]^T
Explanation: S_1 row 1 = (0.8 * 100) + (0.3 * 200) = 80 + 60 = 140. S_1 row 2 = (0.2 * 100) + (0.7 * 200) = 20 + 140 = 160.
9With T = [[0.8, 0.3], [0.2, 0.7]] and S_1 = [140, 160]^T, calculate state vector S_2 = T x S_1.
A.[160, 140]^T
B.[140, 160]^T
C.[175, 125]^T
D.[150, 150]^T
Explanation: S_2 row 1 = (0.8 * 140) + (0.3 * 160) = 112 + 48 = 160. S_2 row 2 = (0.2 * 140) + (0.7 * 160) = 28 + 112 = 140.
10Find the steady-state probability vector S = [x, y]^T for transition matrix T = [[0.7, 0.4], [0.3, 0.6]].
A.[1/2, 1/2]^T
B.[4/7, 3/7]^T
C.[3/7, 4/7]^T
D.[3/5, 2/5]^T
Explanation: At steady state T*S = S: 0.7x + 0.4y = x => 0.4y = 0.3x => x = (4/3)y. Since x + y = 1, (7/3)y = 1 => y = 3/7 and x = 4/7.

About the SACE Stage 2 General Mathematics Exam

SACE Stage 2 General Mathematics is a senior secondary mathematics subject administered by the SACE Board of South Australia. It focuses on the application of discrete mathematics, statistical modeling, optimization algorithms, and financial mathematics to real-world decision-making. Assessment is split into 70% school-based tasks (Skills & Applications Tasks and a Mathematical Investigation) and a 30% 2-hour external written examination. This 100-question practice bank is an English-language MCQ study adaptation created by OpenExamPrep to test conceptual knowledge, numerical calculations, matrix algorithms, network optimization, statistical forecasting, and financial modeling in accordance with the official SACE subject outline.

Assessment

The SACE Stage 2 General Mathematics assessment consists of 70% school-based assessment (comprising 40% Skills and Applications Tasks and 30% Mathematical Investigation) and 30% external written examination (2 hours). The examination covers all four curriculum topics: Topic 1 (Modelling with Matrices), Topic 2 (Networks and Decision Mathematics), Topic 3 (Statistical Analysis), and Topic 4 (Financial Mathematics).

Time Limit

2 hours of working time plus 10 minutes reading time.

Passing Score

SACE Stage 2 subjects are reported on an A+ to E- grading scale; achieving a grade of C- or higher is required for Stage 2 completion credit.

Exam Fee

Included in regular South Australian secondary school tuition and SACE enrolment fees. (SACE Board of South Australia)

SACE Stage 2 General Mathematics Exam Content Outline

25%

Topic 1: Modelling with Matrices

Matrix operations, matrix multiplication, adjacency matrices, multi-step connectivity, state transition matrices, steady-state probability vectors, and Leslie matrix models for age-structured population growth.

25%

Topic 2: Networks and Decision Mathematics

Network terminology, planar graphs, Eulerian/Hamiltonian circuits, Prim's and Kruskal's algorithms for minimum spanning trees, Dijkstra's algorithm, Critical Path Analysis (CPA), maximum flow min cut theorem, and the Hungarian algorithm for optimal assignment.

25%

Topic 3: Statistical Analysis

Bivariate data analysis, scatter plot interpretation, Pearson correlation coefficient r, coefficient of determination r^2, least squares linear regression y = a + bx, residual analysis, time series moving averages, seasonal indices, and deseasonalised forecasting.

25%

Topic 4: Financial Mathematics

Simple and compound interest calculations, effective annual rates, inflation adjustments, straight-line and reducing-balance depreciation, reducing-balance loans, recurrence relations, amortisation schedules, future/present value annuities, superannuation growth, and perpetuities.

How to Pass the SACE Stage 2 General Mathematics Exam

What You Need to Know

  • Passing score: SACE Stage 2 subjects are reported on an A+ to E- grading scale; achieving a grade of C- or higher is required for Stage 2 completion credit.
  • Assessment: The SACE Stage 2 General Mathematics assessment consists of 70% school-based assessment (comprising 40% Skills and Applications Tasks and 30% Mathematical Investigation) and 30% external written examination (2 hours). The examination covers all four curriculum topics: Topic 1 (Modelling with Matrices), Topic 2 (Networks and Decision Mathematics), Topic 3 (Statistical Analysis), and Topic 4 (Financial Mathematics).
  • Time limit: 2 hours of working time plus 10 minutes reading time.
  • Exam fee: Included in regular South Australian secondary school tuition and SACE enrolment fees.

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

SACE Stage 2 General Mathematics Study Tips from Top Performers

1Master matrix multiplication order and check dimension compatibility before calculating state transition vectors and steady-state probabilities.
2Practice executing network algorithms by hand, including Dijkstra's algorithm for shortest paths, Prim's/Kruskal's for minimum spanning trees, and Critical Path Analysis (EST, LST, total float).
3Understand statistical measures: calculate Pearson's r, interpret r^2 as the percentage of variation explained, fit least squares regression equations, and perform seasonal adjustment calculations.
4Utilize financial TVM concepts and recurrence relations to solve reducing-balance loan repayments, compound interest effective rates, and annuity growth problems.
5Carefully check distractor calculations for common student errors, such as forgetting to convert annual interest rates to monthly periodic rates or confusing EST and LST.

Frequently Asked Questions

What is the assessment structure for SACE Stage 2 General Mathematics?

Assessment includes 70% school-based assessment (40% Skills and Applications Tasks, 30% Mathematical Investigation) and a 30% 2-hour external written examination.

What core topics are examined in SACE Stage 2 General Mathematics?

The course covers four main topics: Topic 1 (Modelling with Matrices), Topic 2 (Networks and Decision Mathematics), Topic 3 (Statistical Analysis), and Topic 4 (Financial Mathematics).

Are graphics calculators permitted in the SACE Stage 2 General Mathematics exam?

Yes, SACE-approved graphics calculators (CAS/non-CAS graphics calculators) and scientific calculators are permitted in the external examination.

How does this practice bank adapt the official SACE exam structure?

While the official external exam features short-answer and extended written problem-solving tasks, this 100-question practice set adapts the curriculum into English-language multiple-choice questions to test numerical procedures, algorithmic methods, statistical analysis, and rubric awareness.

Does this question bank include step-by-step mathematical solutions?

Yes, every quantitative question features detailed step-by-step arithmetic and algebraic explanations for the correct answer alongside explanations for why each distractor is incorrect.