1. If 3ᵃ = 27 and 3ᵇ = 9, what is 3ᵃ⁺ᵇ?
Since 27 = 3³, a = 3. Since 9 = 3², b = 2. Therefore 3ᵃ⁺ᵇ = 3⁵ = 243.
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Since 27 = 3³, a = 3. Since 9 = 3², b = 2. Therefore 3ᵃ⁺ᵇ = 3⁵ = 243.
Subtract the fixed charge: 31.20 - 4.20 = 27.00. Then divide by 1.80, giving d = 15 km.
Use tan(36°) = height / 42. The height is 42 × tan(36°) = 30.516..., which rounds to 30.5 m.
Areas scale by the square of the length scale factor. The area factor is (3 / 2)² = 9 / 4, so the larger area is 48 × 9 / 4 = 108 cm².
The six known values sum to 85. Seven values with mean 15 must sum to 105, so x = 105 - 85 = 20.
The probability is 5 / 8 for the first blue and 4 / 7 for the second blue after one blue is removed. So P(two blue) = 5 / 8 × 4 / 7 = 20 / 56 = 5 / 14.
Year 9 maths practice should build senior-readiness through index laws, linear modelling, trigonometry, similarity, statistics, and probability. These examples show the worked reasoning before the no-login Year 9 Maths demo.
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