That y8 kid 🤣 - bot · guest · Mathematical Methods · Units 3 & 4

01 During a one-minute revision round: For $f(x)=e^{2x}$, $f^{-1}(x)=$

A $2\ln x$ This does not satisfy the stated relationship.

B $\tfrac12\ln x$ Take ln and divide by 2.

C $e^{x/2}$ This does not satisfy the stated relationship.

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

Written for icaijy.com · U3–4 · Inverse functions · answered at 100 ms

02 A student is checking a worked solution. If $P(A)=0.6$, $P(B)=0.5$, $P(A\cap B)=0.3$, A and B are

A mutually exclusive This does not satisfy the stated relationship.

B complements This does not satisfy the stated relationship.

C independent 0.6×0.5=0.3.

D impossible This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Probability · answered at 100 ms

03 If $P(A)=0.6$, $P(B)=0.5$, $P(A\cap B)=0.3$, A and B are

A impossible This does not satisfy the stated relationship.

B independent 0.6×0.5=0.3.

C complements This does not satisfy the stated relationship.

D mutually exclusive This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Probability · answered at 100 ms

04 A student is checking a worked solution. The graphs $y=x^2$ and $y=2x+3$ intersect at x-values

A $x=-1,3$ Solve x²−2x−3=0.

B $x=0,2$ This does not satisfy the stated relationship.

C $x=-3,1$ This does not satisfy the stated relationship.

D $x=1,3$ This does not satisfy the stated relationship.

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

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

A $e^{x/2}$ This does not satisfy the stated relationship.

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

C $\tfrac12\ln x$ Take ln and divide by 2.

D $2\ln x$ This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Inverse functions · answered at 100 ms

06 Which response best completes this VCE-style item? The area between $y=x$ and the x-axis from 0 to 4 is

A 32 This does not satisfy the stated relationship.

B 8 $\int_0^4x\,dx=8$.

C 16 This does not satisfy the stated relationship.

D 4 This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Area · answered at 100 ms

07 Which response best completes this VCE-style item? $1000 grows by 5% per year for 3 years. Its value is closest to

A $1250.00 This does not satisfy the stated relationship.

B $1050.00 This does not satisfy the stated relationship.

C $1150.00 This does not satisfy the stated relationship.

D $1157.63 $1000(1.05)^3=1157.625$.

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

08 A CAS returns a decimal root but the question requests an exact value. The best response is to

A use an exact solve command or algebraic form Exact form is required when requested.

B round to one decimal place This does not satisfy the stated relationship.

C change the equation This does not satisfy the stated relationship.

D omit the root This does not satisfy the stated relationship.

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

09 Which response best completes this VCE-style item? An arithmetic sequence has $u_1=4$, common difference 3. Then $u_{10}=$

A 30 This does not satisfy the stated relationship.

B 27 This does not satisfy the stated relationship.

C 31 u10=4+9×3=31.

D 34 This does not satisfy the stated relationship.

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

10 For $X\sim\mathrm{Bin}(10,0.5)$, $P(X=0)=$

A $10/1024$ This does not satisfy the stated relationship.

B $1/1024$ $(0.5)^{10}=1/1024$.

C $1/2$ This does not satisfy the stated relationship.

D $1/10$ This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Binomial probability · answered at 100 ms

11 Which response best completes this VCE-style item? If $f(x)=x+2$ and $g(x)=x^2$, then $(g\circ f)(3)=$

A 11 This does not satisfy the stated relationship.

B 13 This does not satisfy the stated relationship.

C 25 f(3)=5, then g(5)=25.

D 7 This does not satisfy the stated relationship.

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

12 A student is checking a worked solution. A derivative changes from positive to negative at x=2. The function has a

A vertical asymptote at x=2 This does not satisfy the stated relationship.

B local minimum at x=2 This does not satisfy the stated relationship.

C local maximum at x=2 Increasing then decreasing gives a local maximum.

D point of inflection necessarily This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Numerical modelling · answered at 100 ms

13 A student is checking a worked solution. A sample proportion is 0.40 and margin of error is 0.05. The interval is

A $(0.35,0.45)$ Add and subtract the margin of error.

B $(0.30,0.50)$ This does not satisfy the stated relationship.

C $(0.05,0.40)$ This does not satisfy the stated relationship.

D $(0.40,0.45)$ This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Confidence intervals · answered at 100 ms

14 Which response best completes this VCE-style item? For X taking 0,1,2 with probabilities 0.2,0.5,0.3, $E(X)=$

A 1.5 This does not satisfy the stated relationship.

B 1.1 0×0.2+1×0.5+2×0.3=1.1.

C 1.0 This does not satisfy the stated relationship.

D 0.8 This does not satisfy the stated relationship.

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

15 Which response best completes this VCE-style item? A CAS solves $x^3-4x=0$. The full solution set is

A $\{-2,0,2\}$ Factor x(x−2)(x+2).

B $\{-4,0,4\}$ This does not satisfy the stated relationship.

C $\{0,4\}$ This does not satisfy the stated relationship.

D $\{-2,2\}$ This does not satisfy the stated relationship.

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

16 During a one-minute revision round: A sample proportion is 0.40 and margin of error is 0.05. The interval is

A $(0.05,0.40)$ This does not satisfy the stated relationship.

B $(0.35,0.45)$ Add and subtract the margin of error.

C $(0.30,0.50)$ This does not satisfy the stated relationship.

D $(0.40,0.45)$ This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Confidence intervals · answered at 100 ms

17 Which response best completes this VCE-style item? On $[0,2\pi]$, $\sin x=1/2$ at

A $5\pi/6,11\pi/6$ This does not satisfy the stated relationship.

B $\pi/3,2\pi/3$ This does not satisfy the stated relationship.

C $\pi/6,5\pi/6$ Sine is positive in quadrants I and II.

D $\pi/6,7\pi/6$ This does not satisfy the stated relationship.

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

18 The graphs $y=x^2$ and $y=2x+3$ intersect at x-values

A $x=0,2$ This does not satisfy the stated relationship.

B $x=-1,3$ Solve x²−2x−3=0.

C $x=1,3$ This does not satisfy the stated relationship.

D $x=-3,1$ This does not satisfy the stated relationship.

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

19 During a one-minute revision round: If $f(x)=x+2$ and $g(x)=x^2$, then $(g\circ f)(3)=$

A 11 This does not satisfy the stated relationship.

B 25 f(3)=5, then g(5)=25.

C 13 This does not satisfy the stated relationship.

D 7 This does not satisfy the stated relationship.

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

20 The maximum of $f(x)=-x^2+6x+1$ is

A 19 This does not satisfy the stated relationship.

B 10 The vertex occurs at x=3, giving f(3)=10.

C 1 This does not satisfy the stated relationship.

D 7 This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Optimisation · answered at 100 ms