TOK Math Jeopardy

Functions

100

f(x) = 2x + 3 and g(x) = x², find (f ∘ g)(2).

11

200

Find the inverse of f(x) = (x + 1)/(x − 2)

f⁻¹(x) = (2x + 1)/(x − 1)

300

The graph of y = f(x) is transformed to 

y = 2f(x − 3) + 1. 

Where does the point (1, 4) on f end up?

(4, 9)

400

Find the values of k for which x² + kx + 9 = 0 has two distinct real roots.

k < −6 or k > 6

500

Solve |x − 1| > |2x + 3|

−4 < x < −2/3

Algebra, Sequences & Logs

100

Find the 10th term of the arithmetic sequence 5, 8, 11, ...

32

200

Find the sum to infinity of the geometric series 12 + 4 + 4/3 + ...

18

300

Find the coefficient of x³ in the expansion of (2 + x)⁵

40

400

Solve ln x + ln(x − 3) = ln 4

x = 4

500

Solve 2^(2x) − 5(2^x) + 4 = 0

x = 0 or x = 2

Trigonometry

100

Convert 210° to radians.

7π/6

200

Find the exact value of sin(π/3)·cos(π/6).

3/4

300

If sin θ = 3/5 and θ is acute, find sin 2θ.

24/25

400

Solve sin 2x = cos x for 0 ≤ x ≤ 2π.

x = π/6, π/2, 5π/6, 3π/2

500

Solve 2sin²x = 1 + cos x for 0 ≤ x ≤ 2π.

x = π/3, π, 5π/3

Differentiation

100

Differentiate f(x) = 3x⁴ − 5x.

f′(x) = 12x³ − 5

200

Differentiate y = e^(2x) sin x.

dy/dx = e^(2x)(2sin x + cos x)

300

Differentiate y = ln(x² + 1).

dy/dx = 2x/(x² + 1)

400

Use implicit differentiation to find dy/dx at (3, 4) on the curve x² + y² = 25.

-3/4

500

Find the x-coordinate of the minimum point of f(x) = x² − 6x + 5.

x=3

Integration

100

Find ∫(6x² + 4) dx

2x³ + 4x + C

200

Evaluate ∫₀² 3x² dx.

8

300

Find ∫2x·e^(x²) dx using substitution.

e^(x²) + C

400

Find the area enclosed between y = x² and y = 2x.

4/3

500

The region under y = √x from x = 0 to x = 4 is rotated 360° about the x-axis. Find the volume.

8π