The maximum value of f(x) = sin x + √(3)cos x is:

R = √(1 + 3) = 2, so f(x) = 2sin(x + π/3). Max value: 2.

Daily Math Problems — June 12, 2026: Financial Mathematics, Descriptive Statistics & Sampling, Trigonometry

Problems & worked solutions

RO M1

A deposit of $$ 2,000$ earns annual compound interest at $5 %$ . The balance after $2$ years is:

Show answer & worked solution

$A = 2000 \cdot {1.05}^{2} = 2000 \cdot 1.1025 = $ 2,205$ .

RO M1

The range of ${12, 7, 22, 9, 18, 4}$ is:

Show answer & worked solution

Max $= 22$ , min $= 4$ , so range $= 22 - 4 = 18$ .

RO M1

The maximum value of $f (x) = \sin x + \sqrt{3} \cos x$ is:

Show answer & worked solution

$R = \sqrt{1 + 3} = 2$ , so $f (x) = 2 \sin (x + π / 3)$ . Max value: $2$ .

Problems & worked solutions

RO M1

A deposit of $$ 2,000$ earns annual compound interest at $5 %$ . The balance after $2$ years is:

Show answer & worked solution

$A = 2000 \cdot {1.05}^{2} = 2000 \cdot 1.1025 = $ 2,205$ .

RO M1

The range of ${12, 7, 22, 9, 18, 4}$ is:

Show answer & worked solution

Max $= 22$ , min $= 4$ , so range $= 22 - 4 = 18$ .

RO M1

The maximum value of $f (x) = \sin x + \sqrt{3} \cos x$ is:

Show answer & worked solution

$R = \sqrt{1 + 3} = 2$ , so $f (x) = 2 \sin (x + π / 3)$ . Max value: $2$ .