Anonymous Student · guest · Mathematical Methods · Units 3 & 4

01 Which response best completes this VCE-style item? For \(f(x)=2x-1\), \(f^{-1}(x)\) is

A \(2x+1\) This does not satisfy the stated relationship.

B \((x-1)/2\) This does not satisfy the stated relationship.

C \((x+1)/2\) Swap x and y, then solve for y.

D \(1/(2x-1)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Functions · answered at 9464 ms

02 A student is checking a worked solution. A standard normal random variable has mean and variance

A 0 and 0 This does not satisfy the stated relationship.

B 0 and 1 Standardisation produces mean 0 and variance 1.

C 1 and 1 This does not satisfy the stated relationship.

D 1 and 0 This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Normal distribution · answered at 13789 ms

03 Which response best completes this VCE-style item? The expected value of a discrete random variable is

A \(\sqrt{\mathrm{Var}(X)}\) This does not satisfy the stated relationship.

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

C \(\sum P(X=x)\) This does not satisfy the stated relationship.

D \(\sum xP(X=x)\) Expectation is the probability-weighted mean.

Written for icaijy.com · U1–2 · Probability · answered at 23184 ms

04 A student is checking a worked solution. The vertex of \(y=(x-2)^2-5\) is

A \((2,-5)\) Vertex form y=(x−h)²+k has vertex (h,k).

B \((-5,2)\) This does not satisfy the stated relationship.

C \((-2,-5)\) This does not satisfy the stated relationship.

D \((2,5)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Quadratics · answered at 26616 ms

05 Which response best completes this VCE-style item? A solution to \(dy/dt=ky\) has the form

A \(y=Ae^{kt}\) A quantity with rate proportional to itself changes exponentially.

B \(y=Akt\) This does not satisfy the stated relationship.

C \(y=A+k/t\) This does not satisfy the stated relationship.

D \(y=A\sin kt\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Exponentials · answered at 33591 ms

06 During a one-minute revision round: The graph of \(y=f(x-2)+3\) is translated

A 2 right and 3 down This does not satisfy the stated relationship.

B 2 right and 3 up Horizontal translation uses the opposite sign inside.

C 3 right and 2 down This does not satisfy the stated relationship.

D 2 left and 3 up This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Transformations · answered at 36815 ms

07 If \(f(x)=x^3\), then \(f\prime(x)=\)

A \(3x\) This does not satisfy the stated relationship.

B \(x^4/4\) This does not satisfy the stated relationship.

C \(3x^2\) Apply the power rule.

D \(x^2\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Differentiation · answered at 42376 ms

08 During a one-minute revision round: The average rate of change from x=a to x=b is

A \(\frac{f(b)-f(a)}{b-a}\) It is change in output divided by change in input.

B \(f(b)-f(a)\) This does not satisfy the stated relationship.

C \(f(a)+f(b)\) This does not satisfy the stated relationship.

D \(\frac{b-a}{f(b)-f(a)}\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Rates of change · answered at 47720 ms

09 Which response best completes this VCE-style item? For \(X\sim\mathrm{Bin}(n,p)\), \(E(X)=\)

A \(np(1-p)\) This does not satisfy the stated relationship.

B \(n+p\) This does not satisfy the stated relationship.

C \(np\) The binomial mean is np.

D \(p/n\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Binomial distribution · answered at 52678 ms

10 The expected value of a discrete random variable is

A \(\sum P(X=x)\) This does not satisfy the stated relationship.

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

C \(\sum xP(X=x)\) Expectation is the probability-weighted mean.

D \(\sqrt{\mathrm{Var}(X)}\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 55884 ms

11 During a one-minute revision round: The expected value of a discrete random variable is

A \(\sum xP(X=x)\) Expectation is the probability-weighted mean.

B \(\sum P(X=x)\) This does not satisfy the stated relationship.

C \(\sqrt{\mathrm{Var}(X)}\) This does not satisfy the stated relationship.

D \(\max x\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · not answered before time expired