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

01 A student is checking a worked solution. A complete graph \(K_6\) has how many edges?

A 30 This does not satisfy the stated relationship.

B 12 This does not satisfy the stated relationship.

C 6 This does not satisfy the stated relationship.

D 15 \(6\times5/2=15\).

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

02 \(\binom{8}{2}=\)

A 64 This does not satisfy the stated relationship.

B 28 8×7/2=28.

C 56 This does not satisfy the stated relationship.

D 16 This does not satisfy the stated relationship.

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

03 The equations \(x+y=5\), \(x-y=1\) have solution

A \((5,0)\) This does not satisfy the stated relationship.

B \((3,2)\) Add the equations to obtain x=3.

C \((2,3)\) This does not satisfy the stated relationship.

D \((4,1)\) This does not satisfy the stated relationship.

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

04 A student is checking a worked solution. A vector calculation returns magnitude −4. The correct interpretation is

A the vector points left This does not satisfy the stated relationship.

B a magnitude cannot be negative, so the setup or output is wrong Magnitude is a non-negative scalar.

C the vector points down This does not satisfy the stated relationship.

D the magnitude is −4 This does not satisfy the stated relationship.

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

05 Which response best completes this VCE-style item? \(1+2+4+8+16=\)

A 32 This does not satisfy the stated relationship.

B 30 This does not satisfy the stated relationship.

C 31 This finite geometric sum is 2⁵−1.

D 64 This does not satisfy the stated relationship.

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

06 During a one-minute revision round: Solve \(2\cos x=1\) on \([0,2\pi]\).

A \(x=\pi/3,2\pi/3\) This does not satisfy the stated relationship.

B \(x=\pi/6,5\pi/6\) This does not satisfy the stated relationship.

C \(x=\pi/3,5\pi/3\) Cosine is 1/2 in quadrants I and IV.

D \(x=2\pi/3,4\pi/3\) This does not satisfy the stated relationship.

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

07 A student is checking a worked solution. A geometric sequence has first term 3 and ratio 2. Its sixth term is

A 48 This does not satisfy the stated relationship.

B 192 This does not satisfy the stated relationship.

C 96 3×2⁵=96.

D 64 This does not satisfy the stated relationship.

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

08 During a one-minute revision round: The principal argument of \(-1+i\) is

A \(5\pi/4\) This does not satisfy the stated relationship.

B \(\pi/4\) This does not satisfy the stated relationship.

C \(3\pi/4\) The point lies in quadrant II.

D \(-3\pi/4\) This does not satisfy the stated relationship.

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

09 During a one-minute revision round: A vector calculation returns magnitude −4. The correct interpretation is

A the vector points down This does not satisfy the stated relationship.

B the magnitude is −4 This does not satisfy the stated relationship.

C the vector points left This does not satisfy the stated relationship.

D a magnitude cannot be negative, so the setup or output is wrong Magnitude is a non-negative scalar.

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

10 A student is checking a worked solution. Solve \(2\cos x=1\) on \([0,2\pi]\).

A \(x=2\pi/3,4\pi/3\) This does not satisfy the stated relationship.

B \(x=\pi/6,5\pi/6\) This does not satisfy the stated relationship.

C \(x=\pi/3,2\pi/3\) This does not satisfy the stated relationship.

D \(x=\pi/3,5\pi/3\) Cosine is 1/2 in quadrants I and IV.

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

11 During a one-minute revision round: For \(\vec a=(1,2,2)\), \(|\vec a|=\)

A 5 This does not satisfy the stated relationship.

B 9 This does not satisfy the stated relationship.

C \(\sqrt5\) This does not satisfy the stated relationship.

D 3 \(\sqrt{1+4+4}=3\).

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

12 The angle between (1,0) and (1,1) is

A \(3\pi/4\) This does not satisfy the stated relationship.

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

C \(\pi/2\) This does not satisfy the stated relationship.

D \(\pi/4\) The dot-product cosine is 1/√2.

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

13 One Newton step for \(f(x)=x^2-2\) from \(x_0=1.5\) gives

A approximately 2.0000 This does not satisfy the stated relationship.

B approximately 1.2500 This does not satisfy the stated relationship.

C approximately 1.5000 This does not satisfy the stated relationship.

D approximately 1.4167 \(x_1=x_0-f(x_0)/f\prime(x_0)\).

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

14 Which response best completes this VCE-style item? Testing 10 000 cases with CAS establishes a universal integer claim

A whenever no counterexample appears This does not satisfy the stated relationship.

B with certainty by itself This does not satisfy the stated relationship.

C only if paired with a valid general proof Finite checking alone does not prove an infinite claim.

D only for prime inputs This does not satisfy the stated relationship.

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

15 Testing 10 000 cases with CAS establishes a universal integer claim

A whenever no counterexample appears This does not satisfy the stated relationship.

B only if paired with a valid general proof Finite checking alone does not prove an infinite claim.

C only for prime inputs This does not satisfy the stated relationship.

D with certainty by itself This does not satisfy the stated relationship.

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

16 A student is checking a worked solution. Testing 10 000 cases with CAS establishes a universal integer claim

A whenever no counterexample appears This does not satisfy the stated relationship.

B only if paired with a valid general proof Finite checking alone does not prove an infinite claim.

C only for prime inputs This does not satisfy the stated relationship.

D with certainty by itself This does not satisfy the stated relationship.

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

17 During a one-minute revision round: Testing 10 000 cases with CAS establishes a universal integer claim

A whenever no counterexample appears This does not satisfy the stated relationship.

B with certainty by itself This does not satisfy the stated relationship.

C only if paired with a valid general proof Finite checking alone does not prove an infinite claim.

D only for prime inputs This does not satisfy the stated relationship.

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

18 A student is checking a worked solution. The angle between (1,0) and (1,1) is

A \(\pi\) This does not satisfy the stated relationship.

B \(\pi/4\) The dot-product cosine is 1/√2.

C \(3\pi/4\) This does not satisfy the stated relationship.

D \(\pi/2\) This does not satisfy the stated relationship.

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

19 Which response best completes this VCE-style item? A matrix inverse command fails because det(A)=0. This means A is

A orthogonal This does not satisfy the stated relationship.

B diagonal with non-zero entries This does not satisfy the stated relationship.

C the identity This does not satisfy the stated relationship.

D singular Zero determinant means no inverse.

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

20 During a one-minute revision round: \(1+2+4+8+16=\)

A 64 This does not satisfy the stated relationship.

B 32 This does not satisfy the stated relationship.

C 31 This finite geometric sum is 2⁵−1.

D 30 This does not satisfy the stated relationship.

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