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

01 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

02 A student is checking a worked solution. The solutions of \(z^2=-1\) are

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

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

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

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

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

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

A \(-3\pi/4\) 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 \(5\pi/4\) This does not satisfy the stated relationship.

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

04 A student is checking a worked solution. One Newton step for \(f(x)=x^2-2\) from \(x_0=1.5\) gives

A approximately 1.2500 This does not satisfy the stated relationship.

B approximately 2.0000 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

05 A student is checking a worked solution. If \(\sigma=12\) and \(n=36\), the standard error is

A 2 \(12/\sqrt{36}=2\).

B 72 This does not satisfy the stated relationship.

C 6 This does not satisfy the stated relationship.

D 0.33 This does not satisfy the stated relationship.

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

06 During a one-minute revision round: One Newton step for \(f(x)=x^2-2\) from \(x_0=1.5\) gives

A approximately 1.2500 This does not satisfy the stated relationship.

B approximately 2.0000 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

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 Which response best completes this VCE-style item? 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

09 A 2 kg particle has acceleration 3 m s⁻². Net force magnitude is

A 6 N F=ma=6 N.

B 9 N This does not satisfy the stated relationship.

C 5 N This does not satisfy the stated relationship.

D 1.5 N This does not satisfy the stated relationship.

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

10 During a one-minute revision round: \((1,0,0)\times(0,1,0)=\)

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

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

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

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

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

11 Which response best completes this VCE-style item? 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 1.4167 \(x_1=x_0-f(x_0)/f\prime(x_0)\).

C approximately 1.2500 This does not satisfy the stated relationship.

D approximately 1.5000 This does not satisfy the stated relationship.

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

12 A student is checking a worked solution. A 2 kg particle has acceleration 3 m s⁻². Net force magnitude is

A 6 N F=ma=6 N.

B 9 N This does not satisfy the stated relationship.

C 1.5 N This does not satisfy the stated relationship.

D 5 N This does not satisfy the stated relationship.

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

13 Which response best completes this VCE-style item? 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

14 During a one-minute revision round: A matrix inverse command fails because det(A)=0. This means A is

A singular Zero determinant means no inverse.

B the identity This does not satisfy the stated relationship.

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

D orthogonal This does not satisfy the stated relationship.

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

15 An estimate 20 has margin of error 3. The interval is

A \((3,20)\) This does not satisfy the stated relationship.

B \((14,26)\) This does not satisfy the stated relationship.

C \((20,23)\) This does not satisfy the stated relationship.

D \((17,23)\) Add and subtract the margin.

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

16 Which response best completes this VCE-style item? An estimate 20 has margin of error 3. The interval is

A \((17,23)\) Add and subtract the margin.

B \((14,26)\) This does not satisfy the stated relationship.

C \((20,23)\) This does not satisfy the stated relationship.

D \((3,20)\) This does not satisfy the stated relationship.

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

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

A only for prime inputs 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 whenever no counterexample appears 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

18 Which response best completes this VCE-style item? If \(u_{n+1}=u_n+3\) and \(u_1=2\), then \(u_5=\)

A 14 Four increments of 3 give 14.

B 15 This does not satisfy the stated relationship.

C 17 This does not satisfy the stated relationship.

D 11 This does not satisfy the stated relationship.

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

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

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

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

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

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

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

20 Solve \(dy/dx=2y\), \(y(0)=3\).

A \(y=3e^x\) This does not satisfy the stated relationship.

B \(y=3e^{2x}\) Exponential growth rate is 2 with initial value 3.

C \(y=2e^{3x}\) This does not satisfy the stated relationship.

D \(y=3+2x\) This does not satisfy the stated relationship.

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