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

01 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

02 A residual is defined as

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

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

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

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

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

03 Which response best completes this VCE-style item? 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 impossible This does not satisfy the stated relationship.

D independent 0.6×0.5=0.3.

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

04 How many x-intercepts does \(y=x^4-5x^2+4\) have?

A 5 This does not satisfy the stated relationship.

B 0 This does not satisfy the stated relationship.

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

D 2 This does not satisfy the stated relationship.

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

05 A student is checking a worked solution. Solve \(2^x=10\), correct to two decimal places.

A 3.32 \(x=\log_2 10\approx3.32\).

B 10.00 This does not satisfy the stated relationship.

C 2.30 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

06 During a one-minute revision round: 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 point of inflection necessarily This does not satisfy the stated relationship.

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

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

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

07 A student is checking a worked solution. \(\int_0^2 (3x^2+1)\,dx=\)

A 10 \([x^3+x]_0^2=10\).

B 12 This does not satisfy the stated relationship.

C 9 This does not satisfy the stated relationship.

D 8 This does not satisfy the stated relationship.

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

08 A graphing window hides all turning points. The sound next step is to

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

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

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

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

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

09 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

10 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

11 During a one-minute revision round: How many x-intercepts does \(y=x^4-5x^2+4\) have?

A 2 This does not satisfy the stated relationship.

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

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

12 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

13 A student is checking a worked solution. For X with mean 50 and standard deviation 5, x=60 has z-score

A 5 This does not satisfy the stated relationship.

B 12 This does not satisfy the stated relationship.

C −2 This does not satisfy the stated relationship.

D 2 \(z=(60-50)/5=2\).

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

14 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

15 A correlation coefficient near −1 indicates

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

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

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

D causation This does not satisfy the stated relationship.

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

16 During a one-minute revision round: For \(X\sim\mathrm{Bin}(10,0.5)\), \(P(X=0)=\)

A \(1/10\) This does not satisfy the stated relationship.

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

C \(10/1024\) This does not satisfy the stated relationship.

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

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

17 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

18 During a one-minute revision round: 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 1 This does not satisfy the stated relationship.

D 19 This does not satisfy the stated relationship.

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

19 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

20 In a sample, 40 of 100 students play sport and 10 play sport and music. \(P(\text{music}\mid\text{sport})=\)

A 0.10 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 0.50 This does not satisfy the stated relationship.

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