15 Questions
What is the expression for $f3$ given the angles with the horizontal as shown?
C) $f3 = (F1 ext{ sin }35° - 2)i + (F1 ext{ cos }35° - 2)j$
At the circular table, how many ways can Abby, Betty, Cara, and their relatives sit so that each student sits adjacent to their relative?
B) $3! \times 2^3$
If $f(2) = 5$ and $f'(2) = -2$, what is the gradient of the tangent on the inverse function at $x = 5$?
B) $-\frac{1}{2}$
What is the centre and radius of the circle represented by the parametric equations x = 4 + 3cos θ, y = 2 + 3sin θ?
(4, 2), r = 3
Which of the following polynomials has a root of multiplicity 2 at x = 1 in the equation f(x) = 0?
f(x) = x^2 - 5x + 4
In the domain 0 ≤ x ≤ π, which of the following is true?
sin sin^{-1} x = x
Identify the expression identical to 2 sin(3x) sin(5x).
cos(2x) - cos(8x)
Sketch the graph of y = x^2 - 4. Which option represents the correct sketch?
Option C
Find the integral of the function ∫(9 - 4x^2)dx from 3 to 3.
3sin^{-1}(2x/3) + C
What is the formula for the volume V of sand in the cone?
V = 1/3 πh
How many different teams can be created if at least two members must be women?
126
What is the number of fish remaining after 6 months?
7 million fish
What is the solution to 3sin(2x) - 5cos(2x) = 5 for 0 ≤ x ≤ 2π?
x = π/6, 5π/6, 13π/6
Show the relationship between vectors a, b, and the angle θ using the dot product identity.
Area of triangle OAB = 1/2 |a||b|sin(θ)
Calculate the value of h when the depth of sand is decreasing at a rate of 0.05 cm/s.
h = 0.15 cm
Test your knowledge on integration, functions, and polynomials with questions involving finding integrals, differentiation, and identifying polynomial roots. See if you can correctly solve the given math problems.
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