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

01 Which response best completes this VCE-style item? A complete graph \(K_6\) has how many edges?

A 12 This does not satisfy the stated relationship.

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

C 30 This does not satisfy the stated relationship.

D 6 This does not satisfy the stated relationship.

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

02 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

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 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

04 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

05 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 64 This does not satisfy the stated relationship.

C 96 3×2⁵=96.

D 192 This does not satisfy the stated relationship.

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

06 A student is checking a worked solution. The arc-length integrand for \(y=f(x)\) is

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

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

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

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

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

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

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

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

C \(x=\pi/6,5\pi/6\) 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

08 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

09 Which response best completes this VCE-style item? The plane \(2x-y+2z=6\) has normal vector

A \((6,0,0)\) This does not satisfy the stated relationship.

B \((x,y,z)\) This does not satisfy the stated relationship.

C \((2,1,2)\) This does not satisfy the stated relationship.

D \((2,-1,2)\) The coefficients form a normal vector.

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

10 During a one-minute revision round: An estimate 20 has margin of error 3. The interval is

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

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

C \((14,26)\) 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

11 The arc-length integrand for \(y=f(x)\) is

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

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

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

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

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

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

A 31 This finite geometric sum is 2⁵−1.

B 64 This does not satisfy the stated relationship.

C 30 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

13 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

14 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

15 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

16 During a one-minute revision round: A numerical solver reports one root. To check for omitted roots, first

A differentiate the answer This does not satisfy the stated relationship.

B inspect the domain and graph or use complete solve settings Numerical solvers depend on domain, guesses and settings.

C round the root more This does not satisfy the stated relationship.

D assume uniqueness This does not satisfy the stated relationship.

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

17 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

18 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

19 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 5 This does not satisfy the stated relationship.

D 9 This does not satisfy the stated relationship.

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

20 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