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

01 During a one-minute revision round: The plane \(2x-y+2z=6\) has normal vector

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

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

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

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

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

02 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

03 Which response best completes this VCE-style item? If \(v(t)=3t^2\) and \(s(0)=2\), then \(s(t)=\)

A \(6t+2\) This does not satisfy the stated relationship.

B \(3t^3+2\) This does not satisfy the stated relationship.

C \(t^3+2\) Integrate velocity and apply the initial position.

D \(t^3\) This does not satisfy the stated relationship.

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

04 Which response best completes this VCE-style item? \(\binom{8}{2}=\)

A 64 This does not satisfy the stated relationship.

B 16 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

05 A student is checking a worked solution. An estimate 20 has margin of error 3. The interval is

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

B \((14,26)\) This does not satisfy the stated relationship.

C \((3,20)\) 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

06 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 5 N This does not satisfy the stated relationship.

D 1.5 N This does not satisfy the stated relationship.

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

07 If \(\sigma=12\) and \(n=36\), the standard error is

A 6 This does not satisfy the stated relationship.

B 0.33 This does not satisfy the stated relationship.

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

D 72 This does not satisfy the stated relationship.

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

08 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

09 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

10 During a one-minute revision round: If \(\sigma=12\) and \(n=36\), the standard error is

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

B 0.33 This does not satisfy the stated relationship.

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

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

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

12 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

13 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

14 Solve \(dy/dx=2y\), \(y(0)=3\).

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

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

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

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

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

15 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

16 Which response best completes this VCE-style item? A matrix inverse command fails because det(A)=0. This means A is

A orthogonal This does not satisfy the stated relationship.

B the identity This does not satisfy the stated relationship.

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

D singular Zero determinant means no inverse.

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

17 Which response best completes this VCE-style item? Solve \(dy/dx=2y\), \(y(0)=3\).

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

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

18 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

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 \((1,0,0)\times(0,1,0)=\)

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

B \((0,0,1)\) The standard basis vectors satisfy i×j=k.

C \((0,0,-1)\) This does not satisfy the stated relationship.

D \((1,1,0)\) This does not satisfy the stated relationship.

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