That y8 kid 🤣 - bot · guest · Specialist Mathematics · Units 1 & 2

01 Which response best completes this VCE-style item? The determinant of \(\begin{pmatrix}2&1\\3&4\end{pmatrix}\) is

A 8 This does not satisfy the stated relationship.

B −5 This does not satisfy the stated relationship.

C 11 This does not satisfy the stated relationship.

D 5 2×4−1×3=5.

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

02 The determinant of \(\begin{pmatrix}2&1\\3&4\end{pmatrix}\) is

A 8 This does not satisfy the stated relationship.

B 11 This does not satisfy the stated relationship.

C 5 2×4−1×3=5.

D −5 This does not satisfy the stated relationship.

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

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

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

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

C \((2,3)\) 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

04 A student is checking a worked solution. 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 \(3\pi/4\) This does not satisfy the stated relationship.

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

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

05 During a one-minute revision round: 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

06 Which response best completes this VCE-style item? 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 magnitude is −4 This does not satisfy the stated relationship.

D the vector points left This does not satisfy the stated relationship.

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

07 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 11 This does not satisfy the stated relationship.

D 17 This does not satisfy the stated relationship.

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

08 Which response best completes this VCE-style item? 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 9 This does not satisfy the stated relationship.

D 5 This does not satisfy the stated relationship.

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

09 During a one-minute revision round: If \(u_{n+1}=u_n+3\) and \(u_1=2\), then \(u_5=\)

A 11 This does not satisfy the stated relationship.

B 15 This does not satisfy the stated relationship.

C 17 This does not satisfy the stated relationship.

D 14 Four increments of 3 give 14.

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

10 During a one-minute revision round: The angle between (1,0) and (1,1) is

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

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

C \(\pi\) 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

11 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 1.4167 \(x_1=x_0-f(x_0)/f\prime(x_0)\).

C approximately 1.5000 This does not satisfy the stated relationship.

D approximately 2.0000 This does not satisfy the stated relationship.

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

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

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

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

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

D the magnitude is −4 This does not satisfy the stated relationship.

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

13 The angle between (1,0) and (1,1) is

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

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

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

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

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

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

A \(6-i\) This does not satisfy the stated relationship.

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

C \(7+i\) Expand and use i²=−1.

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

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

15 A student is checking a worked solution. For \(\vec a=(1,2,2)\), \(|\vec a|=\)

A 5 This does not satisfy the stated relationship.

B 9 This does not satisfy the stated relationship.

C 3 \(\sqrt{1+4+4}=3\).

D \(\sqrt5\) 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: \(\binom{8}{2}=\)

A 56 This does not satisfy the stated relationship.

B 28 8×7/2=28.

C 16 This does not satisfy the stated relationship.

D 64 This does not satisfy the stated relationship.

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

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

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

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

C \((2,3)\) 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

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

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

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

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

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

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

19 During a one-minute revision round: A geometric sequence has first term 3 and ratio 2. Its sixth term is

A 64 This does not satisfy the stated relationship.

B 48 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

20 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