Math Club Jeopardy

Algebra

100

Find the slope of the line passing through the points (-1, -1) and (2, 2).

m = -1

200

The sum of an integer N and its reciprocal is equal to 78/15. What is the value of N?

N = 5

300

If x <2, simplify |x - 2| - 4|-6|

- x - 22

400

m and n are integers so that 4m / 125 = 5n / 64. Find values for m and n.

m = - 3, n = - 3

Geometry

100

What is the geometric mean of 4 and 25 

10

200

What is the Geometric Mean of 1, 3, 9, 27, and 81?

a. 9       b. 1,800       c. 11       d. 19

a. 9

300

AOBC is a rectangle whose three vertices are vertices A(0, 3), O(0, 0), and B(5, 0). The length of its diagonal is 

a. 2       b. 5       c. √3       d. √34

√34

400

The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is

53

Pre-calc

100

Simplify the expression 

x²/x

x

200

Find the domain and range for f(x) = √(9-x² ). 

Domain: [-3, 3]

Range: [0,3]

300

sin(11/6) = ?

-1/2

400

Simplify the expression ln[(x+5)⁵ √(2x-7)]

3ln(x+5) + 1/2 ln(2x-7)

Calculus

100

∫ x² dx

1/3 x^3

200

Find the average value of the function on the given interval. 

f(x) = 6x - x^2, [0,3].

6

300

Find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is xy. 

y = e^{(x^2)/2}

400

If the birth rate of a population is b(t) = 2200e^0.024t and the death rate of a population is d(t) = 1460e^0.018t people per year, what is the area between these curves for 0 ≤ t ≤ 10. 

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