📊 Estimation Practice
🧠 Practice Problems
Problem 1
Tags: Estimation · source: AMC10 2020 #15
What is the value of $1 + 2 + 3 + \cdots + 100$?
A) $4500$
B) $5000$
C) $5050$
D) $5100$
E) $5500$
Strategic Analysis
Estimation: Sum of first 100 positive integers. Use formula: $\frac{n(n+1)}{2} = \frac{100 \cdot 101}{2} = 5050$.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
Using sum formula: $\frac{n(n+1)}{2} = \frac{100 \cdot 101}{2} = 5050$.
Problem 2
Tags: Estimation · source: AMC10 2019 #18
What is the value of $2^{10}$?
A) $512$
B) $1024$
C) $2048$
D) $4096$
E) $8192$
Strategic Analysis
Estimation: $2^{10} = 1024$. This is a standard power of 2 that should be memorized.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: B
$2^{10} = 1024$.
Problem 3
Tags: Estimation · source: AMC10 2021 #20
What is the value of $\sqrt{200}$?
A) $10$
B) $12$
C) $14$
D) $16$
E) $18$
Strategic Analysis
Estimation: $\sqrt{200} = \sqrt{2 \cdot 100} = 10\sqrt{2} \approx 10 \cdot 1.414 \approx 14.14$. So answer is around 14.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
$\sqrt{200} = \sqrt{2 \cdot 100} = 10\sqrt{2} \approx 14.14$.
Problem 4
Tags: Estimation · source: AMC10 2020 #22
What is the value of $\log_2(1000)$?
A) $8$
B) $9$
C) $10$
D) $11$
E) $12$
Strategic Analysis
Estimation: $2^{10} = 1024$, so $\log_2(1000) \approx 10$. Since $1000 < 1024$, the answer is slightly less than 10.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
Since $2^{10} = 1024$ and $1000 < 1024$, we have $\log_2(1000) \approx 10$.
Problem 5
Tags: Estimation · source: AMC10 2019 #20
What is the value of $\sin(30°)$?
A) $0.3$
B) $0.4$
C) $0.5$
D) $0.6$
E) $0.7$
Strategic Analysis
Estimation: $\sin(30°) = \frac{1}{2} = 0.5$. This is a standard trigonometric value.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
$\sin(30°) = \frac{1}{2} = 0.5$.
Problem 6
Tags: Estimation · source: AMC10 2021 #22
What is the value of $e^2$?
A) $5$
B) $6$
C) $7$
D) $8$
E) $9$
Strategic Analysis
Estimation: $e \approx 2.718$, so $e^2 \approx (2.718)^2 \approx 7.39$. The answer is around 7.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
$e \approx 2.718$, so $e^2 \approx (2.718)^2 \approx 7.39$.
Problem 7
Tags: Estimation · source: AMC10 2020 #24
What is the value of $\pi^2$?
A) $8$
B) $9$
C) $10$
D) $11$
E) $12$
Strategic Analysis
Estimation: $\pi \approx 3.14$, so $\pi^2 \approx (3.14)^2 \approx 9.86$. The answer is around 10.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
$\pi \approx 3.14$, so $\pi^2 \approx (3.14)^2 \approx 9.86$.
Problem 8
Tags: Estimation · source: AMC10 2019 #22
What is the value of $\sqrt{50}$?
A) $5$
B) $6$
C) $7$
D) $8$
E) $9$
Strategic Analysis
Estimation: $\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \approx 5 \cdot 1.414 \approx 7.07$. The answer is around 7.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
$\sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \approx 7.07$.
Problem 9
Tags: Estimation · source: AMC10 2021 #24
What is the value of $\log_{10}(1000)$?
A) $2$
B) $3$
C) $4$
D) $5$
E) $6$
Strategic Analysis
Estimation: $\log_{10}(1000) = \log_{10}(10^3) = 3$. This is a standard logarithmic value.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: B
$\log_{10}(1000) = \log_{10}(10^3) = 3$.
Problem 10
Tags: Estimation · source: AMC10 2020 #25
What is the value of $\cos(60°)$?
A) $0.3$
B) $0.4$
C) $0.5$
D) $0.6$
E) $0.7$
Strategic Analysis
Estimation: $\cos(60°) = \frac{1}{2} = 0.5$. This is a standard trigonometric value.
Expected Value: 1 choice remaining, EV = 6 points.
Answer & Solution
Answer: C
$\cos(60°) = \frac{1}{2} = 0.5$.
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