elephgant · guest · Mathematical Methods · Units 3 & 4

01 Which response best completes this VCE-style item? The average rate of change from x=a to x=b is

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

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

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

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

Written for icaijy.com · U1–2 · Rates of change · answered at 2425 ms

02 A student is checking a worked solution. If \(y=(3x+1)^5\), then \(dy/dx=\)

A \(5(3x+1)^4\) This does not satisfy the stated relationship.

B \(15(3x+1)^5\) This does not satisfy the stated relationship.

C \(15(3x+1)^4\) Differentiate the outside and multiply by the inner derivative.

D \((3x+1)^4\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Chain rule · answered at 7936 ms

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

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

Written for icaijy.com · U1–2 · Probability · answered at 11720 ms

04 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 14445 ms

05 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 18919 ms

06 Which response best completes this VCE-style item? For \(a>1\), \(y=a^x\) is

A strictly decreasing This does not satisfy the stated relationship.

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

C periodic This does not satisfy the stated relationship.

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

Written for icaijy.com · U1–2 · Exponentials · answered at 27618 ms

07 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 \([3,\infty)\) The radicand requires x−3 ≥ 0.

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

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

Written for icaijy.com · U1–2 · Functions · answered at 32602 ms

08 A student is checking a worked solution. The solution of \(|x|<3\) is

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

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

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

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

Written for icaijy.com · U1–2 · Algebra · answered at 39244 ms

09 Which response best completes this VCE-style item? A standard normal random variable has mean and variance

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

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

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

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

Written for icaijy.com · U3–4 · Normal distribution · answered at 47320 ms

10 For \(X\sim\mathrm{Bin}(n,p)\), \(E(X)=\)

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

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

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

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

Written for icaijy.com · U3–4 · Binomial distribution · answered at 49754 ms

11 For \(a>1\), \(y=a^x\) is

A periodic This does not satisfy the stated relationship.

B strictly decreasing This does not satisfy the stated relationship.

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

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

Written for icaijy.com · U1–2 · Exponentials · answered at 51693 ms

12 During a one-minute revision round: \(\log_a(xy)\) 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 \(x+y\) This does not satisfy the stated relationship.

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

Written for icaijy.com · U1–2 · Logarithms · answered at 53864 ms

13 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 \(3x\) This does not satisfy the stated relationship.

C \(x^2\) 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 56569 ms

14 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 · answered at 59660 ms

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

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

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

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

D \(\pi\) Period is 2π/2 = π.

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