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

01 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

02 For $f(x)=\log(x-4)$, the domain is

A $[4,\infty)$ This does not satisfy the stated relationship.

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

C $\mathbb R$ This does not satisfy the stated relationship.

D $(4,\infty)$ The logarithm argument must be positive.

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

03 A student is checking a worked solution. The area between $y=x$ and the x-axis from 0 to 4 is

A 4 This does not satisfy the stated relationship.

B 32 This does not satisfy the stated relationship.

C 16 This does not satisfy the stated relationship.

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

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

04 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

05 Which response best completes this VCE-style item? For $X\sim\mathrm{Bin}(10,0.5)$, $P(X=0)=$

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

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

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

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

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

06 During a one-minute revision round: $1000 grows by 5% per year for 3 years. Its value is closest to

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

B $1150.00 This does not satisfy the stated relationship.

C $1250.00 This does not satisfy the stated relationship.

D $1050.00 This does not satisfy the stated relationship.

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

07 A student is checking a worked solution. The maximum of $f(x)=-x^2+6x+1$ is

A 7 This does not satisfy the stated relationship.

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

C 19 This does not satisfy the stated relationship.

D 1 This does not satisfy the stated relationship.

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

08 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

09 A student is checking a worked solution. 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

10 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

11 During a one-minute revision round: In a sample, 40 of 100 students play sport and 10 play sport and music. $P(\text{music}\mid\text{sport})=$

A 0.50 This does not satisfy the stated relationship.

B 0.40 This does not satisfy the stated relationship.

C 0.25 10 of the 40 sport players also play music.

D 0.10 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Two-way tables · answered at 100 ms

12 During a one-minute revision round: A CAS returns a decimal root but the question requests an exact value. The best response is to

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

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

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

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

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

13 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

14 A student is checking a worked solution. On $[0,2\pi]$, $\sin x=1/2$ at

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

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

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

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

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

15 During a one-minute revision round: On $[0,2\pi]$, $\sin x=1/2$ at

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

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

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

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

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

16 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

17 A student is checking a worked solution. 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 change the equation This does not satisfy the stated relationship.

C round to one decimal place 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

18 Which response best completes this VCE-style item? 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 $(0.40,0.45)$ This does not satisfy the stated relationship.

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

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

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

19 Which response best completes this VCE-style item? A residual is defined as

A observed value minus predicted value Residual = y−ŷ.

B predicted minus observed only This does not satisfy the stated relationship.

C gradient minus intercept This does not satisfy the stated relationship.

D observed times predicted This does not satisfy the stated relationship.

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

20 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