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2023 Higher English
Mathematics
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Mathematics
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Mathematics
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ClassReady-authored practice items tagged by syllabus topic (Algebra, Geometry, Number?). Build a timed pack for class ? not a scrape of SEC wording.
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Simplify: 3(x + 4) − 2(x − 1)
Worked solution
- Expand the brackets: 3×x + 3×4 − 2×x − 2×(−1)
- That gives: 3x + 12 − 2x + 2
- Collect like terms: (3x − 2x) + (12 + 2)
- Simplify: x + 14
Answer: x + 14
A rectangle is 8 cm by 5 cm. Find the area and the perimeter.
Worked solution
- Area = length × width = 8 × 5 = 40 cm²
- Perimeter = 2(length + width) = 2(8 + 5) = 2 × 13 = 26 cm
Answer: Area 40 cm²; perimeter 26 cm
What is 25% of 80?
Worked solution
- 25% means 25 out of 100, or one quarter.
- One quarter of 80: 80 ÷ 4 = 20
- Or: 0.25 × 80 = 20
Answer: 20
In a right triangle, opposite = 5, adjacent = 12. Find sin θ, cos θ and tan θ.
Worked solution
- Hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13
- sin θ = opposite/hyp = 5/13
- cos θ = adjacent/hyp = 12/13
- tan θ = opposite/adjacent = 5/12
Answer: sin = 5/13; cos = 12/13; tan = 5/12
Find the mean and median of: 4, 7, 7, 9, 13.
Worked solution
- Mean = (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8
- Ordered already; median is the middle value = 7
Answer: Mean 8; median 7
Solve: 2x + 5 = 17
Worked solution
- Subtract 5 from both sides: 2x = 12
- Divide both sides by 2: x = 6
- Check: 2(6) + 5 = 12 + 5 = 17 ✓
Answer: x = 6
Practice samples (ClassReady demos)
Not SEC papers ? short examples so maths step-by-step UI works offline.
Simplify: 3(x + 4) − 2(x − 1)
Worked solution
- Expand the brackets: 3×x + 3×4 − 2×x − 2×(−1)
- That gives: 3x + 12 − 2x + 2
- Collect like terms: (3x − 2x) + (12 + 2)
- Simplify: x + 14
Answer: x + 14
Solve: 2x + 5 = 17
Worked solution
- Subtract 5 from both sides: 2x = 12
- Divide both sides by 2: x = 6
- Check: 2(6) + 5 = 12 + 5 = 17 ✓
Answer: x = 6
Expand and simplify: (x + 3)(x − 2)
Worked solution
- FOIL / distribute: x·x + x·(−2) + 3·x + 3·(−2)
- That gives: x² − 2x + 3x − 6
- Collect like terms: x² + x − 6
Answer: x² + x − 6
Solve: 3(2x − 1) = 4x + 7
Worked solution
- Expand: 6x − 3 = 4x + 7
- Subtract 4x from both sides: 2x − 3 = 7
- Add 3 to both sides: 2x = 10
- Divide by 2: x = 5
- Check: 3(10 − 1) = 27 and 4(5) + 7 = 27 ✓
Answer: x = 5