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

01 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

02 During a one-minute revision round: The modulus of \(3+4i\) is

A 5 Use the Pythagorean theorem.

B 25 This does not satisfy the stated relationship.

C 7 This does not satisfy the stated relationship.

D 1 This does not satisfy the stated relationship.

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

03 A student is checking a worked solution. The negation of “all integers are positive” is

A all integers are not positive This does not satisfy the stated relationship.

B no integers exist This does not satisfy the stated relationship.

C at least one integer is not positive Negating a universal statement produces an existential counterexample.

D at least one integer is positive This does not satisfy the stated relationship.

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

04 \(i^2=\)

A 0 This does not satisfy the stated relationship.

B 1 This does not satisfy the stated relationship.

C −1 This defines the imaginary unit.

D i This does not satisfy the stated relationship.

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

05 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

06 Which response best completes this VCE-style item? 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

07 During a one-minute revision round: \(i^2=\)

A −1 This defines the imaginary unit.

B i This does not satisfy the stated relationship.

C 0 This does not satisfy the stated relationship.

D 1 This does not satisfy the stated relationship.

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

08 During a one-minute revision round: 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

09 Which response best completes this VCE-style item? \(i^2=\)

A i This does not satisfy the stated relationship.

B −1 This defines the imaginary unit.

C 1 This does not satisfy the stated relationship.

D 0 This does not satisfy the stated relationship.

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

10 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

11 The modulus of \(3+4i\) is

A 5 Use the Pythagorean theorem.

B 7 This does not satisfy the stated relationship.

C 1 This does not satisfy the stated relationship.

D 25 This does not satisfy the stated relationship.

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

12 A student is checking a worked solution. \(i^2=\)

A 0 This does not satisfy the stated relationship.

B −1 This defines the imaginary unit.

C i This does not satisfy the stated relationship.

D 1 This does not satisfy the stated relationship.

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

13 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

14 Which response best completes this VCE-style item? 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 \(ac-bd\) This does not satisfy the stated relationship.

D \(ad-bc\) Use ad−bc.

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

15 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

16 A connected graph with n vertices and n−1 edges is a

A cycle This does not satisfy the stated relationship.

B complete graph This does not satisfy the stated relationship.

C multigraph necessarily 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

17 During a one-minute revision round: A geometric sequence with ratio r has \(u_n=\)

A \(u_1r^n\) This does not satisfy the stated relationship.

B \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.

C \(u_1+(n-1)r\) This does not satisfy the stated relationship.

D \(nr\) This does not satisfy the stated relationship.

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

18 Which response best completes this VCE-style item? The negation of “all integers are positive” is

A all integers are not positive This does not satisfy the stated relationship.

B at least one integer is not positive Negating a universal statement produces an existential counterexample.

C at least one integer is positive This does not satisfy the stated relationship.

D no integers exist This does not satisfy the stated relationship.

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

19 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

20 The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is

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

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

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

D \(ad-bc\) Use ad−bc.

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