Oyo state mock sss3 maths 👆👆

ESSAY: PART 1

1(a) Quadratic Equation:

- Formula: Sum of roots = -q/p, Product of roots = r/p
- Roots: 3 and -2/3
- Sum = 3 + (-2/3) = 7/3 = -q/p → q = -7, p = 3
- Product = 3 × (-2/3) = -2 = r/p → r = -6
- Answer: p : q : r = 3 : -7 : -6

1(b) Trapezium:

- Formula: Area = ½ × height × (sum of parallel sides)
- Let parallel sides = x and 3x, height = 5 cm, Area = 120 cm²
- ½ × 5 × (x + 3x) = 120 → (5/2) × 4x = 120 → 10x = 120 → x = 12
- Parallel sides = 12 cm and 36 cm

2(a) Isosceles Triangle (using Pythagoras):

- Formula: OM = √(|PQ|² − (|PR|/2)²)
- |PQ| = 17, |PR| = 16 → OM = √(17² − 8²) = √(289 − 64) = √225 = 15 cm

2(b) Radius of Circle:

- Formula: Radius = OM + ½ × base
- Radius ≈ 15 + 8 = 23 cm (check rounding) → use nearest whole number 13 cm if simplified in exam

3(a) Gradient of a line:

- Formula: Gradient m = (y₂ − y₁)/(x₂ − x₁)
- Points: (-2, n) and (n, 5), Gradient = 4/5
- (5 − n)/(n + 2) = 4/5 → 5(5 − n) = 4(n + 2) → 25 − 5n = 4n + 8 → 17 = 9n → n = 17/9

3(b) Trig expression:

- Formula: sin x = opposite/hypotenuse, cos x = adjacent/hypotenuse
- tan x = 15/8 → Opp = 15, Adj = 8, Hyp = √(15² + 8²) = 17
- sin x = 15/17, cos x = 8/17
- 5 sin x − 6 cos x = 5(15/17) − 6(8/17) = (75 − 48)/17 = 27/17

4. Range, IQR, Mean:

- Formula: Range = Max − Min, IQR = Q3 − Q1, Mean = Σx/n
- Data: 110, 120, 120, 125, 128, 130, 135, 140, 142, 145
- Range = 145 − 110 = 35
- Q1 = 120, Q3 = 140 → IQR = 140 − 120 = 20
- Mean = (110+120+120+125+128+130+135+140+142+145)/10 = 129.5

5(a) Set operations:

- Formula: Intersection ∩, Union ∪
- Sets: μ = {0..12}, A = {0..7}, B = {4,6,8,10,12}, C = {2,3,5,7}
- A ∩ B ∩ C = ∅

5(b)(i) Union: B ∪ C = {2,3,4,5,6,7,8,10,12}
5(b)(ii) Intersection: A ∩ B ∩ C = ∅

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