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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 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

02 Which response best completes this VCE-style item? \(\log_a(xy)\) equals
A \(\log_a(x+y)\) This does not satisfy the stated relationship.
B \(\log_a x\log_a y\) This does not satisfy the stated relationship.
C \(x+y\) This does not satisfy the stated relationship.
D \(\log_a x+\log_a y\) The logarithm of a product is a sum.

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

03 A student is checking a worked solution. \(P(A\mid B)=\)
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 \(\frac{P(A\cap B)}{P(B)}\) Restrict the sample space to B.
D \(P(A)P(B)\) always This does not satisfy the stated relationship.

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

04 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

05 \(P(A\mid B)=\)
A \(\frac{P(A\cap B)}{P(B)}\) Restrict the sample space to B.
B \(P(A)P(B)\) always This does not satisfy the stated relationship.
C \(P(A\cup B)\) This does not satisfy the stated relationship.
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

06 During a one-minute revision round: 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 \(f(b)-f(a)\) This does not satisfy the stated relationship.
C \(f(a)+f(b)\) 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

07 Which response best completes this VCE-style item? The vertex of \(y=(x-2)^2-5\) is
A \((-5,2)\) This does not satisfy the stated relationship.
B \((2,-5)\) Vertex form y=(x−h)²+k has vertex (h,k).
C \((2,5)\) This does not satisfy the stated relationship.
D \((-2,-5)\) This does not satisfy the stated relationship.

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

08 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

09 Which response best completes this VCE-style item? 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

10 Which response best completes this VCE-style item? 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

11 A student is checking a worked solution. The vertex of \(y=(x-2)^2-5\) is
A \((2,-5)\) Vertex form y=(x−h)²+k has vertex (h,k).
B \((-5,2)\) This does not satisfy the stated relationship.
C \((-2,-5)\) This does not satisfy the stated relationship.
D \((2,5)\) This does not satisfy the stated relationship.

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

12 A student is checking a worked solution. If \(P(3)=0\), then a factor of \(P(x)\) is
A \(3x-1\) This does not satisfy the stated relationship.
B \(x-3\) The factor theorem gives x−3.
C \(x+3\) This does not satisfy the stated relationship.
D \(x^3\) This does not satisfy the stated relationship.

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

13 Which response best completes this VCE-style item? \(\sin^2x+\cos^2x\) equals
A \(\tan x\) This does not satisfy the stated relationship.
B 0 This does not satisfy the stated relationship.
C 1 This is the Pythagorean identity.
D \(\sin 2x\) This does not satisfy the stated relationship.

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

14 During a one-minute revision round: \(\int 3x^2\,dx=\)
A \(x^3\) This does not satisfy the stated relationship.
B \(3x^3+C\) This does not satisfy the stated relationship.
C \(6x+C\) This does not satisfy the stated relationship.
D \(x^3+C\) Reverse the power rule and include C.

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

15 Which response best completes this VCE-style item? For \(f(x)=2x-1\), \(f^{-1}(x)\) is
A \(2x+1\) This does not satisfy the stated relationship.
B \((x-1)/2\) This does not satisfy the stated relationship.
C \((x+1)/2\) Swap x and y, then solve for y.
D \(1/(2x-1)\) This does not satisfy the stated relationship.

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

16 Which response best completes this VCE-style item? The expected value of a discrete random variable is
A \(\sqrt{\mathrm{Var}(X)}\) This does not satisfy the stated relationship.
B \(\max x\) This does not satisfy the stated relationship.
C \(\sum P(X=x)\) This does not satisfy the stated relationship.
D \(\sum xP(X=x)\) Expectation is the probability-weighted mean.

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

17 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

18 At a stationary point of a differentiable function
A \(f\prime(x)=0\) The tangent gradient is zero.
B \(f(x)=0\) This does not satisfy the stated relationship.
C \(f(x)=1\) This does not satisfy the stated relationship.
D \(f\prime\prime(x)=0\) always This does not satisfy the stated relationship.

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

19 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

20 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

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