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

That y8 kid 🤣 - bot · guest

11 Sep 2026, 9:15 p.m.

20Serious score
01 During a one-minute revision round: The graphs \(y=x^2\) and \(y=2x+3\) intersect at x-values
A \(x=1,3\) This does not satisfy the stated relationship.
B \(x=-3,1\) This does not satisfy the stated relationship.
C \(x=-1,3\) Solve x²−2x−3=0.
D \(x=0,2\) This does not satisfy the stated relationship.

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

02 Which response best completes this VCE-style item? 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 round all coefficients This does not satisfy the stated relationship.
C conclude none exist This does not satisfy the stated relationship.
D delete the function This does not satisfy the stated relationship.

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

03 Which response best completes this VCE-style item? How many x-intercepts does \(y=x^4-5x^2+4\) have?
A 4 Let u=x²: (u−1)(u−4)=0 gives x=±1,±2.
B 2 This does not satisfy the stated relationship.
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

04 Solve \(2^x=10\), correct to two decimal places.
A 2.30 This does not satisfy the stated relationship.
B 10.00 This does not satisfy the stated relationship.
C 5.00 This does not satisfy the stated relationship.
D 3.32 \(x=\log_2 10\approx3.32\).

Written for icaijy.com · U1–2 · Exponentials · 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 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

07 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

08 Which response best completes this VCE-style item? For \(f(x)=\log(x-4)\), the domain is
A \([4,\infty)\) This does not satisfy the stated relationship.
B \(\mathbb R\) This does not satisfy the stated relationship.
C \(({-\infty},4)\) 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

09 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

10 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

11 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

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

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

13 The area between \(y=x\) and the x-axis from 0 to 4 is
A 4 This does not satisfy the stated relationship.
B 16 This does not satisfy the stated relationship.
C 32 This does not satisfy the stated relationship.
D 8 \(\int_0^4x\,dx=8\).

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

14 A student is checking a worked solution. 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 local minimum at x=2 This does not satisfy the stated relationship.
C local maximum at x=2 Increasing then decreasing gives a local maximum.
D point of inflection necessarily This does not satisfy the stated relationship.

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

15 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

16 The graphs \(y=x^2\) and \(y=2x+3\) intersect at x-values
A \(x=0,2\) This does not satisfy the stated relationship.
B \(x=-1,3\) Solve x²−2x−3=0.
C \(x=1,3\) This does not satisfy the stated relationship.
D \(x=-3,1\) This does not satisfy the stated relationship.

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

17 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

18 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

19 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

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

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

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