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

01 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 100 ms

02 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

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 \(\log_a(xy)\) 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

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 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 100 ms

06 During a one-minute revision round: If \(f(x)=x^3\), then \(f\prime(x)=\)

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

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

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

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

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

07 The period of \(\sin(2x)\) is

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

B \(\pi\) Period is 2π/2 = π.

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

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

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

08 Which response best completes this VCE-style item? 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 · answered at 100 ms

09 For events A and B, \(P(A\cup B)=\)

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

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

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

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

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

10 A student is checking a worked solution. 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 \(f(b)-f(a)\) This does not satisfy the stated relationship.

C \(f(a)+f(b)\) 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

11 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

12 During a one-minute revision round: 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

13 A student is checking a worked solution. The period of \(\sin(2x)\) is

A \(\pi\) Period is 2π/2 = π.

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

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

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

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

14 Which response best completes this VCE-style item? The graph of \(y=f(x-2)+3\) is translated

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

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

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

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

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

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

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

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

C \([-3,3]\) 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

16 A student is checking a worked solution. 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 100 ms

17 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

18 Which response best completes this VCE-style item? 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 \(\frac{f(b)-f(a)}{b-a}\) 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 \(f(b)-f(a)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Rates of change · answered at 100 ms

19 A student is checking a worked solution. For \(f(x)=2x-1\), \(f^{-1}(x)\) is

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

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

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

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

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

20 The domain of \(f(x)=\sqrt{x-3}\) is

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

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

C \((3,\infty)\) 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