Math Club Jeopardy

Functions

100

Express 2x² - 18x + 49 in the form a(x - b)² + c

2(x - 9/2)² +17/2

200

When the function q (x) = x³ + kx² − 7x + 3 is divided by (x +1) the remainder is seven times the remainder that is found when the function is divided by (x + 2) . 

Find the value of k.

k=-2

300

In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.

How many students like only one of tea or coffee?

100

400

Expand (2-3x)⁵

32-240x+720x²-1080x³+810x⁴-243x⁵

500

Find the sum of all integers between 10 and 100 that are divisible by 7

728

Logarithm

100

Solve the equation Log₃ 243+Log₃ 9=

7

200

find log₁₀(4) - log₁₀(40)

-1

300

Consider a = log₂3 × log₃4 × log₄5 × … × log ₃₁32. Given that a∈Z, find the value of a.

a=5

400

Find integer values of m and n for which

m - nlog₃2 = 10 log₉6

m=5

n=-5

500

Solve the equation 4^x + 2^x+2 = 3

x= log₂ (-2+root7)

Trigonometry

100

Given that sin(x)=3/5 where "x" is an acute angle, find cos(x)

4/5

200

In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee. 

How many students like only tea?

60

300

 In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basket ball both. 5% liked watching none of these games.

How many students like watching all the three games?

49%

400

Solve the equation 0.5(x+2) = |x-2|

x=2/3

x=6

500

Find the solution to 

|x+1| = |x-3|

1

something

100

Find the number of ways in which 7 toys can be arranged on a shelf

7! = 5040

200

Out of forty students, 14 are taking English Composition and 29 are taking Chemistry.

If five students are in both classes, how many students are in neither class?

2

300

Four numbers have mean of 13, median is 14, and mode is 15

Find the four numbers

9, 13, 15, 15

400

log₃x - log₃5 = 1 + log₃4

60

500

3ln3 - ln9 = -lnx

find x

x = 1/3

Miscellaneous

100

x + 5y = 7

−2x − 7y = −5

x = -8

y=3

200

Is there a solution to this system?

x − 2y − 6z = 12

2x + 4y + 12z = −17

x − 4y − 12z = 22

No

300

2x + z = −8

x − 2y − 3z = 0

−x + y + 2z = 3

x=-4

y=-5

z=2

400

The sum of the squares of five consecutive positive integers is 9255. What is the value of the square of the next integer?

2116

500

x^x...=1/3

1/27