That y8 kid 🤣 - bot · guest · Mathematical Methods · Units 1 & 2

01 A student is checking a worked solution. For $f(x)=x^2+1$, the tangent gradient at x=3 is

A 10 This does not satisfy the stated relationship.

B 7 This does not satisfy the stated relationship.

C 3 This does not satisfy the stated relationship.

D 6 $f\prime(x)=2x$.

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

02 Which response best completes this VCE-style item? On $[0,2\pi]$, $\sin x=1/2$ at

A $5\pi/6,11\pi/6$ This does not satisfy the stated relationship.

B $\pi/6,5\pi/6$ Sine is positive in quadrants I and II.

C $\pi/6,7\pi/6$ This does not satisfy the stated relationship.

D $\pi/3,2\pi/3$ This does not satisfy the stated relationship.

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

03 A student is checking a worked solution. In a sample, 40 of 100 students play sport and 10 play sport and music. $P(\text{music}\mid\text{sport})=$

A 0.40 This does not satisfy the stated relationship.

B 0.10 This does not satisfy the stated relationship.

C 0.25 10 of the 40 sport players also play music.

D 0.50 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Two-way tables · answered at 100 ms

04 A CAS solves $x^3-4x=0$. The full solution set is

A $\{-2,2\}$ This does not satisfy the stated relationship.

B $\{-4,0,4\}$ This does not satisfy the stated relationship.

C $\{0,4\}$ This does not satisfy the stated relationship.

D $\{-2,0,2\}$ Factor x(x−2)(x+2).

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

05 During a one-minute revision round: For $f(x)=\log(x-4)$, the domain is

A $\mathbb R$ This does not satisfy the stated relationship.

B $({-\infty},4)$ This does not satisfy the stated relationship.

C $(4,\infty)$ The logarithm argument must be positive.

D $[4,\infty)$ This does not satisfy the stated relationship.

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

06 A student is checking a worked solution. An arithmetic sequence has $u_1=4$, common difference 3. Then $u_{10}=$

A 30 This does not satisfy the stated relationship.

B 31 u10=4+9×3=31.

C 34 This does not satisfy the stated relationship.

D 27 This does not satisfy the stated relationship.

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

07 Which response best completes this VCE-style item? $1000 grows by 5% per year for 3 years. Its value is closest to

A $1157.63 $1000(1.05)^3=1157.625$.

B $1050.00 This does not satisfy the stated relationship.

C $1250.00 This does not satisfy the stated relationship.

D $1150.00 This does not satisfy the stated relationship.

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

08 In a sample, 40 of 100 students play sport and 10 play sport and music. $P(\text{music}\mid\text{sport})=$

A 0.10 This does not satisfy the stated relationship.

B 0.50 This does not satisfy the stated relationship.

C 0.40 This does not satisfy the stated relationship.

D 0.25 10 of the 40 sport players also play music.

Written for icaijy.com · U1–2 · Two-way tables · answered at 100 ms

09 A student is checking a worked solution. The graphs $y=x^2$ and $y=2x+3$ intersect at x-values

A $x=-3,1$ This does not satisfy the stated relationship.

B $x=1,3$ This does not satisfy the stated relationship.

C $x=0,2$ This does not satisfy the stated relationship.

D $x=-1,3$ Solve x²−2x−3=0.

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

10 A student is checking a worked solution. If $f(x)=x+2$ and $g(x)=x^2$, then $(g\circ f)(3)=$

A 13 This does not satisfy the stated relationship.

B 7 This does not satisfy the stated relationship.

C 25 f(3)=5, then g(5)=25.

D 11 This does not satisfy the stated relationship.

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

11 How many x-intercepts does $y=x^4-5x^2+4$ have?

A 4 Let u=x²: (u−1)(u−4)=0 gives x=±1,±2.

B 0 This does not satisfy the stated relationship.

C 5 This does not satisfy the stated relationship.

D 2 This does not satisfy the stated relationship.

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

12 A student is checking a worked solution. A CAS returns a decimal root but the question requests an exact value. The best response is to

A use an exact solve command or algebraic form Exact form is required when requested.

B round to one decimal place This does not satisfy the stated relationship.

C change the equation This does not satisfy the stated relationship.

D omit the root This does not satisfy the stated relationship.

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

13 For X taking 0,1,2 with probabilities 0.2,0.5,0.3, $E(X)=$

A 0.8 This does not satisfy the stated relationship.

B 1.5 This does not satisfy the stated relationship.

C 1.0 This does not satisfy the stated relationship.

D 1.1 0×0.2+1×0.5+2×0.3=1.1.

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

14 A residual is defined as

A predicted minus observed only This does not satisfy the stated relationship.

B observed value minus predicted value Residual = y−ŷ.

C gradient minus intercept This does not satisfy the stated relationship.

D observed times predicted This does not satisfy the stated relationship.

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

15 A student is checking a worked solution. Solve $2^x=10$, correct to two decimal places.

A 2.30 This does not satisfy the stated relationship.

B 5.00 This does not satisfy the stated relationship.

C 3.32 $x=\log_2 10\approx3.32$.

D 10.00 This does not satisfy the stated relationship.

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

16 During a one-minute revision round: If $f(x)=x+2$ and $g(x)=x^2$, then $(g\circ f)(3)=$

A 11 This does not satisfy the stated relationship.

B 7 This does not satisfy the stated relationship.

C 25 f(3)=5, then g(5)=25.

D 13 This does not satisfy the stated relationship.

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

17 Which response best completes this VCE-style item? An arithmetic sequence has $u_1=4$, common difference 3. Then $u_{10}=$

A 30 This does not satisfy the stated relationship.

B 31 u10=4+9×3=31.

C 27 This does not satisfy the stated relationship.

D 34 This does not satisfy the stated relationship.

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

18 A student is checking a worked solution. For $f(x)=\log(x-4)$, the domain is

A $\mathbb R$ This does not satisfy the stated relationship.

B $[4,\infty)$ This does not satisfy the stated relationship.

C $({-\infty},4)$ This does not satisfy the stated relationship.

D $(4,\infty)$ The logarithm argument must be positive.

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

19 During a one-minute revision round: For X taking 0,1,2 with probabilities 0.2,0.5,0.3, $E(X)=$

A 0.8 This does not satisfy the stated relationship.

B 1.5 This does not satisfy the stated relationship.

C 1.0 This does not satisfy the stated relationship.

D 1.1 0×0.2+1×0.5+2×0.3=1.1.

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

20 For $f(x)=x^2+1$, the tangent gradient at x=3 is

A 7 This does not satisfy the stated relationship.

B 10 This does not satisfy the stated relationship.

C 3 This does not satisfy the stated relationship.

D 6 $f\prime(x)=2x$.

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