Albert · guest · Mathematical Methods · Units 1 & 2

01 Which response best completes this VCE-style item? 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 \(\max x\) This does not satisfy the stated relationship.

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

Written for icaijy.com · U1–2 · Probability · answered at 2042 ms

02 Which response best completes this VCE-style item? The vertex of \(y=(x-2)^2-5\) is

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

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

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

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

Written for icaijy.com · U1–2 · Quadratics · answered at 5940 ms

03 During a one-minute revision round: The period of \(\sin(2x)\) is

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

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

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

D \(\pi\) Period is 2π/2 = π.

Written for icaijy.com · U1–2 · Trigonometry · answered at 9763 ms

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

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

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

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

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

Written for icaijy.com · U1–2 · Rates of change · answered at 12793 ms

05 If A and B are independent, then

A \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.

B \(P(A\cap B)=0\) This does not satisfy the stated relationship.

C \(P(A)=P(B)\) This does not satisfy the stated relationship.

D \(P(A\mid B)=0\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 14827 ms

06 During a one-minute revision round: For events A and B, \(P(A\cup B)=\)

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

B \(P(A)+P(B)-P(A\cap B)\) Subtract the intersection counted twice.

C \(P(A)P(B)\) This does not satisfy the stated relationship.

D \(P(A)+P(B)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 17795 ms

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

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

B \(\sum P(X=x)\) 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 21272 ms

08 Which response best completes this VCE-style item? If \(f(x)=x^3\), then \(f\prime(x)=\)

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

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

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

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

Written for icaijy.com · U1–2 · Differentiation · answered at 24771 ms

09 A student is checking a worked solution. The graph of \(y=f(x-2)+3\) is translated

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

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

C 2 right and 3 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 28405 ms

10 Which response best completes this VCE-style item? \(\sin^2x+\cos^2x\) equals

A 1 This is the Pythagorean identity.

B 0 This does not satisfy the stated relationship.

C \(\sin 2x\) This does not satisfy the stated relationship.

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

Written for icaijy.com · U1–2 · Trigonometry · answered at 30451 ms

11 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 33544 ms

12 A student is checking a worked solution. \(\sin^2x+\cos^2x\) equals

A 0 This does not satisfy the stated relationship.

B \(\sin 2x\) This does not satisfy the stated relationship.

C \(\tan x\) This does not satisfy the stated relationship.

D 1 This is the Pythagorean identity.

Written for icaijy.com · U1–2 · Trigonometry · answered at 36065 ms

13 During a one-minute revision round: If A and B are independent, then

A \(P(A\cap B)=0\) This does not satisfy the stated relationship.

B \(P(A\mid B)=0\) This does not satisfy the stated relationship.

C \(P(A)=P(B)\) This does not satisfy the stated relationship.

D \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.

Written for icaijy.com · U1–2 · Probability · answered at 39274 ms

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

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

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

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

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

Written for icaijy.com · U1–2 · Functions · answered at 51061 ms

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

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

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

Written for icaijy.com · U1–2 · Transformations · answered at 55934 ms

16 A student is checking a worked solution. If A and B are independent, then

A \(P(A\mid B)=0\) This does not satisfy the stated relationship.

B \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.

C \(P(A)=P(B)\) This does not satisfy the stated relationship.

D \(P(A\cap B)=0\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 58604 ms

17 Which response best completes this VCE-style item? For events A and B, \(P(A\cup B)=\)

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

B \(P(A)+P(B)-P(A\cap B)\) Subtract the intersection counted twice.

C \(1-P(A)\) This does not satisfy the stated relationship.

D \(P(A)+P(B)\) This does not satisfy the stated relationship.

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