Math worksheet for evaluating algebraic expressions with provided values.

Here are the step-by-step solutions for each problem on the worksheet.

1) $p^2 + m$; where $m = 2, p = 1$
* Substitute the values: $(1)^2 + 2$
* Square the 1: $1 \times 1 = 1$
* Add 2: $1 + 2 = 3$
* Answer: 3

2) $x - x^2 + 1 + y$; where $x = 1, y = -1$
* Substitute the values: $1 - (1)^2 + 1 + (-1)$
* Square the 1: $1 - 1 + 1 - 1$
* Calculate from left to right:
* $1 - 1 = 0$
* $0 + 1 = 1$
* $1 - 1 = 0$
* Answer: 0

3) $p(r + q)$; where $p = 3, q = 6, r = 4$
* Substitute the values: $3(4 + 6)$
* Solve inside the parentheses first: $4 + 6 = 10$
* Multiply by 3: $3 \times 10 = 30$
* Answer: 30

4) $y - (x - x)$; where $x = 6, y = 2$
* Substitute the values: $2 - (6 - 6)$
* Solve inside the parentheses first: $6 - 6 = 0$
* Subtract from y: $2 - 0 = 2$
* Answer: 2

5) $p(p + m)$; where $m = 1, p = 6$
* Substitute the values: $6(6 + 1)$
* Solve inside the parentheses first: $6 + 1 = 7$
* Multiply: $6 \times 7 = 42$
* Answer: 42

6) $j^2 h$; where $h = 2, j = 4$
* Substitute the values: $4^2 \times 2$
* Square the 4 first: $4 \times 4 = 16$
* Multiply by 2: $16 \times 2 = 32$
* Answer: 32

7) $xy \div 6$; where $x = 5, y = 6$
* Substitute the values: $5 \times 6 \div 6$
* Multiply first: $5 \times 6 = 30$
* Divide by 6: $30 \div 6 = 5$
* Answer: 5

8) $2p - q$; where $p = 4, q = -2$
* Substitute the values: $2(4) - (-2)$
* Multiply: $8 - (-2)$
* Subtracting a negative is the same as adding: $8 + 2 = 10$
* Answer: 10

9) $y^2 - x$; where $x = 1, y = 5$
* Substitute the values: $5^2 - 1$
* Square the 5: $5 \times 5 = 25$
* Subtract 1: $25 - 1 = 24$
* Answer: 24

10) $6 - (p - m)$; where $m = 1, p = -5$
* Substitute the values: $6 - ((-5) - 1)$
* Solve inside the parentheses: $-5 - 1 = -6$
* Now the equation is: $6 - (-6)$
* Subtracting a negative becomes addition: $6 + 6 = 12$
* Answer: 12

11) $(x - y) \div 2$; where $x = 3, y = 1$
* Substitute the values: $(3 - 1) \div 2$
* Solve inside the parentheses: $3 - 1 = 2$
* Divide by 2: $2 \div 2 = 1$
* Answer: 1

12) $(x + y)^2$; where $x = 1, y = 1$
* Substitute the values: $(1 + 1)^2$
* Solve inside the parentheses: $1 + 1 = 2$
* Square the result: $2^2 = 4$
* Answer: 4

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Final Answer:
1) 3
2) 0
3) 30
4) 2
5) 42
6) 32
7) 5
8) 10
9) 24
10) 12
11) 1
12) 4