Trigonometry
Determine the coordinates of a point (x,y)(x,y) on the unit circle if you are givenθ=30°, where θ is in standard position.
Answer: (√3/2,1/2)
What is the difference between permutation and combination?
Permutation: order matters
Combination: order doesn't matter
g(x)=x1/2+2 a polynomial?
No because polynomials needs whole number exponents (like 0,1,2, etc.)
y=√x. State the domain
x>=0
What’s the only number that doesn’t change when multiplied by any number?
0
Find the value of cos(θ) if sin(θ)=3/5 and θ is in Quadrant II.
−4/5
Simplify 7!
5040
Verify whether (x−3) is a factor of f(x)=x³−6x²+11x−6 using synthetic division.
Synthetic division with 3 gives remainder 0, so yes (x−3) is a factor.
y=√x−2. State the domain and range.
Domain: x>=2. Range: y>=0
If a graph fails the vertical line test, what is it NOT?
A function
Find two coterminal angles of 70 degrees (one positive and one negative).
430°,−290°
In how many ways can you arrange the letters in the word 'MATH'?
24
Give an example of a cubic polynomial with positive leading coefficient and x-intercept at x=−2.
Answers will vary
e.g. f(x)=(x+2)(x−1)(x−3)
y=√−x+5. Identify the transformations applied to y=√x.
reflection over the y-axis and shifts right 5
Solve 92x+1=27x.
x=-2
For θ=11π/6θ=11π/6, find the values of sin(θ), cos(θ), and tan(θ).
sin(11π/6)=−1/2,
cos(11π/6)=√3/2
tan(11π/6)= −√3/3
Solve for n: n!/(n−3)!=120.
n=6
Use the Remainder Theorem: find remainder when f(x)=x4−3x+2 is divided by (x+1).
Remainder=6
Determine the vertical and horizontal asymptotes of y=(x+1)/(x−3)
Vertical asymptote x=3. Horizontal asymptote y=1.
What graph looks like a smile?
a parabola that opens upwards.
Solve 2cos(θ)+2=0 for 0≤θ<2π.
3π/4,
5π/4
In (3+x)⁹, what is the 4th term?
61 236x³
Given that (x−2) is a factor of p(x)=x3+kx2−x−6, find k.
k=0
Identify the asymptotes and holes of y=(x−2)(x−4)/
(x−2)(x+3).
Hole at x=2, vertical asymptote x=4, horizontal asymptote y=1.
Givenf(x)=x2, g(x)=3−x , evaluate the composite function of f(g(4)).
-16