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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 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

02 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 11 This does not satisfy the stated relationship.
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

03 A simulation estimates a probability as 0.37 from 10 000 trials. The expected count is
A 370 This does not satisfy the stated relationship.
B 10 000 This does not satisfy the stated relationship.
C 9630 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

04 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

05 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

06 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

07 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

08 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

09 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

10 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

11 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

12 A student is checking a worked solution. A residual is defined as
A observed value minus predicted value Residual = y−ŷ.
B observed times predicted This does not satisfy the stated relationship.
C predicted minus observed only This does not satisfy the stated relationship.
D gradient minus intercept This does not satisfy the stated relationship.

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

13 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

14 A student is checking a worked solution. $1000 grows by 5% per year for 3 years. Its value is closest to
A $1050.00 This does not satisfy the stated relationship.
B $1150.00 This does not satisfy the stated relationship.
C $1157.63 \(1000(1.05)^3=1157.625\).
D $1250.00 This does not satisfy the stated relationship.

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

15 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

16 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

17 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

18 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

19 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

20 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

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