67 · guest · Specialist Mathematics · Units 1 & 2

01 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 3516 ms

02 During a one-minute revision round: A square matrix is invertible exactly when its determinant is

A non-zero A zero determinant means singular.

B zero This does not satisfy the stated relationship.

C negative only This does not satisfy the stated relationship.

D one only This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Matrices · answered at 13786 ms

03 \(i^2=\)

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 16695 ms

04 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 30666 ms

05 During a one-minute revision round: A proof by contradiction begins by assuming

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

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

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

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

Written for icaijy.com · U1–2 · Proof · answered at 39459 ms

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

C \(u_1+(n-1)r\) 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 54938 ms