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

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11 Sep 2026, 9:23 p.m.

20Serious score
01 A student is checking a worked solution. A connected graph with n vertices and n−1 edges is a
A tree This is a standard characterisation of a tree.
B complete graph This does not satisfy the stated relationship.
C cycle This does not satisfy the stated relationship.
D multigraph necessarily This does not satisfy the stated relationship.

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

02 During a one-minute revision round: A vector equation of a line is
A \(\vec r=\vec a+\lambda\vec d\) A point plus a scalar multiple of a direction defines the line.
B \(\vec r=\lambda\) This does not satisfy the stated relationship.
C \(\vec r=\vec a\times\vec d\) This does not satisfy the stated relationship.
D \(\vec r=\vec a\cdot\vec d\) This does not satisfy the stated relationship.

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

03 If \(a\mid b\) and \(a\mid c\), then
A \(a=b+c\) This does not satisfy the stated relationship.
B \(a\mid(b+c)\) Divisibility is preserved under integer linear combinations.
C \(bc\mid a\) This does not satisfy the stated relationship.
D \(b\mid a\) This does not satisfy the stated relationship.

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

04 Which response best completes this VCE-style item? \(i^2=\)
A 1 This does not satisfy the stated relationship.
B i This does not satisfy the stated relationship.
C 0 This does not satisfy the stated relationship.
D −1 This defines the imaginary unit.

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

05 The negation of “all integers are positive” is
A at least one integer is positive This does not satisfy the stated relationship.
B all integers are not positive This does not satisfy the stated relationship.
C no integers exist This does not satisfy the stated relationship.
D at least one integer is not positive Negating a universal statement produces an existential counterexample.

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

06 Which response best completes this VCE-style item? \(\int e^{ax}\,dx=\)
A \(\frac1x e^{ax}\) This does not satisfy the stated relationship.
B \(\frac1a e^{ax}+C\) Differentiate to verify the factor 1/a.
C \(ae^{ax}+C\) This does not satisfy the stated relationship.
D \(e^{ax}+C\) This does not satisfy the stated relationship.

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

07 During a one-minute revision round: A connected graph with n vertices and n−1 edges is a
A cycle This does not satisfy the stated relationship.
B multigraph necessarily This does not satisfy the stated relationship.
C complete graph This does not satisfy the stated relationship.
D tree This is a standard characterisation of a tree.

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

08 During a one-minute revision round: If position is \(\vec r(t)\), acceleration is
A \(|\vec r(t)|\) This does not satisfy the stated relationship.
B \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.
C \(\vec r\prime(t)\) This does not satisfy the stated relationship.
D \(\int\vec r(t)dt\) This does not satisfy the stated relationship.

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

09 A square matrix is invertible exactly when its determinant is
A one only This does not satisfy the stated relationship.
B zero This does not satisfy the stated relationship.
C negative only This does not satisfy the stated relationship.
D non-zero A zero determinant means singular.

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

10 A student is checking a worked solution. For a particle in equilibrium, the vector sum of forces is
A \(m\vec v\) This does not satisfy the stated relationship.
B \(\vec r\) This does not satisfy the stated relationship.
C \(\vec0\) Zero net force is the equilibrium condition.
D \(m\vec g\) always This does not satisfy the stated relationship.

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

11 Which response best completes this VCE-style item? For \(dy/dx=f(x)g(y)\), separation gives
A \(dx/dy=f(x)g(y)\) This does not satisfy the stated relationship.
B \(g(y)dy=f(x)dx\) This does not satisfy the stated relationship.
C \(dy=f(x)+g(y)\) This does not satisfy the stated relationship.
D \(\frac{dy}{g(y)}=f(x)\,dx\) Move the y factor with dy and x factor with dx.

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

12 A student is checking a worked solution. The vector from A to B is
A \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.
B \(\vec b-\vec a\) Endpoint position minus start position.
C \(\vec a-\vec b\) This does not satisfy the stated relationship.
D \(\vec a+\vec b\) This does not satisfy the stated relationship.

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

13 During a one-minute revision round: A geometric sequence with ratio r has \(u_n=\)
A \(nr\) This does not satisfy the stated relationship.
B \(u_1r^n\) This does not satisfy the stated relationship.
C \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.
D \(u_1+(n-1)r\) This does not satisfy the stated relationship.

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

14 During a one-minute revision round: The modulus of \(3+4i\) is
A 5 Use the Pythagorean theorem.
B 25 This does not satisfy the stated relationship.
C 7 This does not satisfy the stated relationship.
D 1 This does not satisfy the stated relationship.

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

15 During a one-minute revision round: A square matrix is invertible exactly when its determinant is
A non-zero A zero determinant means singular.
B negative only This does not satisfy the stated relationship.
C one only This does not satisfy the stated relationship.
D zero This does not satisfy the stated relationship.

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

16 During a one-minute revision round: The number of ways to choose r objects from n without order is
A \(n!\) This does not satisfy the stated relationship.
B \(n^r\) This does not satisfy the stated relationship.
C \(n-r\) This does not satisfy the stated relationship.
D \(\binom nr\) Combinations ignore order.

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

17 During a one-minute revision round: A small p-value is evidence
A that the alternative has probability p This does not satisfy the stated relationship.
B that the null is certainly true This does not satisfy the stated relationship.
C of zero sampling variation This does not satisfy the stated relationship.
D against the null hypothesis It means the observed statistic is unusual under the null.

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

18 Which response best completes this VCE-style item? If \(a\mid b\) and \(a\mid c\), then
A \(a\mid(b+c)\) Divisibility is preserved under integer linear combinations.
B \(b\mid a\) This does not satisfy the stated relationship.
C \(a=b+c\) This does not satisfy the stated relationship.
D \(bc\mid a\) This does not satisfy the stated relationship.

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

19 A student is checking a worked solution. If \(a\mid b\) and \(a\mid c\), then
A \(a=b+c\) This does not satisfy the stated relationship.
B \(b\mid a\) This does not satisfy the stated relationship.
C \(bc\mid a\) This does not satisfy the stated relationship.
D \(a\mid(b+c)\) Divisibility is preserved under integer linear combinations.

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

20 A student is checking a worked solution. A vector equation of a line is
A \(\vec r=\vec a\times\vec d\) This does not satisfy the stated relationship.
B \(\vec r=\vec a\cdot\vec d\) This does not satisfy the stated relationship.
C \(\vec r=\vec a+\lambda\vec d\) A point plus a scalar multiple of a direction defines the line.
D \(\vec r=\lambda\) This does not satisfy the stated relationship.

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

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