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

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

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

02 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

03 Which response best completes this VCE-style item? 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 \(\sqrt{f(x)}\) 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

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

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

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

C the vector points left 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 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

06 A matrix inverse command fails because det(A)=0. This means A is

A orthogonal This does not satisfy the stated relationship.

B singular Zero determinant means no inverse.

C the identity This does not satisfy the stated relationship.

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

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

07 Which response best completes this VCE-style item? If \(\sigma=12\) and \(n=36\), the standard error is

A 0.33 This does not satisfy the stated relationship.

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

C 6 This does not satisfy the stated relationship.

D 72 This does not satisfy the stated relationship.

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

08 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

09 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

10 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

11 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

12 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

13 During a one-minute revision round: \((2+i)(3-i)=\)

A \(5-i\) 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 \(7-i\) This does not satisfy the stated relationship.

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

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

A 31 This finite geometric sum is 2⁵−1.

B 30 This does not satisfy the stated relationship.

C 32 This does not satisfy the stated relationship.

D 64 This does not satisfy the stated relationship.

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

15 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

16 During a one-minute revision round: A 2 kg particle has acceleration 3 m s⁻². Net force magnitude is

A 1.5 N This does not satisfy the stated relationship.

B 9 N This does not satisfy the stated relationship.

C 5 N This does not satisfy the stated relationship.

D 6 N F=ma=6 N.

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

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

A 6 This does not satisfy the stated relationship.

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

C 30 This does not satisfy the stated relationship.

D 12 This does not satisfy the stated relationship.

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

18 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

19 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

20 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