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

elephant!!!!!! · guest

13 Oct 2026, 12:26 p.m.

34Serious score
01 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 949 ms

02 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 2734 ms

03 Which response best completes this VCE-style item? A solution to \(dy/dt=ky\) has the form
A \(y=Ae^{kt}\) A quantity with rate proportional to itself changes exponentially.
B \(y=Akt\) This does not satisfy the stated relationship.
C \(y=A+k/t\) This does not satisfy the stated relationship.
D \(y=A\sin kt\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Exponentials · answered at 4418 ms

04 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 8240 ms

05 During a one-minute revision round: Increasing sample size while all else is fixed makes a confidence interval generally
A unchanged This does not satisfy the stated relationship.
B narrower Standard error decreases as sample size grows.
C centred at zero This does not satisfy the stated relationship.
D wider This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Confidence intervals · answered at 9715 ms

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

Written for icaijy.com · U1–2 · Differentiation · answered at 11473 ms

07 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 13439 ms

08 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 15040 ms

09 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 17605 ms

10 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 18687 ms

11 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 19953 ms

12 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 21584 ms

13 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 23418 ms

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

Written for icaijy.com · U3–4 · Confidence intervals · answered at 24798 ms

15 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 26230 ms

16 During a one-minute revision round: For \(f(x)=2x-1\), \(f^{-1}(x)\) is
A \(2x+1\) This does not satisfy the stated relationship.
B \(1/(2x-1)\) This does not satisfy the stated relationship.
C \((x+1)/2\) Swap x and y, then solve for y.
D \((x-1)/2\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Functions · answered at 28065 ms

17 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 30131 ms

18 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 31654 ms

19 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 32773 ms

20 Which response best completes this VCE-style item? The period of \(\sin(2x)\) is
A \(\pi/2\) This does not satisfy the stated relationship.
B \(4\pi\) This does not satisfy the stated relationship.
C \(2\pi\) This does not satisfy the stated relationship.
D \(\pi\) Period is 2π/2 = π.

Written for icaijy.com · U1–2 · Trigonometry · answered at 34279 ms

21 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 36087 ms

22 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 38135 ms

23 \(\int 3x^2\,dx=\)
A \(x^3+C\) Reverse the power rule and include C.
B \(x^3\) This does not satisfy the stated relationship.
C \(6x+C\) This does not satisfy the stated relationship.
D \(3x^3+C\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Integration · answered at 39809 ms

24 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 42200 ms

25 During a one-minute revision round: For events A and B, \(P(A\cup B)=\)
A \(P(A)+P(B)-P(A\cap B)\) Subtract the intersection counted twice.
B \(P(A)+P(B)\) This does not satisfy the stated relationship.
C \(1-P(A)\) 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 43643 ms

26 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 44898 ms

27 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 46450 ms

28 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 48104 ms

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

Written for icaijy.com · U1–2 · Functions · answered at 49948 ms

30 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 51790 ms

31 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 53511 ms

32 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 55671 ms

33 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 57872 ms

34 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 59264 ms

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