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

01 During a one-minute revision round: The area between $y=x$ and the x-axis from 0 to 4 is

A 4 This does not satisfy the stated relationship.

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

C 32 This does not satisfy the stated relationship.

D 16 This does not satisfy the stated relationship.

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

02 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

03 Which response best completes this VCE-style item? How many x-intercepts does $y=x^4-5x^2+4$ have?

A 4 Let u=x²: (u−1)(u−4)=0 gives x=±1,±2.

B 2 This does not satisfy the stated relationship.

C 5 This does not satisfy the stated relationship.

D 0 This does not satisfy the stated relationship.

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

04 A CAS solves $x^3-4x=0$. The full solution set is

A $\{-2,0,2\}$ Factor x(x−2)(x+2).

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

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

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

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

05 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

06 Which response best completes this VCE-style item? 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

07 A student is checking a worked solution. A simulation estimates a probability as 0.37 from 10 000 trials. The expected count is

A 10 000 This does not satisfy the stated relationship.

B 3700 Expected count = trials × probability.

C 370 This does not satisfy the stated relationship.

D 9630 This does not satisfy the stated relationship.

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

08 During a one-minute revision round: Solve $2^x=10$, correct to two decimal places.

A 2.30 This does not satisfy the stated relationship.

B 3.32 $x=\log_2 10\approx3.32$.

C 10.00 This does not satisfy the stated relationship.

D 5.00 This does not satisfy the stated relationship.

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

09 Which response best completes this VCE-style item? A simulation estimates a probability as 0.37 from 10 000 trials. The expected count is

A 10 000 This does not satisfy the stated relationship.

B 9630 This does not satisfy the stated relationship.

C 370 This does not satisfy the stated relationship.

D 3700 Expected count = trials × probability.

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

10 A student is checking a worked solution. A graphing window hides all turning points. The sound next step is to

A conclude none exist This does not satisfy the stated relationship.

B delete the function This does not satisfy the stated relationship.

C round all coefficients This does not satisfy the stated relationship.

D determine a suitable domain/range analytically or with zoom Window settings are not mathematical evidence.

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

11 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 $(0.05,0.40)$ This does not satisfy the stated relationship.

C $(0.40,0.45)$ 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

12 During a one-minute revision round: A correlation coefficient near −1 indicates

A strong negative linear association Values near −1 show strong negative linear association.

B weak positive association This does not satisfy the stated relationship.

C a horizontal residual plot only This does not satisfy the stated relationship.

D causation This does not satisfy the stated relationship.

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

13 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

14 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

15 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

16 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

17 $1000 grows by 5% per year for 3 years. Its value is closest to

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

B $1050.00 This does not satisfy the stated relationship.

C $1150.00 This does not satisfy the stated relationship.

D $1250.00 This does not satisfy the stated relationship.

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

18 For $f(x)=e^{2x}$, $f^{-1}(x)=$

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

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

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

19 Which response best completes this VCE-style item? For $f(x)=x^2+1$, the tangent gradient at x=3 is

A 7 This does not satisfy the stated relationship.

B 10 This does not satisfy the stated relationship.

C 3 This does not satisfy the stated relationship.

D 6 $f\prime(x)=2x$.

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

20 During a one-minute revision round: For X with mean 50 and standard deviation 5, x=60 has z-score

A −2 This does not satisfy the stated relationship.

B 2 $z=(60-50)/5=2$.

C 5 This does not satisfy the stated relationship.

D 12 This does not satisfy the stated relationship.

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