Algebra, trigonometry, coordinate geometry and calculus
Model answer and review guidance
-4
(x−3)²−4 has minimum −4.
ORIGINAL WRITTEN REHEARSAL
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Algebra, trigonometry, coordinate geometry and calculus
-4
(x−3)²−4 has minimum −4.
Algebra, trigonometry, coordinate geometry and calculus
2
(8−2)/(4−1)=2.
Algebra, trigonometry, coordinate geometry and calculus
1
The identity is 1 for every real angle.
Algebra, trigonometry, coordinate geometry and calculus
[x³] from 0 to 2 = 8.
Show antiderivative and both bounds.
Algebra, trigonometry, coordinate geometry and calculus
(x−2)(x−3)=0, so x=2 or 3; both give zero on substitution.
Show both roots and a check.
For the worked-case reasoning question, a rectangle has perimeter 20 length units. Let one side be x, with 0 < x < 10. Other questions state their own dimensions.
Multi-step numerical reasoning and checking solutions
9
Half-perimeter is 14; 14−5=9.
Multi-step numerical reasoning and checking solutions
49
The 7×7 square gives 49.
Multi-step numerical reasoning and checking solutions
5
18/3.6=5.
Multi-step numerical reasoning and checking solutions
A=10x−x²=25−(x−5)²≤25, with equality at x=5.
Use the domain and equality condition.
Multi-step numerical reasoning and checking solutions
It violates the original physical domain.
Check original constraints rather than the transformed equation alone.
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