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

01 A student is checking a worked solution. \((2+i)(3-i)=\)

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

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

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

A 11 This does not satisfy the stated relationship.

B 17 This does not satisfy the stated relationship.

C 15 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

03 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

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

A −5 This does not satisfy the stated relationship.

B 11 This does not satisfy the stated relationship.

C 8 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

05 \((2+i)(3-i)=\)

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

06 During a one-minute revision round: 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

07 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 30 This does not satisfy the stated relationship.

C 6 This does not satisfy the stated relationship.

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

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

08 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

09 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

10 A student is checking a worked solution. If \(u_{n+1}=u_n+3\) and \(u_1=2\), then \(u_5=\)

A 14 Four increments of 3 give 14.

B 17 This does not satisfy the stated relationship.

C 15 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

11 \(\binom{8}{2}=\)

A 64 This does not satisfy the stated relationship.

B 28 8×7/2=28.

C 56 This does not satisfy the stated relationship.

D 16 This does not satisfy the stated relationship.

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

12 \(1+2+4+8+16=\)

A 30 This does not satisfy the stated relationship.

B 64 This does not satisfy the stated relationship.

C 31 This finite geometric sum is 2⁵−1.

D 32 This does not satisfy the stated relationship.

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

13 A student is checking a worked solution. \(\binom{8}{2}=\)

A 16 This does not satisfy the stated relationship.

B 64 This does not satisfy the stated relationship.

C 56 This does not satisfy the stated relationship.

D 28 8×7/2=28.

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

14 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

15 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

16 Which response best completes this VCE-style item? Solve \(2\cos x=1\) on \([0,2\pi]\).

A \(x=\pi/6,5\pi/6\) This does not satisfy the stated relationship.

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

C \(x=\pi/3,5\pi/3\) Cosine is 1/2 in quadrants I and IV.

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

17 During a one-minute revision round: Solve \(2\cos x=1\) on \([0,2\pi]\).

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

B \(x=\pi/6,5\pi/6\) This does not satisfy the stated relationship.

C \(x=\pi/3,5\pi/3\) Cosine is 1/2 in quadrants I and IV.

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

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

18 Which response best completes this VCE-style item? The principal argument of \(-1+i\) is

A \(3\pi/4\) The point lies in quadrant II.

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

C \(5\pi/4\) This does not satisfy the stated relationship.

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

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

19 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 1.2500 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

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

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

B \(x=\pi/6,5\pi/6\) This does not satisfy the stated relationship.

C \(x=\pi/3,2\pi/3\) 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