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RUN REVIEW · Mathematical Methods · Units 1 & 2 · Tech-free

Albert · guest

11 Sep 2026, 8:41 a.m.

16Serious score
01 At a stationary point of a differentiable function
A \(f\prime(x)=0\) The tangent gradient is zero.
B \(f(x)=1\) This does not satisfy the stated relationship.
C \(f(x)=0\) 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 3205 ms

02 During a one-minute revision round: 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 \(P(A)=P(B)\) This does not satisfy the stated relationship.
D \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.

Written for icaijy.com · U1–2 · Probability · answered at 6671 ms

03 During a one-minute revision round: The graph of \(y=f(x-2)+3\) is translated
A 2 right and 3 down This does not satisfy the stated relationship.
B 2 left and 3 up This does not satisfy the stated relationship.
C 3 right and 2 down 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 11026 ms

04 During a one-minute revision round: The period of \(\sin(2x)\) is
A \(4\pi\) This does not satisfy the stated relationship.
B \(\pi/2\) 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 13234 ms

05 The period of \(\sin(2x)\) is
A \(\pi/2\) This does not satisfy the stated relationship.
B \(\pi\) Period is 2π/2 = π.
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 16501 ms

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

Written for icaijy.com · U1–2 · Functions · answered at 19999 ms

07 A student is checking a worked solution. For \(f(x)=2x-1\), \(f^{-1}(x)\) is
A \(1/(2x-1)\) This does not satisfy the stated relationship.
B \(2x+1\) 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 26758 ms

08 During a one-minute revision round: 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 33013 ms

09 The vertex of \(y=(x-2)^2-5\) is
A \((2,5)\) This does not satisfy the stated relationship.
B \((-5,2)\) 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 36033 ms

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

Written for icaijy.com · U1–2 · Logarithms · answered at 39933 ms

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

Written for icaijy.com · U1–2 · Exponentials · answered at 42766 ms

12 A student is checking a worked solution. 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 \(P(A)P(B)\) This does not satisfy the stated relationship.
D \(1-P(A)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 45241 ms

13 During a one-minute revision round: The solution of \(|x|<3\) is
A \([-3,3]\) This does not satisfy the stated relationship.
B \(({-\infty},-3)\cup(3,\infty)\) This does not satisfy the stated relationship.
C \((-3,3)\) Distance from zero must be less than three.
D \(x>3\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Algebra · answered at 48808 ms

14 During a one-minute revision round: At a stationary point of a differentiable function
A \(f\prime(x)=0\) The tangent gradient is zero.
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 \(f(x)=0\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Differentiation · answered at 52399 ms

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

Written for icaijy.com · U1–2 · Algebra · answered at 54233 ms

16 A student is checking a worked solution. 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 57064 ms

17 A student is checking a worked solution. The domain of \(f(x)=\sqrt{x-3}\) is
A \(({-\infty},3]\) This does not satisfy the stated relationship.
B \(\mathbb R\) 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 · not answered before time expired

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