That y8 kid 🤣 - bot · guest · Specialist Mathematics · Units 1 & 2

01 A student is checking a worked solution. The vector from A to B is

A \(\vec b-\vec a\) Endpoint position minus start position.

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

C \(\vec a-\vec b\) This does not satisfy the stated relationship.

D \(\vec a+\vec b\) This does not satisfy the stated relationship.

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

02 A student is checking a worked solution. The modulus of \(3+4i\) is

A 1 This does not satisfy the stated relationship.

B 25 This does not satisfy the stated relationship.

C 7 This does not satisfy the stated relationship.

D 5 Use the Pythagorean theorem.

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

03 A student is checking a worked solution. The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is

A \(ac-bd\) This does not satisfy the stated relationship.

B \(ab-cd\) This does not satisfy the stated relationship.

C \(a+d\) This does not satisfy the stated relationship.

D \(ad-bc\) Use ad−bc.

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

04 Which response best completes this VCE-style item? The scalar projection of a onto non-zero b is

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

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

C \(|\vec a||\vec b|\) 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 100 ms

05 During a one-minute revision round: The vector from A to B is

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

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

C \(\vec a-\vec b\) This does not satisfy the stated relationship.

D \(\vec b-\vec a\) Endpoint position minus start position.

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

06 The vector from A to B is

A \(\vec b-\vec a\) Endpoint position minus start position.

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

C \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.

D \(\vec a-\vec b\) This does not satisfy the stated relationship.

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

07 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 100 ms

08 Which response best completes this VCE-style item? \(\cos(A-B)=\)

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

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

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

09 Which response best completes this VCE-style item? A proof by contradiction begins by assuming

A every lemma is false This does not satisfy the stated relationship.

B a numerical example This does not satisfy the stated relationship.

C the negation of the desired conclusion A contradiction disproves the negation.

D the conclusion itself This does not satisfy the stated relationship.

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

10 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 \(3+2i\) 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

11 A student is checking a worked solution. The sum of degrees in an undirected graph equals

A the number of vertices This does not satisfy the stated relationship.

B the number of edges This does not satisfy the stated relationship.

C twice 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

12 The number of ways to choose r objects from n without order is

A \(n-r\) This does not satisfy the stated relationship.

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

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 100 ms

13 Which response best completes this VCE-style item? The number of ways to choose r objects from n without order is

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

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

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

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 A student is checking a worked solution. A proof by contradiction begins by assuming

A every lemma is false This does not satisfy the stated relationship.

B a numerical example This does not satisfy the stated relationship.

C the conclusion itself 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

16 Which response best completes this VCE-style item? The sum of degrees in an undirected graph equals

A twice the number of edges Each edge contributes two degree incidences.

B twice the number of vertices This does not satisfy the stated relationship.

C 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

17 During a one-minute revision round: 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

18 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 100 ms

19 During a one-minute revision round: 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 always 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

20 A student is checking a worked solution. Two non-zero vectors are perpendicular when their dot product is

A 1 This does not satisfy the stated relationship.

B 0 The dot product includes cos 90° = 0.

C −1 always This does not satisfy the stated relationship.

D their magnitude product This does not satisfy the stated relationship.

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