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

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11 Sep 2026, 9:12 p.m.

20Serious score
01 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

02 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

03 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

04 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

05 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

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

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

07 During a one-minute revision round: 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 \(p/n\) This does not satisfy the stated relationship.
D \(n+p\) This does not satisfy the stated relationship.

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

08 A student is checking a worked solution. The graph of \(y=f(x-2)+3\) is translated
A 2 right and 3 down This does not satisfy the stated relationship.
B 3 right and 2 down This does not satisfy the stated relationship.
C 2 left and 3 up This does not satisfy the stated relationship.
D 2 right and 3 up Horizontal translation uses the opposite sign inside.

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

09 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

10 Which response best completes this VCE-style item? A standard normal random variable has mean and variance
A 0 and 1 Standardisation produces mean 0 and variance 1.
B 1 and 1 This does not satisfy the stated relationship.
C 1 and 0 This does not satisfy the stated relationship.
D 0 and 0 This does not satisfy the stated relationship.

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

11 Which response best completes this VCE-style item? If \(f(x)=x^3\), then \(f\prime(x)=\)
A \(3x^2\) Apply the power rule.
B \(3x\) This does not satisfy the stated relationship.
C \(x^2\) This does not satisfy the stated relationship.
D \(x^4/4\) This does not satisfy the stated relationship.

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

12 During a one-minute revision round: \(\frac d{dx}[xe^x]=\)
A \(e^x\) This does not satisfy the stated relationship.
B \(x^2e^x\) This does not satisfy the stated relationship.
C \(e^x(1+x)\) Use uv′+u′v.
D \(xe^x\) This does not satisfy the stated relationship.

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

13 During a one-minute revision round: The domain of \(f(x)=\sqrt{x-3}\) is
A \(\mathbb R\) This does not satisfy the stated relationship.
B \([3,\infty)\) The radicand requires x−3 ≥ 0.
C \(({-\infty},3]\) This does not satisfy the stated relationship.
D \((3,\infty)\) This does not satisfy the stated relationship.

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

14 The period of \(\sin(2x)\) is
A \(\pi\) Period is 2π/2 = π.
B \(\pi/2\) This does not satisfy the stated relationship.
C \(2\pi\) This does not satisfy the stated relationship.
D \(4\pi\) This does not satisfy the stated relationship.

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

15 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

16 If A and B are independent, then
A \(P(A\cap B)=0\) This does not satisfy the stated relationship.
B \(P(A\mid B)=0\) This does not satisfy the stated relationship.
C \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.
D \(P(A)=P(B)\) This does not satisfy the stated relationship.

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

17 During a one-minute revision round: A solution to \(dy/dt=ky\) has the form
A \(y=A+k/t\) This does not satisfy the stated relationship.
B \(y=A\sin kt\) This does not satisfy the stated relationship.
C \(y=Ae^{kt}\) A quantity with rate proportional to itself changes exponentially.
D \(y=Akt\) This does not satisfy the stated relationship.

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

18 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

19 Which response best completes this VCE-style item? Increasing sample size while all else is fixed makes a confidence interval generally
A centred at zero This does not satisfy the stated relationship.
B wider This does not satisfy the stated relationship.
C unchanged This does not satisfy the stated relationship.
D narrower Standard error decreases as sample size grows.

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

20 During a one-minute revision round: If A and B are independent, then
A \(P(A)=P(B)\) This does not satisfy the stated relationship.
B \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.
C \(P(A\cap B)=0\) This does not satisfy the stated relationship.
D \(P(A\mid B)=0\) This does not satisfy the stated relationship.

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

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