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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 During a one-minute revision round: If \(P(A)=0.6\), \(P(B)=0.5\), \(P(A\cap B)=0.3\), A and B are
A independent 0.6×0.5=0.3.
B complements This does not satisfy the stated relationship.
C impossible 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

02 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

03 During a one-minute revision round: A CAS solves \(x^3-4x=0\). The full solution set is
A \(\{0,4\}\) This does not satisfy the stated relationship.
B \(\{-4,0,4\}\) This does not satisfy the stated relationship.
C \(\{-2,2\}\) This does not satisfy the stated relationship.
D \(\{-2,0,2\}\) Factor x(x−2)(x+2).

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

04 During a one-minute revision round: An arithmetic sequence has \(u_1=4\), common difference 3. Then \(u_{10}=\)
A 27 This does not satisfy the stated relationship.
B 30 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

05 On \([0,2\pi]\), \(\sin x=1/2\) at
A \(\pi/6,5\pi/6\) Sine is positive in quadrants I and II.
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 \(\pi/3,2\pi/3\) This does not satisfy the stated relationship.

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

06 Which response best completes this VCE-style item? The maximum of \(f(x)=-x^2+6x+1\) is
A 10 The vertex occurs at x=3, giving f(3)=10.
B 19 This does not satisfy the stated relationship.
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

07 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

08 During a one-minute revision round: For X taking 0,1,2 with probabilities 0.2,0.5,0.3, \(E(X)=\)
A 1.1 0×0.2+1×0.5+2×0.3=1.1.
B 0.8 This does not satisfy the stated relationship.
C 1.5 This does not satisfy the stated relationship.
D 1.0 This does not satisfy the stated relationship.

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

09 Which response best completes this VCE-style item? 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 0.10 This does not satisfy the stated relationship.
C 0.40 This does not satisfy the stated relationship.
D 0.25 10 of the 40 sport players also play music.

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

10 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

11 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

12 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

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 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

15 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

16 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

17 Which response best completes this VCE-style item? A derivative changes from positive to negative at x=2. The function has a
A local minimum at x=2 This does not satisfy the stated relationship.
B point of inflection necessarily This does not satisfy the stated relationship.
C local maximum at x=2 Increasing then decreasing gives a local maximum.
D vertical asymptote at x=2 This does not satisfy the stated relationship.

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

18 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

19 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

20 A student is checking a worked solution. For \(f(x)=x^2+1\), the tangent gradient at x=3 is
A 6 \(f\prime(x)=2x\).
B 3 This does not satisfy the stated relationship.
C 7 This does not satisfy the stated relationship.
D 10 This does not satisfy the stated relationship.

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

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