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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 Which response best completes this VCE-style item? 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 \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.
D \(\vec r\prime(t)\) This does not satisfy the stated relationship.

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

02 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

03 Which response best completes this VCE-style item? The sum of degrees in an undirected graph equals
A twice the number of vertices This does not satisfy the stated relationship.
B the number of edges This does not satisfy the stated relationship.
C the number of vertices This does not satisfy the stated relationship.
D twice the number of edges Each edge contributes two degree incidences.

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

04 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

05 Which response best completes this VCE-style item? The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is
A \(ad-bc\) Use ad−bc.
B \(a+d\) This does not satisfy the stated relationship.
C \(ab-cd\) This does not satisfy the stated relationship.
D \(ac-bd\) This does not satisfy the stated relationship.

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

06 \(\int e^{ax}\,dx=\)
A \(\frac1a e^{ax}+C\) Differentiate to verify the factor 1/a.
B \(\frac1x e^{ax}\) This does not satisfy the stated relationship.
C \(e^{ax}+C\) This does not satisfy the stated relationship.
D \(ae^{ax}+C\) 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: The standard deviation of the sample mean is
A \(\sigma/\sqrt n\) This is the standard error of the mean.
B \(\sigma\sqrt n\) This does not satisfy the stated relationship.
C \(\sigma/n\) This does not satisfy the stated relationship.
D \(n/\sigma\) This does not satisfy the stated relationship.

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

08 Which response best completes this VCE-style item? A geometric sequence with ratio r has \(u_n=\)
A \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.
B \(u_1+(n-1)r\) This does not satisfy the stated relationship.
C \(nr\) This does not satisfy the stated relationship.
D \(u_1r^n\) This does not satisfy the stated relationship.

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

09 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

10 A student is checking a worked solution. A small p-value is evidence
A of zero sampling variation This does not satisfy the stated relationship.
B that the alternative has probability p This does not satisfy the stated relationship.
C that the null is certainly true 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

11 The roots of \(z^n=1\) are equally spaced on the
A parabola This does not satisfy the stated relationship.
B imaginary axis This does not satisfy the stated relationship.
C real 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

12 During a one-minute revision round: \(\int e^{ax}\,dx=\)
A \(e^{ax}+C\) This does not satisfy the stated relationship.
B \(\frac1x e^{ax}\) This does not satisfy the stated relationship.
C \(\frac1a e^{ax}+C\) Differentiate to verify the factor 1/a.
D \(ae^{ax}+C\) This does not satisfy the stated relationship.

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

13 The standard deviation of the sample mean is
A \(\sigma/n\) This does not satisfy the stated relationship.
B \(\sigma\sqrt n\) This does not satisfy the stated relationship.
C \(\sigma/\sqrt n\) This is the standard error of the mean.
D \(n/\sigma\) This does not satisfy the stated relationship.

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

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

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

15 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

16 A proof by contradiction begins by assuming
A the conclusion itself This does not satisfy the stated relationship.
B every lemma is false This does not satisfy the stated relationship.
C a numerical example This does not satisfy the stated relationship.
D the negation of the desired conclusion A contradiction disproves the negation.

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

17 Which response best completes this VCE-style item? The standard deviation of the sample mean is
A \(n/\sigma\) This does not satisfy the stated relationship.
B \(\sigma/n\) This does not satisfy the stated relationship.
C \(\sigma\sqrt n\) This does not satisfy the stated relationship.
D \(\sigma/\sqrt n\) This is the standard error of the mean.

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

18 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

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

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

20 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

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