Practice HAT questions with answers and explanations.
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The exterior angles of any polygon sum to 360°.
For a regular octagon, each is 360° ÷ 8 = 45°.
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The number of diagonals is n(n - 3)/2.
For n = 6, this gives 6 × 3 ÷ 2 = 9.
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Substitute x = 5 into the function.
Then f(5) = 2(5) + 1 = 11.
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An angle subtended by a diameter at the circumference is a right angle.
This result is known as Thales' theorem.
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The three interior angles of every Euclidean triangle sum to 180°.
This is a fundamental angle property.
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The diameter is twice the radius.
Thus, 2 × 7 = 14 cm.
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The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
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The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
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A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
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When multiplying powers with the same base, add the exponents.
Thus, a³ × a⁵ = a⁸.
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When dividing powers with the same base, subtract the exponents.
Thus, x⁷ ÷ x³ = x⁴.
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Square the coefficient and multiply the exponent by 2.
This gives 2²a⁶ = 4a⁶.
