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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: 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

02 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

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 A student is checking a worked solution. \(\cos(A-B)=\)
A \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.
B \(\sin A\cos B\) This does not satisfy the stated relationship.
C \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.
D \(\cos A-\cos B\) This does not satisfy the stated relationship.

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

05 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

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

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

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

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

08 Which response best completes this VCE-style item? 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

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

10 Which response best completes this VCE-style item? The conjugate of \(3-2i\) is
A \(3-2i\) This does not satisfy the stated relationship.
B \(-3+2i\) This does not satisfy the stated relationship.
C \(2+3i\) 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

11 During a one-minute revision round: Two non-zero vectors are perpendicular when their dot product is
A 1 This does not satisfy the stated relationship.
B −1 always This does not satisfy the stated relationship.
C 0 The dot product includes cos 90° = 0.
D their magnitude product This does not satisfy the stated relationship.

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

12 During a one-minute revision round: \(\cos(A-B)=\)
A \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.
B \(\sin A\cos B\) This does not satisfy the stated relationship.
C \(\cos A-\cos B\) This does not satisfy the stated relationship.
D \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.

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

13 During a one-minute revision round: 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 \(\mathrm{Var}(X)-\mathrm{Var}(Y)\) This does not satisfy the stated relationship.
C \(\mathrm{Var}(X)+\mathrm{Var}(Y)\) Covariance is zero under independence.
D \(0\) This does not satisfy the stated relationship.

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

14 \(\cos(A-B)=\)
A \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.
B \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.
C \(\cos A-\cos B\) This does not satisfy the stated relationship.
D \(\sin A\cos B\) This does not satisfy the stated relationship.

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

15 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

16 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

17 Which response best completes this VCE-style item? Two non-zero vectors are perpendicular when their dot product is
A 0 The dot product includes cos 90° = 0.
B −1 always This does not satisfy the stated relationship.
C their magnitude product This does not satisfy the stated relationship.
D 1 This does not satisfy the stated relationship.

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

18 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

19 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

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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