Mathematics Solutions (SSS2)

Edwin Ogie Library — Math Solutions

Question 1 — Simplify

(2x² - 8) / (4x) × (6x) / (x² - 4)

Working:

2x² - 8 = 2(x² - 4)

x² - 4 = (x - 2)(x + 2)

So (2x² - 8)/(4x) × (6x)/(x² - 4) = [2(x² - 4)]/(4x) × (6x)/(x² - 4)

Cancel (x² - 4): = [2/(4x)] × 6x = 12x/(4x) = 3

Answer: 3 (x ≠ 0, ±2)

Question 2 — Solve for x

3x² - 7x + 2 = 0

Working:

Factor the quadratic:

3x² - 7x + 2 = (3x - 1)(x - 2)

So 3x - 1 = 0 ⇒ x = 1/3 or x - 2 = 0 ⇒ x = 2

Answer: x = 1/3 or x = 2

Question 3 — Variation

If y varies directly as x and inversely as z, and y = 4 when x = 8 and z = 2, find y when x = 10 and z = 4.

Working:

y = k * x / z

Given y = 4 when x = 8 and z = 2 4 = k*(8/2) ⇒ 4 = 4k ⇒ k = 1 So y = x / z For x = 10, z = 4 ⇒ y = 10/4 = 5/2 = 2.5

Answer: 5/2 (2.5)

Question 4 — Trigonometry

If sin θ = 3/5 and θ is in the first quadrant, find cos θ and tan θ.

Working:

sin θ = 3/5 ⇒ opposite = 3, hypotenuse = 5

Adjacent = √(5² - 3²) = √16 = 4

cos θ = adjacent/hypotenuse = 4/5 tan θ = opposite/adjacent = 3/4

Answer: cos θ = 4/5, tan θ = 3/4

Prepared by Edwin Ogie Library — edwinogie.blogspot.com