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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 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 During a one-minute revision round: The vertex of \(y=(x-2)^2-5\) is
A \((-5,2)\) This does not satisfy the stated relationship.
B \((-2,-5)\) This does not satisfy the stated relationship.
C \((2,-5)\) Vertex form y=(x−h)²+k has vertex (h,k).
D \((2,5)\) This does not satisfy the stated relationship.

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

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

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

04 Which response best completes this VCE-style item? \(P(A\mid B)=\)
A \(P(A\cup B)\) This does not satisfy the stated relationship.
B \(P(A)P(B)\) always This does not satisfy the stated relationship.
C \(\frac{P(A\cap B)}{P(B)}\) Restrict the sample space to B.
D \(\frac{P(A)}{P(B)}\) This does not satisfy the stated relationship.

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

05 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

06 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

07 Which response best completes this VCE-style item? The graph of \(y=f(x-2)+3\) is translated
A 3 right and 2 down This does not satisfy the stated relationship.
B 2 right and 3 down This does not satisfy the stated relationship.
C 2 right and 3 up Horizontal translation uses the opposite sign inside.
D 2 left and 3 up This does not satisfy the stated relationship.

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

08 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

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

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

10 For \(a>1\), \(y=a^x\) is
A periodic This does not satisfy the stated relationship.
B strictly decreasing This does not satisfy the stated relationship.
C strictly increasing An exponential with base greater than one increases.
D undefined at x=0 This does not satisfy the stated relationship.

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

11 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

12 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

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

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

14 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

15 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

16 Which response best completes this VCE-style item? For \(a>1\), \(y=a^x\) is
A strictly decreasing This does not satisfy the stated relationship.
B strictly increasing An exponential with base greater than one increases.
C periodic This does not satisfy the stated relationship.
D undefined at x=0 This does not satisfy the stated relationship.

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

17 During a one-minute revision round: The period of \(\sin(2x)\) is
A \(\pi/2\) This does not satisfy the stated relationship.
B \(2\pi\) This does not satisfy the stated relationship.
C \(4\pi\) This does not satisfy the stated relationship.
D \(\pi\) Period is 2π/2 = π.

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

18 A student is checking a worked solution. The solution of \(|x|<3\) is
A \(x>3\) This does not satisfy the stated relationship.
B \([-3,3]\) This does not satisfy the stated relationship.
C \((-3,3)\) Distance from zero must be less than three.
D \(({-\infty},-3)\cup(3,\infty)\) This does not satisfy the stated relationship.

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

19 For \(X\sim\mathrm{Bin}(n,p)\), \(\mathrm{Var}(X)=\)
A \(\sqrt{np(1-p)}\) This does not satisfy the stated relationship.
B \(np(1-p)\) The binomial variance is np(1−p).
C \(np\) This does not satisfy the stated relationship.
D \(n^2p\) This does not satisfy the stated relationship.

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

20 A student is checking a worked solution. For \(a>1\), \(y=a^x\) is
A strictly decreasing This does not satisfy the stated relationship.
B undefined at x=0 This does not satisfy the stated relationship.
C strictly increasing An exponential with base greater than one increases.
D periodic This does not satisfy the stated relationship.

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

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