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

01 A numerical solver reports one root. To check for omitted roots, first

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

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

02 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

03 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

04 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

05 A student is checking a worked solution. The plane \(2x-y+2z=6\) has normal vector

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

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

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

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

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

06 A student is checking a worked solution. Solve \(dy/dx=2y\), \(y(0)=3\).

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

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

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

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

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

07 During a one-minute revision round: The determinant of \(\begin{pmatrix}2&1\\3&4\end{pmatrix}\) is

A 8 This does not satisfy the stated relationship.

B 5 2×4−1×3=5.

C −5 This does not satisfy the stated relationship.

D 11 This does not satisfy the stated relationship.

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

08 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

09 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

10 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

11 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

12 Which response best completes this VCE-style item? \((2+i)(3-i)=\)

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

13 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

14 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

15 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

16 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

17 During a one-minute revision round: Solve \(dy/dx=2y\), \(y(0)=3\).

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

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

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

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

Written for icaijy.com · U3–4 · Differential equations · 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 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

20 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