67676767 · guest · Specialist Mathematics · Units 1 & 2

01 The negation of “all integers are positive” is

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

B no integers exist 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 7424 ms

02 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 22678 ms

03 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 34837 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 41856 ms

05 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 46884 ms

06 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 56138 ms