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

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11 Sep 2026, 9:24 p.m.

20Serious score
01 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

02 During a one-minute revision round: The roots of \(z^n=1\) are equally spaced on the
A real axis This does not satisfy the stated relationship.
B parabola This does not satisfy the stated relationship.
C imaginary axis This does not satisfy the stated relationship.
D unit circle Their moduli are one and arguments differ by 2π/n.

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

03 A student is checking a worked solution. The scalar projection of a onto non-zero b is
A \(|\vec a||\vec b|\) This does not satisfy the stated relationship.
B \(\vec a\times\vec b\) This does not satisfy the stated relationship.
C \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.
D \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.

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

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

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

05 During a one-minute revision round: The scalar projection of a onto non-zero b is
A \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.
B \(\vec a\times\vec b\) This does not satisfy the stated relationship.
C \(|\vec a||\vec b|\) This does not satisfy the stated relationship.
D \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.

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

06 A student is checking a worked solution. If position is \(\vec r(t)\), acceleration is
A \(\int\vec r(t)dt\) This does not satisfy the stated relationship.
B \(|\vec r(t)|\) This does not satisfy the stated relationship.
C \(\vec r\prime(t)\) This does not satisfy the stated relationship.
D \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.

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

07 Which response best completes this VCE-style item? A connected graph with n vertices and n−1 edges is a
A complete graph This does not satisfy the stated relationship.
B tree This is a standard characterisation of a tree.
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

08 A student is checking a worked solution. The conjugate of \(3-2i\) is
A \(2+3i\) This does not satisfy the stated relationship.
B \(3-2i\) This does not satisfy the stated relationship.
C \(-3+2i\) This does not satisfy the stated relationship.
D \(3+2i\) Change the sign of the imaginary part.

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

09 A student is checking a worked solution. The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is
A \(a+d\) This does not satisfy the stated relationship.
B \(ac-bd\) This does not satisfy the stated relationship.
C \(ab-cd\) This does not satisfy the stated relationship.
D \(ad-bc\) Use ad−bc.

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

10 For independent random variables X and Y, \(\mathrm{Var}(X+Y)=\)
A \(\mathrm{Var}(X)-\mathrm{Var}(Y)\) This does not satisfy the stated relationship.
B \(0\) This does not satisfy the stated relationship.
C \(\mathrm{Var}(X)\mathrm{Var}(Y)\) This does not satisfy the stated relationship.
D \(\mathrm{Var}(X)+\mathrm{Var}(Y)\) Covariance is zero under independence.

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

11 During a one-minute revision round: For \(dy/dx=f(x)g(y)\), separation gives
A \(dx/dy=f(x)g(y)\) This does not satisfy the stated relationship.
B \(dy=f(x)+g(y)\) This does not satisfy the stated relationship.
C \(\frac{dy}{g(y)}=f(x)\,dx\) Move the y factor with dy and x factor with dx.
D \(g(y)dy=f(x)dx\) This does not satisfy the stated relationship.

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

12 The conjugate of \(3-2i\) is
A \(-3+2i\) This does not satisfy the stated relationship.
B \(2+3i\) This does not satisfy the stated relationship.
C \(3-2i\) This does not satisfy the stated relationship.
D \(3+2i\) Change the sign of the imaginary part.

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

13 The cross product \(\vec a\times\vec b\) is
A parallel to both vectors This does not satisfy the stated relationship.
B always zero This does not satisfy the stated relationship.
C a scalar This does not satisfy the stated relationship.
D perpendicular to both vectors Its direction follows the right-hand rule.

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

14 During a one-minute revision round: The conjugate of \(3-2i\) is
A \(3-2i\) This does not satisfy the stated relationship.
B \(2+3i\) This does not satisfy the stated relationship.
C \(3+2i\) Change the sign of the imaginary part.
D \(-3+2i\) This does not satisfy the stated relationship.

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

15 The scalar projection of a onto non-zero b is
A \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.
B \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.
C \(|\vec a||\vec b|\) This does not satisfy the stated relationship.
D \(\vec a\times\vec b\) This does not satisfy the stated relationship.

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

16 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

17 A student is checking a worked solution. For \(dy/dx=f(x)g(y)\), separation gives
A \(dx/dy=f(x)g(y)\) This does not satisfy the stated relationship.
B \(dy=f(x)+g(y)\) This does not satisfy the stated relationship.
C \(g(y)dy=f(x)dx\) 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

18 Two non-zero vectors are perpendicular when their dot product is
A 0 The dot product includes cos 90° = 0.
B their magnitude product This does not satisfy the stated relationship.
C 1 This does not satisfy the stated relationship.
D −1 always This does not satisfy the stated relationship.

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

19 Which response best completes this VCE-style item? The vector from A to B is
A \(\vec a+\vec b\) 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 \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.

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

20 Which response best completes this VCE-style item? 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 \(\vec r=\lambda\) This does not satisfy the stated relationship.
D \(\vec r=\vec a+\lambda\vec d\) A point plus a scalar multiple of a direction defines the line.

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

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