Question 1

Which of the following is the correct simplification of $$\sqrt[3]{x^6$}$$ for $$x \geq 0$$?

Accepted Answer

$$x^2$$

Question 2

A pharmaceutical company needs to mix two solutions: one with a concentration of 10% and another with 30%. If they want 100 mL of a 20% solution, how much of the 10% solution should they use?

Accepted Answer

$$50\ 	ext{mL}$$

Question 3

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 4

A rational function $$f(x) = \frac{2x}{x^2$ - 4}$$ has which of the following vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 5

If $$f(x) = 3x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$7$$

Question 6

Which of the following is the inverse function of $$f(x) = 2x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{2}$$

Question 7

A projectile is launched and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 5. $$What is the maximum height reached by the projectile?

Accepted Answer

$$25.41\ 	ext{meters}$$

Question 8

Which of the following is the correct solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 9

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, how many will there be after 9 hours?

Accepted Answer

$$4000$$

Question 10

Which of the following is the correct value of $$\log_{2} 16$$?

Accepted Answer

$$4$$

Question 11

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 12

Which of the following is the correct solution to the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 13

Which of the following is the correct value of $$	an 45^\circ$$?

Accepted Answer

$$1$$

Question 14

If $$f(x) = x^2$ - 2x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, 0)$$

Question 15

Which of the following is the correct simplification of $$\frac{x^2$ - 4}{x - 2}$$ for $$x 
eq 2$$?

Accepted Answer

$$x + 2$$

Question 16

Which of the following is the correct value of $$\sin$$^{-1}$$(\frac{1}{2}) in $$radians?

Accepted Answer

$$\frac{\pi}{6}$$

Question 17

Which of the following is the correct identity for $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 18

A right triangle has legs of length 6 cm and 8 cm. What is the length of the hypotenuse?

Accepted Answer

$$10\ 	ext{cm}$$

Question 19

Which of the following is the correct solution to $$\log_{10} x = 2$$?

Accepted Answer

$$x = 100$$

MATH 1250: Basic Mathematics for Science & Engineering – Syllabus and Learning Outcomes

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