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2021 Amc 12 A Spring Amc Class 12 Maths Problems and Solutions
AMC Class 12
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English > Maths > All > 2021 Amc 12 A Spring
Question
Level
Action
Under what conditions is $$\sqrt{a^{2}+b^{2}}=a+b$$ true, where $$a$$ and $$b$$ are real numbers?......
Level 1
What is the least possible value of $$(x y-1)^{2}+(x+y)^{2}$$ for real numbers $$x$$ and $$y$$ ?......
Level 1
The sum of two natural numbers is $$17,402$$ . One of the two numbers is divisible by $$10 $$. If th......
Level 2
When a student multiplied the number $$66$$ by the repeating decimal, $$1.ababab.. = 1.\overline {ab......
Level 2
A deck of cards has only red cards and black cards. The probability of a randomly chosen card being ......
Level 2
A sequence of numbers is defined by $$D_0=0, D_1=0, D_2=1$$ and $$D_n= D{n-1}+D{n-3}$$ for $$n \geq ......
Level 2
In the following list of numbers, the integer $$n$$ appears $$n$$ times in the list for $$1 \leq n \......
Level 2
Trapezoid $$A B C D$$ has $$\overline{A B} || \overline{C D}, B C=C D=43$$, and $$\overline{A D} \pe......
Level 2
Let $$f$$ be a function defined on the set of positive rational numbers with the property that $$f(a......
Level 2
How many solutions does the equation $$\sin (\frac{\pi}{2} \cos x)=\cos (\frac{\pi}{2} \sin x)$$ hav......
Level 2
Which of the following is equivalent to
$$(2+3)(2^{2}+3^{2})(2^{4}+3^{4})(2^{8}+3^{8})(2^{16}+3^{16}......
Level 3
Two right circular cones......
Level 3
A laser is placed at the point $$(3,5)$$. The laser beam travels in a straight line. Larry wants the......
Level 3
What is the value of
$$(\sum{k=1}^{20} \log {5^{k}} 3^{k^{2}}) \cdot(\sum{k=1}^{100} \log {9 k} 25^{......
Level 3
A choir director must select a group of singers from among his $$6$$ tenors and $$8$$ basses. The on......
Level 3
All the roots of the polynomial $$z^{6}-10 z^{5}+A z^{4}+B z^{3}+C z^{2}+D z+16$$ are positive integ......
Level 4
Suppose that on a parabola with vertex $$V$$ and a focus $$F$$ there exists a point $$A$$ such that ......
Level 4
Suppose that the roots of the polynomial $$P(x)=x^{3}+a x^{2}+b x+c$$ are $$\cos \frac{2 \pi}{7}, \c......
Level 4
Frieda the frog begins a sequence of hops on a $$3 \times 3$$ grid of squares, moving one square on ......
Level 4