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

That y8 kid 🤣 - bot · guest

11 Sep 2026, 9:12 p.m.

20Serious score
01 During a one-minute revision round: \(\sin^2x+\cos^2x\) equals
A 0 This does not satisfy the stated relationship.
B 1 This is the Pythagorean identity.
C \(\tan x\) 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 100 ms

02 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 100 ms

03 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 100 ms

04 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 100 ms

05 During a one-minute revision round: 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 100 ms

06 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 100 ms

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

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

08 Which response best completes this VCE-style item? \(\int_a^b f(x)\,dx\) 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 the gradient at b This does not satisfy the stated relationship.
D total unsigned area always This does not satisfy the stated relationship.

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

09 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

10 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

11 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 100 ms

12 \(\int_a^b f(x)\,dx\) represents
A the mean of a and b This does not satisfy the stated relationship.
B signed area between the graph and x-axis A definite integral is signed area.
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 100 ms

13 \(\int 3x^2\,dx=\)
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 100 ms

14 \(\sin^2x+\cos^2x\) equals
A \(\sin 2x\) This does not satisfy the stated relationship.
B 1 This is the Pythagorean identity.
C \(\tan x\) This does not satisfy the stated relationship.
D 0 This does not satisfy the stated relationship.

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

15 During a one-minute revision round: If \(P(3)=0\), then a factor of \(P(x)\) is
A \(x^3\) 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 \(3x-1\) This does not satisfy the stated relationship.

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

16 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 100 ms

17 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 100 ms

18 A student is checking a worked solution. A standard normal random variable has mean and variance
A 0 and 0 This does not satisfy the stated relationship.
B 0 and 1 Standardisation produces mean 0 and variance 1.
C 1 and 1 This does not satisfy the stated relationship.
D 1 and 0 This does not satisfy the stated relationship.

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

19 A student is checking a worked solution. A solution to \(dy/dt=ky\) has the form
A \(y=A+k/t\) This does not satisfy the stated relationship.
B \(y=Ae^{kt}\) A quantity with rate proportional to itself changes exponentially.
C \(y=A\sin kt\) This does not satisfy the stated relationship.
D \(y=Akt\) This does not satisfy the stated relationship.

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

20 A student is checking a worked solution. If A and B are independent, then
A \(P(A\mid B)=0\) This does not satisfy the stated relationship.
B \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.
C \(P(A)=P(B)\) This does not satisfy the stated relationship.
D \(P(A\cap B)=0\) This does not satisfy the stated relationship.

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

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