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RUN REVIEW · Mathematical Methods · Units 3 & 4 · Tech-active

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11 Sep 2026, 9:15 p.m.

20Serious score
01 A student is checking a worked solution. If \(f(x)=x+2\) and \(g(x)=x^2\), then \((g\circ f)(3)=\)
A 25 f(3)=5, then g(5)=25.
B 7 This does not satisfy the stated relationship.
C 11 This does not satisfy the stated relationship.
D 13 This does not satisfy the stated relationship.

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

02 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

03 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

04 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

05 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

06 During a one-minute revision round: \(\int_0^2 (3x^2+1)\,dx=\)
A 8 This does not satisfy the stated relationship.
B 12 This does not satisfy the stated relationship.
C 10 \([x^3+x]_0^2=10\).
D 9 This does not satisfy the stated relationship.

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

07 Which response best completes this VCE-style item? For X with mean 50 and standard deviation 5, x=60 has z-score
A −2 This does not satisfy the stated relationship.
B 5 This does not satisfy the stated relationship.
C 12 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

08 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

09 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

10 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

11 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

12 Which response best completes this VCE-style item? For \(f(x)=e^{2x}\), \(f^{-1}(x)=\)
A \(e^{x/2}\) This does not satisfy the stated relationship.
B \(2\ln x\) This does not satisfy the stated relationship.
C \(\tfrac12\ln x\) Take ln and divide by 2.
D \(\ln(2x)\) This does not satisfy the stated relationship.

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

13 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

14 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

15 During a one-minute revision round: For \(f(x)=x^2+1\), the tangent gradient at x=3 is
A 10 This does not satisfy the stated relationship.
B 7 This does not satisfy the stated relationship.
C 6 \(f\prime(x)=2x\).
D 3 This does not satisfy the stated relationship.

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

16 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

17 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

18 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

19 A student is checking a worked solution. For \(f(x)=\log(x-4)\), the domain is
A \(({-\infty},4)\) This does not satisfy the stated relationship.
B \((4,\infty)\) The logarithm argument must be positive.
C \([4,\infty)\) This does not satisfy the stated relationship.
D \(\mathbb R\) This does not satisfy the stated relationship.

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

20 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

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