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

sandywang14341434

6 Oct 2026, 10:17 a.m.

22Serious 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 1463 ms

02 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 2639 ms

03 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 6985 ms

04 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 8968 ms

05 During a one-minute revision round: \(\int_a^b f(x)\,dx\) represents
A signed area between the graph and x-axis A definite integral is signed area.
B the mean of a and b This does not satisfy the stated relationship.
C total unsigned area always This does not satisfy the stated relationship.
D the gradient at b This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Fundamental theorem · answered at 10789 ms

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

Written for icaijy.com · U3–4 · Binomial distribution · answered at 12876 ms

07 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 14538 ms

08 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 18152 ms

09 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 22104 ms

10 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 29193 ms

11 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 30841 ms

12 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 33776 ms

13 \(\log_a(xy)\) equals
A \(\log_a x+\log_a y\) The logarithm of a product is a sum.
B \(x+y\) This does not satisfy the stated relationship.
C \(\log_a x\log_a y\) This does not satisfy the stated relationship.
D \(\log_a(x+y)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Logarithms · answered at 35612 ms

14 During a one-minute revision round: \(\log_a(xy)\) equals
A \(\log_a x\log_a y\) This does not satisfy the stated relationship.
B \(\log_a x+\log_a y\) The logarithm of a product is a sum.
C \(x+y\) This does not satisfy the stated relationship.
D \(\log_a(x+y)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Logarithms · answered at 37064 ms

15 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 39725 ms

16 If \(f(x)=x^3\), then \(f\prime(x)=\)
A \(3x\) This does not satisfy the stated relationship.
B \(x^4/4\) This does not satisfy the stated relationship.
C \(3x^2\) Apply the power rule.
D \(x^2\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Differentiation · answered at 41317 ms

17 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 42965 ms

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

Written for icaijy.com · U1–2 · Functions · answered at 44751 ms

19 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 46676 ms

20 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 49140 ms

21 Which response best completes this VCE-style item? If \(P(3)=0\), then a factor of \(P(x)\) is
A \(x-3\) The factor theorem gives x−3.
B \(x^3\) This does not satisfy the stated relationship.
C \(3x-1\) 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 52010 ms

22 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 55026 ms

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

Written for icaijy.com · U1–2 · Probability · answered at 59671 ms

24 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 · not answered before time expired

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