Algebra 2 - Diagnostic Test

For the expression 2x – 10 + 5y, the constants are x and y.

• True

• False

Answer explanation

The constants in the expression 2x – 10 + 5y are the numerical values, which are -10. The variables x and y are not constants; they can change. Therefore, the statement is False.

• True

• False

Answer explanation

The statement is false because in the expression 2πr, π (pi) is a mathematical constant approximately equal to 3.14, not a variable. Variables are typically represented by letters like x or y.

Three consecutive integers can be represented as n, 2n, and 3n.

• True

• False

Answer explanation

The statement is false. Three consecutive integers can be represented as n, n+1, and n+2, not n, 2n, and 3n. Therefore, the correct answer is False.

The expression –11a + 7a simplifies to –18a.

• True

• False

Answer explanation

The expression –11a + 7a simplifies to –4a, not –18a. Therefore, the statement is false.

The expression 3x – (x + 4) simplifies to 2x + 4.

• True

• False

Answer explanation

To simplify 3x - (x + 4), distribute the negative: 3x - x - 4 = 2x - 4, not 2x + 4. Therefore, the statement is false.

• True

• False

Answer explanation

To evaluate the expression, follow the order of operations: 5×4=20, then 3+20=23. The right side is 8×4=32. Since 23 does not equal 32, the statement is false.

• True

• False

Answer explanation

To verify, calculate the left side: (12 - 8) / 2 = 4 / 2 = 2. Now calculate the right side: 6 - 4 = 2. Both sides equal 2, so the statement is True.

• True

• False

Answer explanation

The inequality x ≤ 5 indicates that x can be any value less than 5 or exactly equal to 5. Therefore, the statement is true.

The negation of x > 5 is x < 5.

• True

• False

Answer explanation

The negation of x > 5 is x ≤ 5, not x < 5. Therefore, the statement is false.

7 is a solution to 3r + 4 > 25.

• True

• False

Answer explanation

To check if 7 is a solution, substitute r with 7: 3(7) + 4 = 21 + 4 = 25. The inequality 25 > 25 is false. Therefore, 7 is not a solution to the inequality, making the statement false.