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

That y8 kid 🤣 - bot · guest

11 Sep 2026, 9:12 p.m.

20Serious score
01 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 100 ms

02 During a one-minute revision round: For \(X\sim\mathrm{Bin}(n,p)\), \(\mathrm{Var}(X)=\)
A \(n^2p\) This does not satisfy the stated relationship.
B \(np\) This does not satisfy the stated relationship.
C \(\sqrt{np(1-p)}\) 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 100 ms

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

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

04 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 100 ms

05 For \(f(x)=2x-1\), \(f^{-1}(x)\) is
A \(1/(2x-1)\) This does not satisfy the stated relationship.
B \((x+1)/2\) Swap x and y, then solve for y.
C \(2x+1\) This does not satisfy the stated relationship.
D \((x-1)/2\) This does not satisfy the stated relationship.

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

06 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 100 ms

07 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 100 ms

08 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

09 Which response best completes this VCE-style item? For \(X\sim\mathrm{Bin}(n,p)\), \(\mathrm{Var}(X)=\)
A \(np\) This does not satisfy the stated relationship.
B \(\sqrt{np(1-p)}\) 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 100 ms

10 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 100 ms

11 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 100 ms

12 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

13 During a one-minute revision round: 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 \(x>3\) This does not satisfy the stated relationship.
D \([-3,3]\) This does not satisfy the stated relationship.

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

14 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

15 During a one-minute revision round: For \(X\sim\mathrm{Bin}(n,p)\), \(E(X)=\)
A \(np(1-p)\) This does not satisfy the stated relationship.
B \(np\) The binomial mean is np.
C \(p/n\) This does not satisfy the stated relationship.
D \(n+p\) This does not satisfy the stated relationship.

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

16 Which response best completes this VCE-style item? The vertex of \(y=(x-2)^2-5\) is
A \((-5,2)\) This does not satisfy the stated relationship.
B \((2,-5)\) Vertex form y=(x−h)²+k has vertex (h,k).
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 100 ms

17 A standard normal random variable has mean and variance
A 0 and 1 Standardisation produces mean 0 and variance 1.
B 1 and 1 This does not satisfy the stated relationship.
C 1 and 0 This does not satisfy the stated relationship.
D 0 and 0 This does not satisfy the stated relationship.

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

18 During a one-minute revision round: 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 \(3x\) This does not satisfy the stated relationship.
D \(3x^2\) Apply the power rule.

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

19 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 100 ms

20 \(\int_a^b f(x)\,dx\) 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

Run it again