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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 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

02 \(i^2=\)
A −1 This defines the imaginary unit.
B 1 This does not satisfy the stated relationship.
C 0 This does not satisfy the stated relationship.
D i This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · 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 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

05 A student is checking a worked solution. The sum of degrees in an undirected graph equals
A twice the number of edges Each edge contributes two degree incidences.
B the number of vertices This does not satisfy the stated relationship.
C twice the number of vertices This does not satisfy the stated relationship.
D the number of edges This does not satisfy the stated relationship.

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

06 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

07 A student is checking a worked solution. A geometric sequence with ratio r has \(u_n=\)
A \(nr\) This does not satisfy the stated relationship.
B \(u_1+(n-1)r\) This does not satisfy the stated relationship.
C \(u_1r^n\) This does not satisfy the stated relationship.
D \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.

Written for icaijy.com · U1–2 · Sequences · 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 Which response best completes this VCE-style item? The number of ways to choose r objects from n without order is
A \(n!\) This does not satisfy the stated relationship.
B \(\binom nr\) Combinations ignore order.
C \(n-r\) This does not satisfy the stated relationship.
D \(n^r\) This does not satisfy the stated relationship.

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

10 The number of ways to choose r objects from n without order is
A \(n!\) This does not satisfy the stated relationship.
B \(\binom nr\) Combinations ignore order.
C \(n-r\) This does not satisfy the stated relationship.
D \(n^r\) This does not satisfy the stated relationship.

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

11 During a one-minute revision round: The negation of “all integers are positive” is
A no integers exist This does not satisfy the stated relationship.
B at least one integer is positive This does not satisfy the stated relationship.
C all integers are not positive 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

12 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

13 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

14 The sum of degrees in an undirected graph equals
A the number of edges This does not satisfy the stated relationship.
B twice the number of edges Each edge contributes two degree incidences.
C the number of vertices This does not satisfy the stated relationship.
D twice the number of vertices This does not satisfy the stated relationship.

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

15 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

16 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

17 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

18 During a one-minute revision round: \(i^2=\)
A i This does not satisfy the stated relationship.
B 0 This does not satisfy the stated relationship.
C 1 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 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

20 A vector equation of a line is
A \(\vec r=\lambda\) This does not satisfy the stated relationship.
B \(\vec r=\vec a\times\vec d\) 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 \(\vec r=\vec a\cdot\vec d\) This does not satisfy the stated relationship.

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

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