🧮 Algebra Warmups (15 Easy Mixed Problems)
Recommended: 30–40 minutes. No calculator.
Problems
1.
Tags: Basic Operations · Easy · source: AMC10 2018 #1
What is the value of $2 + 0 + 1 + 8$?
A) $9$
B) $10$
C) $11$
D) $12$
E) $13$
Answer & Solution
Answer: C
$2 + 0 + 1 + 8 = 11$.
2.
Tags: Factoring · Easy · source: Original (AMC-style)
What is $x^2 - 1$ factored?
A) $(x-1)^2$
B) $(x+1)^2$
C) $(x-1)(x+1)$
D) $(x-1)(x-1)$
E) Cannot be factored
Answer & Solution
Answer: C
This is a difference of squares: $x^2 - 1 = x^2 - 1^2 = (x-1)(x+1)$.
3.
Tags: Linear Equations · Easy · source: Original (AMC-style)
If $2x + 3 = 11$, what is $x$?
A) $2$
B) $3$
C) $4$
D) $5$
E) $6$
Answer & Solution
Answer: C
Subtracting 3: $2x = 8$, so $x = 4$.
4.
Tags: Exponents · Easy · source: Original (AMC-style)
What is $2^3$?
A) $4$
B) $6$
C) $8$
D) $9$
E) $12$
Answer & Solution
Answer: C
$2^3 = 2 \cdot 2 \cdot 2 = 8$.
5.
Tags: Absolute Value · Easy · source: Original (AMC-style)
What is $|5|$?
A) $-5$
B) $0$
C) $5$
D) $10$
E) $25$
Answer & Solution
Answer: C
$|5| = 5$ since 5 is positive.
6.
Tags: Systems · Easy · source: Original (AMC-style)
If $x + y = 5$ and $x - y = 1$, what is $x$?
A) $1$
B) $2$
C) $3$
D) $4$
E) $5$
Answer & Solution
Answer: C
Adding the equations: $(x+y) + (x-y) = 5 + 1$, so $2x = 6$ and $x = 3$.
7.
Tags: Radicals · Easy · source: Original (AMC-style)
What is $\sqrt{36}$?
A) $4$
B) $6$
C) $8$
D) $9$
E) $12$
Answer & Solution
Answer: B
$\sqrt{36} = 6$ since $6^2 = 36$.
8.
Tags: Quadratics · Easy · source: Original (AMC-style)
What is the value of $x^2$ when $x = 4$?
A) $8$
B) $12$
C) $16$
D) $20$
E) $24$
Answer & Solution
Answer: C
When $x = 4$, we have $x^2 = 4^2 = 16$.
9.
Tags: Rational Expressions · Easy · source: Original (AMC-style)
What is $\frac{12}{3}$?
A) $3$
B) $4$
C) $6$
D) $9$
E) $12$
Answer & Solution
Answer: B
$\frac{12}{3} = 4$.
10.
Tags: Sequences · Easy · source: Original (AMC-style)
What is the next term in the sequence $2, 4, 6, 8, \ldots$?
A) $9$
B) $10$
C) $11$
D) $12$
E) $13$
Answer & Solution
Answer: B
This is an arithmetic sequence with common difference 2, so the next term is $8 + 2 = 10$.
11.
Tags: Factoring · Easy · source: Original (AMC-style)
What is $x^2 + 2x + 1$ factored?
A) $(x+1)^2$
B) $(x-1)^2$
C) $(x+1)(x-1)$
D) $(x+2)(x+1)$
E) Cannot be factored
Answer & Solution
Answer: A
This is a perfect square: $x^2 + 2x + 1 = (x+1)^2$.
12.
Tags: Linear Equations · Easy · source: Original (AMC-style)
If $3x - 2 = 7$, what is $x$?
A) $1$
B) $2$
C) $3$
D) $4$
E) $5$
Answer & Solution
Answer: C
Adding 2: $3x = 9$, so $x = 3$.
13.
Tags: Exponents · Easy · source: Original (AMC-style)
What is $3^2$?
A) $6$
B) $8$
C) $9$
D) $12$
E) $15$
Answer & Solution
Answer: C
$3^2 = 3 \cdot 3 = 9$.
14.
Tags: Absolute Value · Easy · source: Original (AMC-style)
What is $|-7|$?
A) $-7$
B) $0$
C) $7$
D) $14$
E) $49$
Answer & Solution
Answer: C
$|-7| = 7$ since the absolute value of a negative number is its positive value.
15.
Tags: Systems · Easy · source: Original (AMC-style)
If $2x + y = 7$ and $x + y = 5$, what is $x$?
A) $1$
B) $2$
C) $3$
D) $4$
E) $5$
Answer & Solution
Answer: B
Subtracting the second equation from the first: $(2x+y) - (x+y) = 7 - 5$, so $x = 2$.
Answer Key
| # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ans | C | C | C | C | C | C | B | C | B | B | A | C | C | C | B |