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

Albert · guest

10 Sep 2026, 9:09 p.m.

9Serious score
01 Which response best completes this VCE-style item? The average rate of change from x=a to x=b is
A \(f(a)+f(b)\) This does not satisfy the stated relationship.
B \(\frac{f(b)-f(a)}{b-a}\) It is change in output divided by change in input.
C \(\frac{b-a}{f(b)-f(a)}\) This does not satisfy the stated relationship.
D \(f(b)-f(a)\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Rates of change · answered at 3595 ms

02 If \(P(3)=0\), then a factor of \(P(x)\) is
A \(3x-1\) This does not satisfy the stated relationship.
B \(x+3\) This does not satisfy the stated relationship.
C \(x^3\) This does not satisfy the stated relationship.
D \(x-3\) The factor theorem gives x−3.

Written for icaijy.com · U1–2 · Polynomials · answered at 9860 ms

03 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 \(P(A)+P(B)-P(A\cap B)\) Subtract the intersection counted twice.
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 14671 ms

04 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 19453 ms

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

Written for icaijy.com · U1–2 · Transformations · answered at 25709 ms

06 During a one-minute revision round: For \(a>1\), \(y=a^x\) is
A undefined at x=0 This does not satisfy the stated relationship.
B strictly decreasing This does not satisfy the stated relationship.
C periodic This does not satisfy the stated relationship.
D strictly increasing An exponential with base greater than one increases.

Written for icaijy.com · U1–2 · Exponentials · answered at 31197 ms

07 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 35825 ms

08 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 44925 ms

09 The average rate of change from x=a to x=b is
A \(f(a)+f(b)\) This does not satisfy the stated relationship.
B \(\frac{b-a}{f(b)-f(a)}\) This does not satisfy the stated relationship.
C \(f(b)-f(a)\) This does not satisfy the stated relationship.
D \(\frac{f(b)-f(a)}{b-a}\) It is change in output divided by change in input.

Written for icaijy.com · U1–2 · Rates of change · answered at 51079 ms

10 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 \(({-\infty},-3)\cup(3,\infty)\) 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 53464 ms

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

Written for icaijy.com · U1–2 · Exponentials · answered at 56603 ms

12 Which response best completes this VCE-style item? If A and B are independent, then
A \(P(A\cap B)=P(A)P(B)\) Independence gives the product rule.
B \(P(A)=P(B)\) This does not satisfy the stated relationship.
C \(P(A\cap B)=0\) This does not satisfy the stated relationship.
D \(P(A\mid B)=0\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability · not answered before time expired

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