Polynomials (TF)
Differentiation (TF)
Periodic Functions (TF)
Log Functions (TF)
Fractions or Tech Active
100
Is (x-1) a factor of x3 - 4x2 - 5x + 3?
No
`1^3 -4(1)^2 -5(1)+3ne0`
100
Differentiate
`f(x) = 1/x^3 `
`f(x) = x^-3`
`f'(x) = -3x^-4`
` =-3/x^4`
100
What is the vertical and horizontal shift of:
`y=3cos(2x+pi)-2`
100
Solve for x:
loge (x) + loge (3) = loge (6)
`x=2`
100
Tech Active
Solve to 1 decimal place:
`20=90(0.85^x)`
`x = 9.3`
200
The graph of a cubic has a stationary point of inflection (3, -16), and an x-intercept at (5, 0).
Find the equation.
`y=2(x-3)^3-16`
200
Simplify using log laws and differentiate with respect to x
`y = ln sqrt(4x-3)`
`y = ln(4x - 3)^(1/2)`
` = 1/2 ln(4x - 3)`
`y'=1/2 xx 4/(4x - 3)`
`y'= 2/(4x-3)`
200
What is the exact value of:
`sin ((7pi)/6)`
`-1/2`
200
A population of organisms is growing by the formula: N = Number of Organisms t = time in days
Determine the number of organisms after 25 days.
`N=3xx2^(0.2t)`
96 organisms
200
Tech Free
`2/9-:3/4-1/3`
`-1/27`
300
Apply the discriminant to
`12x^2 -3x + 1`
to determine the number of roots.
a = 12 b = -3 c = 1
300
Calculate the gradient of the tangent to the curve at x = -1.
`f(x) = x^2 -5x + 1`
`f'(x) = 2x - 5`
`f'(-1) = -2 - 5`
` = -7`
300
Solve
`4costheta+1=3 `
`0lethetale2pi`
`(pi/3,(5pi)/3)`
300
Find the x-intercept of: y = loge (x-2)
(3, 0)
300
Tech Active
Solve to 1 decimal place within the specified domain:
`1/5 sin(x+pi)=1/10`
`0<=theta<=2pi`
`x=3.7 and x=5.8`
400
The product of two consecutive odd numbers is 99. Set up an equation and solve it to find one of the numbers.
`x=-11 or x=9`
400
Use derivatives to determine the nature of the stationary point at
`x=1 `
`of f(x)=x^3 - 3x`
`f''(1)=6>0`
:. Minimum Stationary point
400
Determine the equation of the tangent to the curve y = 8cos(x) at the point where:
`x=pi/2`
`y=-8x+4pi`
400
Solve for x, showing all answers:
loge (2x) + loge (x + 2) = loge (6)
x = -3 and x = 1
400
Tech Free Solve for n: 
