Algebra Jeopardy Project

Linear Equations

100

Solve for x:

x - 4 = 9

x = 9 + 4 = 13

200

Solve for x:

2x + 3 = 7

2x = 7 - 3 = 4 > x = 4/2 = 2

300

Find the slope-intercept form of the line that passes through the points (1, 2) and (3, 6).

Slope:

m = 6-2 =4 = 2 

      _______

3 - 1         2

400

Write the equation of the line in standard form that passes through (-2, 3) with slope 1/2.

Y - 3 = 1/2 (X+2) 

500

A line passes through the point (5, -1) and is perpendicular to the line y = -3x + 2. What is the equation of the new line in slope-intercept form?

Slope of original line: m = -3

Perpendicular slope: m = 1/3 (negative reciprocal)

Arithmetic sequences

100

What is the next term in the sequence:

3, 6, 9, 12, ?

15

200

Find the common difference in the sequence:

10, 7, 4, 1, …

-3

300

What is the 10th term of the arithmetic sequence:

2, 5, 8, 11,…

29

400

If the 3rd term of an arithmetic sequence is 12 and the 7th term is 24, what is the first term?

6

500

The sum of the first 20 terms of an arithmetic sequence is 710. The first term is 5. What is the common difference?

3

Polynomials

100

Simplify: (3x + 2) + (2x + 5) 

3x + 2x + 2 + 5 = 5x + 7

200

Simplify:

(4x - 3)(2)

Distribute:

4x • 2 - 3 • 2 = 8x - 6

300

Multiply the polynomials:

(x + 2)(x + 5)

x² + 5x + 2x + 10 = x² + 7x + 10

400

Subtract: (3x² + 4x - 2) - (x² - 5x + 6) 

(3x² - x²) + (4x + 5x) + (-2 - 6) = 2x²

500

Factor completely: x³ + 2x² - x - 2 

(x + 2)(x-1) (x+1) 

systems of equations

100

Solve by substitution: y = 3x

                                 x = 2 

Substitute x = 2  into y = 3x 

y = 3(2) =6 

200

Solve by elimination 
x + y = 10 

x - y = 4 

(7,3)

300

Solve by substitution:

2x + y = 7 

y = x + 1

(2,3)

400

Solve: 

3x - 2y = 6 

x + y = 4 

(14/5, 6/5)

500

A movie theater sells 2 types of tickets: child tickets cost $5 each, and adult tickets cost $8 each. If 120 tickets were sold for a total of $780, how many of each ticket type were sold?

60 child tickets, 60 adult tickets

inequalities

100

Solve the inequality:

x + 3 < 10

x < 10 -3 = x < 7 

200

Solve the inequality: 

5x > 20

x > 20/5 = x > 4

300

Solve and graph the on a number line: 

2x < 8 = x < 4 

2x < 8 = x < 4

400

Solve the compound inequality: 

-3 < 2x - 1 < 5

-1 < x < 3

500

A school club is fundraising by selling T-shirts for $12 and hats for $8. They need to raise at least $240. Let t be the number of T-shirts and h the number of hats sold. Write and solve the inequality if they sell 10 T-shirts.

h > 120/8 = 15