That y8 kid 🤣 - bot · guest · Mathematical Methods · Units 1 & 2

01 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 100 ms

02 \(\log_a(xy)\) equals

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

B \(\log_a x+\log_a y\) The logarithm of a product is a sum.

C \(\log_a(x+y)\) This does not satisfy the stated relationship.

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

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

03 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 100 ms

04 A student is checking a worked solution. If \(P(3)=0\), then a factor of \(P(x)\) is

A \(x-3\) The factor theorem gives x−3.

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

C \(3x-1\) This does not satisfy the stated relationship.

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

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

05 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 · answered at 100 ms

06 If \(P(3)=0\), then a factor of \(P(x)\) is

A \(3x-1\) This does not satisfy the stated relationship.

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

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

D \(x-3\) The factor theorem gives x−3.

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

07 A student is checking a worked solution. For events A and B, \(P(A\cup B)=\)

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

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

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

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

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

08 Which response best completes this VCE-style item? If \(P(3)=0\), then a factor of \(P(x)\) is

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

B \(x-3\) The factor theorem gives x−3.

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

D \(3x-1\) This does not satisfy the stated relationship.

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

09 Which response best completes this VCE-style item? At a stationary point of a differentiable function

A \(f(x)=1\) This does not satisfy the stated relationship.

B \(f\prime\prime(x)=0\) always This does not satisfy the stated relationship.

C \(f\prime(x)=0\) The tangent gradient is zero.

D \(f(x)=0\) This does not satisfy the stated relationship.

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

10 The vertex of \(y=(x-2)^2-5\) is

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

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

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

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

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

11 Which response best completes this VCE-style item? If A and B are independent, then

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

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

C \(P(A\cap B)=0\) 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 100 ms

12 The solution of \(|x|<3\) is

A \((-3,3)\) Distance from zero must be less than three.

B \([-3,3]\) This does not satisfy the stated relationship.

C \(({-\infty},-3)\cup(3,\infty)\) This does not satisfy the stated relationship.

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

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

13 Which response best completes this VCE-style item? The solution of \(|x|<3\) is

A \([-3,3]\) This does not satisfy the stated relationship.

B \((-3,3)\) Distance from zero must be less than three.

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

D \(({-\infty},-3)\cup(3,\infty)\) This does not satisfy the stated relationship.

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

14 During a one-minute revision round: The domain of \(f(x)=\sqrt{x-3}\) is

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

B \((3,\infty)\) This does not satisfy the stated relationship.

C \(({-\infty},3]\) This does not satisfy the stated relationship.

D \([3,\infty)\) The radicand requires x−3 ≥ 0.

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

15 A student is checking a worked solution. For \(a>1\), \(y=a^x\) is

A periodic This does not satisfy the stated relationship.

B strictly increasing An exponential with base greater than one increases.

C undefined at x=0 This does not satisfy the stated relationship.

D strictly decreasing This does not satisfy the stated relationship.

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

16 During a one-minute revision round: The solution of \(|x|<3\) is

A \([-3,3]\) This does not satisfy the stated relationship.

B \(({-\infty},-3)\cup(3,\infty)\) This does not satisfy the stated relationship.

C \((-3,3)\) Distance from zero must be less than three.

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

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

17 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 100 ms

18 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 100 ms

19 The average rate of change from x=a to x=b is

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

B \(\frac{b-a}{f(b)-f(a)}\) 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 100 ms

20 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 100 ms