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Mathematics 2022 — Higher Level (EV)

Junior Cycle · Mathematics · 2022 · Higher · English

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Algebra

Simplify: 3(x + 4) − 2(x − 1)

Worked solution
  1. Expand the brackets: 3×x + 3×4 − 2×x − 2×(−1)
  2. That gives: 3x + 12 − 2x + 2
  3. Collect like terms: (3x − 2x) + (12 + 2)
  4. Simplify: x + 14

Answer: x + 14

Geometry

A rectangle is 8 cm by 5 cm. Find the area and the perimeter.

Worked solution
  1. Area = length × width = 8 × 5 = 40 cm²
  2. Perimeter = 2(length + width) = 2(8 + 5) = 2 × 13 = 26 cm

Answer: Area 40 cm²; perimeter 26 cm

Number

What is 25% of 80?

Worked solution
  1. 25% means 25 out of 100, or one quarter.
  2. One quarter of 80: 80 ÷ 4 = 20
  3. Or: 0.25 × 80 = 20

Answer: 20

Trigonometry

In a right triangle, opposite = 5, adjacent = 12. Find sin θ, cos θ and tan θ.

Worked solution
  1. Hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13
  2. sin θ = opposite/hyp = 5/13
  3. cos θ = adjacent/hyp = 12/13
  4. tan θ = opposite/adjacent = 5/12

Answer: sin = 5/13; cos = 12/13; tan = 5/12

Statistics

Find the mean and median of: 4, 7, 7, 9, 13.

Worked solution
  1. Mean = (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8
  2. Ordered already; median is the middle value = 7

Answer: Mean 8; median 7

Algebra

Solve: 2x + 5 = 17

Worked solution
  1. Subtract 5 from both sides: 2x = 12
  2. Divide both sides by 2: x = 6
  3. Check: 2(6) + 5 = 12 + 5 = 17 ✓

Answer: x = 6

Practice samples (ClassReady demos)

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Sample

Simplify: 3(x + 4) − 2(x − 1)

Worked solution
  1. Expand the brackets: 3×x + 3×4 − 2×x − 2×(−1)
  2. That gives: 3x + 12 − 2x + 2
  3. Collect like terms: (3x − 2x) + (12 + 2)
  4. Simplify: x + 14

Answer: x + 14

Sample

Solve: 2x + 5 = 17

Worked solution
  1. Subtract 5 from both sides: 2x = 12
  2. Divide both sides by 2: x = 6
  3. Check: 2(6) + 5 = 12 + 5 = 17 ✓

Answer: x = 6

Sample

Expand and simplify: (x + 3)(x − 2)

Worked solution
  1. FOIL / distribute: x·x + x·(−2) + 3·x + 3·(−2)
  2. That gives: x² − 2x + 3x − 6
  3. Collect like terms: x² + x − 6

Answer: x² + x − 6

Sample

Solve: 3(2x − 1) = 4x + 7

Worked solution
  1. Expand: 6x − 3 = 4x + 7
  2. Subtract 4x from both sides: 2x − 3 = 7
  3. Add 3 to both sides: 2x = 10
  4. Divide by 2: x = 5
  5. Check: 3(10 − 1) = 27 and 4(5) + 7 = 27 ✓

Answer: x = 5