Math Club

Algebra

100

17x + 12 = 54 - 4x

x=?

x=2

200

5x² + 7x - 9 = 4x² + x - 18

x=?

x=-3

300

(2x+3)/4 = (x+7)/3

x=?

x=9.5

400

x + 2y = 4

7x + 2y = -8

(x,y)?

(-2,3)

500

(x+3)/4 + (y-1)/3 = 1

2x - y = 12

(x,y)?

(5,-2)

Geometry

100

The length of a rectangle is 3 less than 4 times the width. The perimeter is 34. What is the length and width?

Width = 4

Length = 13

200

The length of a rectangle is 5 more than 10 times the width. The perimeter is 230. What is the area of the rectangle?

1050

300

The lengths of the sides of a triangle are x, 16, and 31 where x is the shortest side. If the triangle is not isosceles, what is a possible value of x?

15<x<16

400

Find the geometric mean of 3, 4, 9, and 12.

6

500

A cylinder has a diameter of 6 and a height of 9. If point O is the center of the top of the cylinder and B lies on the circumference of the bottom of the cylinder, what is the straight-line distance between O and B?

Sqrt(90) or 9.49

Algebra 2

100

Simplify (125x⁴)^1/3

5x^4/3

200

Which function is even?

a) f(x) = sin x

b) f(x) = x² - 4

c) f(x) = |x - 2| + 5

d) f(x) = x⁴ + 3x³ + 4

b) f(x) = x² - 4

300

What is the inverse of 6x - 4?

(x + 4)/6

400

If A = -3 + 5i, B = 4 - 2i, and C = 1 + 6i, where i is the imaginary unit, what is A - BC equal to?

A - BC = -19 - 17i

500

Simplify (y³ - 4y² - 29y + 12)/(y + 4)

y² - 8y + 3

Pre-Calc

100

If f(x) = x² - 4 and g(x) = 3 - x, what is f(g(5))?

f(g(5)) = 0

200

Which of the following equations would create a horizontal stretch of the graph of y=x² by a factor of 4?

a) y= 4x²

b) y= .25x²

c) y= (.25x)²

d) y= (4x)²

c) y= (.25x)²

300

What is the domain of the function?

(x² + 4x + 4)/(x³ - 3x² - x + 3)

(-∞,-1)u(-1,1)u(1,3)u(3,∞)

or

X≠-1,1 & 3

400

lim_x➔4 (x² - 5x + 4)/(x + 1)(√x - 2)=?

12/5

500

Find lim_h➔0 [g(x+h) - g(x)]/h

if g(x) = 4x³ + 2x² + 5x - 3

12x² + 4x + 5

Calculus

100

What is the limit definition for derivatives?

lim_h➔0 ( f(x+h)-f(x) )/h

200

If the given function is a composite function. 

f(x)=e^2x

Identify the inner and outer function

Inner = 2x

Outer = e^x

300

If f(x) = 1 - 2x + x² and g(x) = 1 + 2x + x²,

Simplify ∫[f'(x)g(x) + f(x)g'(x)]d/dx

x⁴ - 2x² + 1 = (x² - 1)²

400

If x is a real number, what is the minimum of 

7x⁴ + 10x³ + 3x² + 4x + 4?

Minimum = 0

500

Differentiate the following equation:

f(x) = 4e^2xcos(2x)

8e^2x[cos(2x) - sin(2x)]