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

seven · guest

10 Sep 2026, 9:20 p.m.

14Serious score
01 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 2052 ms

02 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 5452 ms

03 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 9335 ms

04 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 right and 3 up Horizontal translation uses the opposite sign inside.
C 3 right and 2 down This does not satisfy the stated relationship.
D 2 left and 3 up This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Transformations · answered at 12235 ms

05 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 14768 ms

06 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 19102 ms

07 A student is checking a worked solution. \(\int_a^b f(x)\,dx\) represents
A the gradient at b This does not satisfy the stated relationship.
B total unsigned area always This does not satisfy the stated relationship.
C signed area between the graph and x-axis A definite integral is signed area.
D the mean of a and b This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Fundamental theorem · answered at 41218 ms

08 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 43568 ms

09 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 46001 ms

10 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 50068 ms

11 A student is checking a worked solution. The expected value of a discrete random variable is
A \(\max x\) This does not satisfy the stated relationship.
B \(\sum xP(X=x)\) Expectation is the probability-weighted mean.
C \(\sum P(X=x)\) This does not satisfy the stated relationship.
D \(\sqrt{\mathrm{Var}(X)}\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · answered at 54051 ms

12 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 56184 ms

13 A student is checking a worked solution. The period of \(\sin(2x)\) is
A \(4\pi\) This does not satisfy the stated relationship.
B \(2\pi\) This does not satisfy the stated relationship.
C \(\pi\) Period is 2π/2 = π.
D \(\pi/2\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Trigonometry · answered at 58268 ms

14 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 59918 ms

Run it again