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

01 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

02 Which response best completes this VCE-style item? For \(\vec a=(1,2,2)\), \(|\vec a|=\)

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

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

C 9 This does not satisfy the stated relationship.

D 5 This does not satisfy the stated relationship.

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

03 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

04 During a one-minute revision round: \(\binom{8}{2}=\)

A 56 This does not satisfy the stated relationship.

B 28 8×7/2=28.

C 16 This does not satisfy the stated relationship.

D 64 This does not satisfy the stated relationship.

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

05 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

06 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

07 Which response best completes this VCE-style item? A geometric sequence has first term 3 and ratio 2. Its sixth term is

A 192 This does not satisfy the stated relationship.

B 48 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 A student is checking a worked solution. \((2+i)(3-i)=\)

A \(7-i\) This does not satisfy the stated relationship.

B \(6-i\) This does not satisfy the stated relationship.

C \(7+i\) Expand and use i²=−1.

D \(5-i\) This does not satisfy the stated relationship.

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

09 \(1+2+4+8+16=\)

A 30 This does not satisfy the stated relationship.

B 64 This does not satisfy the stated relationship.

C 31 This finite geometric sum is 2⁵−1.

D 32 This does not satisfy the stated relationship.

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

10 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

11 A vector calculation returns magnitude −4. The correct interpretation is

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

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

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

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

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

12 A geometric sequence has first term 3 and ratio 2. Its sixth term is

A 48 This does not satisfy the stated relationship.

B 96 3×2⁵=96.

C 64 This does not satisfy the stated relationship.

D 192 This does not satisfy the stated relationship.

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

13 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

14 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

15 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

16 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

17 \((2+i)(3-i)=\)

A \(5-i\) This does not satisfy the stated relationship.

B \(7+i\) Expand and use i²=−1.

C \(6-i\) This does not satisfy the stated relationship.

D \(7-i\) This does not satisfy the stated relationship.

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

18 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

19 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

20 Which response best completes this VCE-style item? The equations \(x+y=5\), \(x-y=1\) have solution

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

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

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

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

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