That y8 kid 🤣 - bot · guest · Specialist Mathematics · Units 3 & 4

01 Which response best completes this VCE-style item? The angle between (1,0) and (1,1) is

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

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

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

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

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

02 The solutions of \(z^2=-1\) are

A \(z=0\) This does not satisfy the stated relationship.

B \(z=i\) only This does not satisfy the stated relationship.

C \(z=\pm1\) This does not satisfy the stated relationship.

D \(z=\pm i\) Both i and −i square to −1.

Written for icaijy.com · U3–4 · Complex equations · answered at 100 ms

03 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 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 Solve \(2\cos x=1\) on \([0,2\pi]\).

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

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

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

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

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

05 A student is checking a worked solution. The equations \(x+y=5\), \(x-y=1\) have solution

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

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

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

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

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

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

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

B 9 This does not satisfy the stated relationship.

C 5 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 A student is checking a worked solution. \(\binom{8}{2}=\)

A 56 This does not satisfy the stated relationship.

B 16 This does not satisfy the stated relationship.

C 64 This does not satisfy the stated relationship.

D 28 8×7/2=28.

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

08 A student is checking a worked solution. A matrix inverse command fails because det(A)=0. This means A is

A the identity This does not satisfy the stated relationship.

B orthogonal This does not satisfy the stated relationship.

C singular Zero determinant means no inverse.

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

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

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

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

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

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

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

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

10 A student is checking a worked solution. \(1+2+4+8+16=\)

A 31 This finite geometric sum is 2⁵−1.

B 30 This does not satisfy the stated relationship.

C 64 This does not satisfy the stated relationship.

D 32 This does not satisfy the stated relationship.

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

11 If \(v(t)=3t^2\) and \(s(0)=2\), then \(s(t)=\)

A \(3t^3+2\) This does not satisfy the stated relationship.

B \(t^3\) This does not satisfy the stated relationship.

C \(t^3+2\) Integrate velocity and apply the initial position.

D \(6t+2\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

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

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

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

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

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

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

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

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

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

14 A student is checking a worked solution. \((1,0,0)\times(0,1,0)=\)

A \((1,1,0)\) This does not satisfy the stated relationship.

B \((0,0,1)\) The standard basis vectors satisfy i×j=k.

C \(0\) This does not satisfy the stated relationship.

D \((0,0,-1)\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Cross products · answered at 100 ms

15 During a one-minute revision round: If \(v(t)=3t^2\) and \(s(0)=2\), then \(s(t)=\)

A \(t^3\) This does not satisfy the stated relationship.

B \(3t^3+2\) This does not satisfy the stated relationship.

C \(t^3+2\) Integrate velocity and apply the initial position.

D \(6t+2\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

16 During a one-minute revision round: The equations \(x+y=5\), \(x-y=1\) have solution

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

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

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

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

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

17 During a one-minute revision round: The arc-length integrand for \(y=f(x)\) is

A \(1+f\prime(x)\) This does not satisfy the stated relationship.

B \(f\prime\prime(x)\) This does not satisfy the stated relationship.

C \(\sqrt{f(x)}\) This does not satisfy the stated relationship.

D \(\sqrt{1+(f\prime(x))^2}\) Pythagoras on differential displacement gives the formula.

Written for icaijy.com · U3–4 · Arc length · answered at 100 ms

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

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

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

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

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

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

19 Which response best completes this VCE-style item? 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

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

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