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RUN REVIEW · Mathematical Methods · Units 1 & 2 · Tech-active

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11 Sep 2026, 9:10 p.m.

20Serious score
01 A student is checking a worked solution. 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

02 During a one-minute revision round: 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 3700 Expected count = trials × probability.
C 9630 This does not satisfy the stated relationship.
D 10 000 This does not satisfy the stated relationship.

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

03 A CAS solves \(x^3-4x=0\). The full solution set is
A \(\{-2,2\}\) This does not satisfy the stated relationship.
B \(\{-4,0,4\}\) This does not satisfy the stated relationship.
C \(\{0,4\}\) 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: 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

05 During a one-minute revision round: 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 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

06 A student is checking a worked solution. 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 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

07 During a one-minute revision round: An arithmetic sequence has \(u_1=4\), common difference 3. Then \(u_{10}=\)
A 34 This does not satisfy the stated relationship.
B 30 This does not satisfy the stated relationship.
C 31 u10=4+9×3=31.
D 27 This does not satisfy the stated relationship.

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

08 A student is checking a worked solution. A correlation coefficient near −1 indicates
A a horizontal residual plot only This does not satisfy the stated relationship.
B strong negative linear association Values near −1 show strong negative linear association.
C weak positive association 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

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

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

10 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 0.40 This does not satisfy the stated relationship.
C 0.25 10 of the 40 sport players also play music.
D 0.10 This does not satisfy the stated relationship.

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

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

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

12 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 \((4,\infty)\) The logarithm argument must be positive.
D \(\mathbb R\) This does not satisfy the stated relationship.

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

13 A student is checking a worked solution. How many x-intercepts does \(y=x^4-5x^2+4\) have?
A 5 This does not satisfy the stated relationship.
B 4 Let u=x²: (u−1)(u−4)=0 gives x=±1,±2.
C 0 This does not satisfy the stated relationship.
D 2 This does not satisfy the stated relationship.

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

14 During a one-minute revision round: 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 0.40 This does not satisfy the stated relationship.
C 0.25 10 of the 40 sport players also play music.
D 0.10 This does not satisfy the stated relationship.

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

15 For X taking 0,1,2 with probabilities 0.2,0.5,0.3, \(E(X)=\)
A 0.8 This does not satisfy the stated relationship.
B 1.5 This does not satisfy the stated relationship.
C 1.0 This does not satisfy the stated relationship.
D 1.1 0×0.2+1×0.5+2×0.3=1.1.

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

16 A correlation coefficient near −1 indicates
A a horizontal residual plot only This does not satisfy the stated relationship.
B strong negative linear association Values near −1 show strong negative linear association.
C weak positive association 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

17 Which response best completes this VCE-style item? A correlation coefficient near −1 indicates
A a horizontal residual plot only This does not satisfy the stated relationship.
B weak positive association This does not satisfy the stated relationship.
C causation This does not satisfy the stated relationship.
D strong negative linear association Values near −1 show strong negative linear association.

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

18 During a one-minute revision round: Solve \(2^x=10\), correct to two decimal places.
A 5.00 This does not satisfy the stated relationship.
B 2.30 This does not satisfy the stated relationship.
C 3.32 \(x=\log_2 10\approx3.32\).
D 10.00 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Exponentials · 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 6 \(f\prime(x)=2x\).
B 7 This does not satisfy the stated relationship.
C 3 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

20 A student is checking a worked solution. A simulation estimates a probability as 0.37 from 10 000 trials. The expected count is
A 9630 This does not satisfy the stated relationship.
B 3700 Expected count = trials × probability.
C 10 000 This does not satisfy the stated relationship.
D 370 This does not satisfy the stated relationship.

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

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