PracticeVideosBlogFlashcardsEspañol
All Practice Exams

100+ Free SACE Stage 2 General Mathematics Practice Questions

SACE Stage 2 General Mathematics External Assessment practice questions are available now; exam metadata is being verified.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More South Australian Certificate of Education (SACE) Stage 2

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

SACE Stage 2 Aboriginal Studies External Assessment

Practice Questions

SACE Stage 2 Accounting External Assessment

Practice Questions

SACE Stage 2 Activating Identities and Futures External Assessment

Practice Questions

SACE Stage 2 Agricultural Production External Assessment

Practice Questions

SACE Stage 2 Agricultural Systems External Assessment

Practice Questions

SACE Stage 2 Ancient Studies External Assessment

Practice Questions
2026 Statistics

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 Practice Questions

Verified exam format metadata for SACE Stage 2 General Mathematics External Assessment is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.