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

That y8 kid 🤣 - bot · guest

11 Sep 2026, 9:12 p.m.

20Serious score
01 During a one-minute revision round: At a stationary point of a differentiable function
A \(f\prime\prime(x)=0\) always This does not satisfy the stated relationship.
B \(f(x)=0\) This does not satisfy the stated relationship.
C \(f\prime(x)=0\) The tangent gradient is zero.
D \(f(x)=1\) This does not satisfy the stated relationship.

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

02 Which response best completes this VCE-style item? At a stationary point of a differentiable function
A \(f\prime\prime(x)=0\) always This does not satisfy the stated relationship.
B \(f(x)=0\) This does not satisfy the stated relationship.
C \(f\prime(x)=0\) The tangent gradient is zero.
D \(f(x)=1\) This does not satisfy the stated relationship.

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

03 If \(y=(3x+1)^5\), then \(dy/dx=\)
A \(15(3x+1)^4\) Differentiate the outside and multiply by the inner derivative.
B \(15(3x+1)^5\) This does not satisfy the stated relationship.
C \((3x+1)^4\) This does not satisfy the stated relationship.
D \(5(3x+1)^4\) This does not satisfy the stated relationship.

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

04 During a one-minute revision round: \(P(A\mid B)=\)
A \(\frac{P(A)}{P(B)}\) This does not satisfy the stated relationship.
B \(P(A\cup B)\) This does not satisfy the stated relationship.
C \(P(A)P(B)\) always This does not satisfy the stated relationship.
D \(\frac{P(A\cap B)}{P(B)}\) Restrict the sample space to B.

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

05 A student is checking a worked solution. Increasing sample size while all else is fixed makes a confidence interval generally
A wider This does not satisfy the stated relationship.
B narrower Standard error decreases as sample size grows.
C unchanged This does not satisfy the stated relationship.
D centred at zero This does not satisfy the stated relationship.

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

06 A student is checking a worked solution. For events A and B, \(P(A\cup B)=\)
A \(1-P(A)\) This does not satisfy the stated relationship.
B \(P(A)+P(B)-P(A\cap B)\) Subtract the intersection counted twice.
C \(P(A)P(B)\) This does not satisfy the stated relationship.
D \(P(A)+P(B)\) This does not satisfy the stated relationship.

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

07 The expected value of a discrete random variable is
A \(\sum P(X=x)\) This does not satisfy the stated relationship.
B \(\max x\) This does not satisfy the stated relationship.
C \(\sum xP(X=x)\) Expectation is the probability-weighted mean.
D \(\sqrt{\mathrm{Var}(X)}\) This does not satisfy the stated relationship.

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

08 Which response best completes this VCE-style item? \(\int 3x^2\,dx=\)
A \(x^3\) This does not satisfy the stated relationship.
B \(x^3+C\) Reverse the power rule and include C.
C \(3x^3+C\) This does not satisfy the stated relationship.
D \(6x+C\) This does not satisfy the stated relationship.

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

09 For \(f(x)=2x-1\), \(f^{-1}(x)\) is
A \(1/(2x-1)\) This does not satisfy the stated relationship.
B \((x+1)/2\) Swap x and y, then solve for y.
C \(2x+1\) This does not satisfy the stated relationship.
D \((x-1)/2\) This does not satisfy the stated relationship.

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

10 The average rate of change from x=a to x=b is
A \(f(b)-f(a)\) This does not satisfy the stated relationship.
B \(\frac{f(b)-f(a)}{b-a}\) It is change in output divided by change in input.
C \(\frac{b-a}{f(b)-f(a)}\) This does not satisfy the stated relationship.
D \(f(a)+f(b)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Rates of change · answered at 100 ms

11 During a one-minute revision round: \(\sin^2x+\cos^2x\) equals
A 0 This does not satisfy the stated relationship.
B 1 This is the Pythagorean identity.
C \(\tan x\) This does not satisfy the stated relationship.
D \(\sin 2x\) This does not satisfy the stated relationship.

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

12 A student is checking a worked solution. \(\sin^2x+\cos^2x\) equals
A \(\tan x\) This does not satisfy the stated relationship.
B 1 This is the Pythagorean identity.
C 0 This does not satisfy the stated relationship.
D \(\sin 2x\) This does not satisfy the stated relationship.

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

13 A student is checking a worked solution. If A and B are independent, then
A \(P(A\mid B)=0\) This does not satisfy the stated relationship.
B \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.
C \(P(A)=P(B)\) This does not satisfy the stated relationship.
D \(P(A\cap B)=0\) This does not satisfy the stated relationship.

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

14 A student is checking a worked solution. For \(X\sim\mathrm{Bin}(n,p)\), \(E(X)=\)
A \(n+p\) This does not satisfy the stated relationship.
B \(np\) The binomial mean is np.
C \(np(1-p)\) This does not satisfy the stated relationship.
D \(p/n\) This does not satisfy the stated relationship.

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

15 For \(X\sim\mathrm{Bin}(n,p)\), \(E(X)=\)
A \(np(1-p)\) This does not satisfy the stated relationship.
B \(np\) The binomial mean is np.
C \(n+p\) This does not satisfy the stated relationship.
D \(p/n\) This does not satisfy the stated relationship.

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

16 A student is checking a worked solution. A solution to \(dy/dt=ky\) has the form
A \(y=A+k/t\) This does not satisfy the stated relationship.
B \(y=Ae^{kt}\) A quantity with rate proportional to itself changes exponentially.
C \(y=A\sin kt\) This does not satisfy the stated relationship.
D \(y=Akt\) This does not satisfy the stated relationship.

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

17 A student is checking a worked solution. If \(f(x)=x^3\), then \(f\prime(x)=\)
A \(x^4/4\) This does not satisfy the stated relationship.
B \(x^2\) This does not satisfy the stated relationship.
C \(3x^2\) Apply the power rule.
D \(3x\) This does not satisfy the stated relationship.

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

18 Which response best completes this VCE-style item? If \(y=(3x+1)^5\), then \(dy/dx=\)
A \((3x+1)^4\) This does not satisfy the stated relationship.
B \(15(3x+1)^5\) This does not satisfy the stated relationship.
C \(5(3x+1)^4\) This does not satisfy the stated relationship.
D \(15(3x+1)^4\) Differentiate the outside and multiply by the inner derivative.

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

19 During a one-minute revision round: If \(y=(3x+1)^5\), then \(dy/dx=\)
A \(15(3x+1)^5\) This does not satisfy the stated relationship.
B \(15(3x+1)^4\) Differentiate the outside and multiply by the inner derivative.
C \(5(3x+1)^4\) This does not satisfy the stated relationship.
D \((3x+1)^4\) This does not satisfy the stated relationship.

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

20 A student is checking a worked solution. \(\frac d{dx}[xe^x]=\)
A \(x^2e^x\) This does not satisfy the stated relationship.
B \(e^x\) This does not satisfy the stated relationship.
C \(xe^x\) This does not satisfy the stated relationship.
D \(e^x(1+x)\) Use uv′+u′v.

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

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