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RUN REVIEW · Specialist Mathematics · Units 3 & 4 · Tech-active

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11 Sep 2026, 9:26 p.m.

20Serious score
01 Which response best completes this VCE-style item? A matrix inverse command fails because det(A)=0. This means A is
A orthogonal This does not satisfy the stated relationship.
B the identity This does not satisfy the stated relationship.
C diagonal with non-zero entries This does not satisfy the stated relationship.
D singular Zero determinant means no inverse.

Written for icaijy.com · U1–2 · Technology · answered at 100 ms

02 A student is checking a worked solution. Solve \(dy/dx=2y\), \(y(0)=3\).
A \(y=3+2x\) This does not satisfy the stated relationship.
B \(y=2e^{3x}\) This does not satisfy the stated relationship.
C \(y=3e^x\) This does not satisfy the stated relationship.
D \(y=3e^{2x}\) Exponential growth rate is 2 with initial value 3.

Written for icaijy.com · U3–4 · Differential equations · answered at 100 ms

03 Which response best completes this VCE-style item? The solutions of \(z^2=-1\) are
A \(z=0\) This does not satisfy the stated relationship.
B \(z=\pm i\) Both i and −i square to −1.
C \(z=\pm1\) This does not satisfy the stated relationship.
D \(z=i\) only This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Complex equations · answered at 100 ms

04 Which response best completes this VCE-style item? If \(v(t)=3t^2\) and \(s(0)=2\), then \(s(t)=\)
A \(6t+2\) This does not satisfy the stated relationship.
B \(3t^3+2\) This does not satisfy the stated relationship.
C \(t^3+2\) Integrate velocity and apply the initial position.
D \(t^3\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

05 Which response best completes this VCE-style item? A complete graph \(K_6\) has how many edges?
A 12 This does not satisfy the stated relationship.
B 15 \(6\times5/2=15\).
C 30 This does not satisfy the stated relationship.
D 6 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graphs · answered at 100 ms

06 Which response best completes this VCE-style item? The plane \(2x-y+2z=6\) has normal vector
A \((6,0,0)\) This does not satisfy the stated relationship.
B \((x,y,z)\) This does not satisfy the stated relationship.
C \((2,1,2)\) This does not satisfy the stated relationship.
D \((2,-1,2)\) The coefficients form a normal vector.

Written for icaijy.com · U3–4 · Vector planes · answered at 100 ms

07 During a one-minute revision round: A vector calculation returns magnitude −4. The correct interpretation is
A the vector points left This does not satisfy the stated relationship.
B the vector points down This does not satisfy the stated relationship.
C the magnitude is −4 This does not satisfy the stated relationship.
D a magnitude cannot be negative, so the setup or output is wrong Magnitude is a non-negative scalar.

Written for icaijy.com · U1–2 · Modelling · answered at 100 ms

08 Which response best completes this VCE-style item? An estimate 20 has margin of error 3. The interval is
A \((17,23)\) Add and subtract the margin.
B \((14,26)\) This does not satisfy the stated relationship.
C \((20,23)\) This does not satisfy the stated relationship.
D \((3,20)\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Confidence intervals · answered at 100 ms

09 A student is checking a worked solution. A complete graph \(K_6\) has how many edges?
A 6 This does not satisfy the stated relationship.
B 15 \(6\times5/2=15\).
C 30 This does not satisfy the stated relationship.
D 12 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graphs · answered at 100 ms

10 During a one-minute revision round: \((1,0,0)\times(0,1,0)=\)
A \(0\) This does not satisfy the stated relationship.
B \((1,1,0)\) This does not satisfy the stated relationship.
C \((0,0,-1)\) This does not satisfy the stated relationship.
D \((0,0,1)\) The standard basis vectors satisfy i×j=k.

Written for icaijy.com · U3–4 · Cross products · answered at 100 ms

11 \(\binom{8}{2}=\)
A 56 This does not satisfy the stated relationship.
B 28 8×7/2=28.
C 16 This does not satisfy the stated relationship.
D 64 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Counting · answered at 100 ms

12 During a one-minute revision round: A geometric sequence has first term 3 and ratio 2. Its sixth term is
A 48 This does not satisfy the stated relationship.
B 96 3×2⁵=96.
C 64 This does not satisfy the stated relationship.
D 192 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Sequences · answered at 100 ms

13 During a one-minute revision round: A complete graph \(K_6\) has how many edges?
A 30 This does not satisfy the stated relationship.
B 15 \(6\times5/2=15\).
C 6 This does not satisfy the stated relationship.
D 12 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graphs · answered at 100 ms

14 Solve \(dy/dx=2y\), \(y(0)=3\).
A \(y=3e^x\) This does not satisfy the stated relationship.
B \(y=3e^{2x}\) Exponential growth rate is 2 with initial value 3.
C \(y=2e^{3x}\) This does not satisfy the stated relationship.
D \(y=3+2x\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Differential equations · answered at 100 ms

15 One Newton step for \(f(x)=x^2-2\) from \(x_0=1.5\) gives
A approximately 2.0000 This does not satisfy the stated relationship.
B approximately 1.2500 This does not satisfy the stated relationship.
C approximately 1.4167 \(x_1=x_0-f(x_0)/f\prime(x_0)\).
D approximately 1.5000 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Numerical methods · answered at 100 ms

16 Which response best completes this VCE-style item? Testing 10 000 cases with CAS establishes a universal integer claim
A whenever no counterexample appears This does not satisfy the stated relationship.
B only if paired with a valid general proof Finite checking alone does not prove an infinite claim.
C only for prime inputs This does not satisfy the stated relationship.
D with certainty by itself This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Proof checking · answered at 100 ms

17 During a one-minute revision round: A numerical solver reports one root. To check for omitted roots, first
A differentiate the answer This does not satisfy the stated relationship.
B inspect the domain and graph or use complete solve settings Numerical solvers depend on domain, guesses and settings.
C round the root more This does not satisfy the stated relationship.
D assume uniqueness This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Technology · answered at 100 ms

18 During a one-minute revision round: A 2 kg particle has acceleration 3 m s⁻². Net force magnitude is
A 1.5 N This does not satisfy the stated relationship.
B 9 N This does not satisfy the stated relationship.
C 5 N This does not satisfy the stated relationship.
D 6 N F=ma=6 N.

Written for icaijy.com · U3–4 · Mechanics · answered at 100 ms

19 A complete graph \(K_6\) has how many edges?
A 6 This does not satisfy the stated relationship.
B 15 \(6\times5/2=15\).
C 30 This does not satisfy the stated relationship.
D 12 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graphs · answered at 100 ms

20 A student is checking a worked solution. A matrix inverse command fails because det(A)=0. This means A is
A the identity This does not satisfy the stated relationship.
B orthogonal This does not satisfy the stated relationship.
C singular Zero determinant means no inverse.
D diagonal with non-zero entries This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Technology · answered at 100 ms

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