icaijy

10 Sep 2026, 7:54 p.m.

86067 score

5 correct × 172 movement score = 860

67 × VCE evidence60.2 seconds · bandwidth-limited recordingDownload video

01 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 \(2+3i\) 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 5459 ms

02 During a one-minute revision round: The scalar projection of a onto non-zero b is

A \(\vec a\times\vec b\) This does not satisfy the stated relationship.

B \(|\vec a||\vec b|\) This does not satisfy the stated relationship.

C \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.

D \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.

Written for icaijy.com · U1–2 · Geometry · answered at 13479 ms

03 A student is checking a worked solution. A connected graph with n vertices and n−1 edges is a

A multigraph necessarily This does not satisfy the stated relationship.

B cycle This does not satisfy the stated relationship.

C tree This is a standard characterisation of a tree.

D complete graph This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graph theory · answered at 20287 ms

04 During a one-minute revision round: The number of ways to choose r objects from n without order is

A \(\binom nr\) Combinations ignore order.

B \(n^r\) This does not satisfy the stated relationship.

C \(n!\) 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 28715 ms

05 A square matrix is invertible exactly when its determinant is

A one only This does not satisfy the stated relationship.

B negative only This does not satisfy the stated relationship.

C zero This does not satisfy the stated relationship.

D non-zero A zero determinant means singular.

Written for icaijy.com · U1–2 · Matrices · answered at 35808 ms

06 A student is checking a worked solution. \(\cos(A-B)=\)

A \(\cos A-\cos B\) This does not satisfy the stated relationship.

B \(\sin A\cos B\) This does not satisfy the stated relationship.

C \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.

D \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Trigonometry · answered at 44719 ms

07 A student is checking a worked solution. 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 \(3+2i\) Change the sign of the imaginary part.

D \(2+3i\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · answered at 50693 ms