Question 1
Multiple ChoiceIf 3x + 6 = 21, what is the value of x?
Explanation
Subtract 6 from both sides: 3x = 15. Divide by 3: x = 5. Check: 3(5) + 6 = 15 + 6 = 21.
Question 2
Multiple ChoiceWhat is 25% of 80?
Explanation
25% is one quarter, so 80 divided by 4 equals 20. Check: 0.25 times 80 = 20.
Question 3
Multiple ChoiceA right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
Explanation
By the Pythagorean theorem, the hypotenuse is the square root of (3 squared + 4 squared) = square root of (9 + 16) = square root of 25 = 5.
Question 4
Multiple ChoiceWhat is the value of 2^3 × 2^2 ?
Explanation
When multiplying powers with the same base, add the exponents: 2^(3+2) = 2^5 = 32. Check: 8 times 4 = 32.
Question 5
Multiple ChoiceWhat is the area of a rectangle with length 8 and width 5?
Explanation
Area of a rectangle is length times width: 8 times 5 = 40.
Question 6
Multiple ChoiceWhat is the mean (average) of the numbers 4, 8, and 6?
Explanation
Add the values: 4 + 8 + 6 = 18. Divide by the count, 3: 18 divided by 3 = 6.
Question 7
True FalseIn the expression 2 + 3 × 4, following the order of operations, the result is 14.
Explanation
By order of operations, multiply first: 3 times 4 = 12, then add 2 to get 14. The statement is true.
Question 8
True FalseThe line y = 4x + 1 has a slope of 1.
Explanation
In slope-intercept form y = mx + b, the slope m is the coefficient of x, which is 4, not 1. So the statement is false.
Question 9
Multiple SelectWhich of the following are solutions to the equation x^2 = 9 ? (Select all that apply.)
Explanation
Both 3 and -3 satisfy x^2 = 9, because 3 squared = 9 and (-3) squared = 9. The value 9 is not a solution since 9 squared = 81.
Question 10
Multiple SelectThe ratio of boys to girls in a class is 2 to 3. Which statements must be true? (Select all that apply.)
Explanation
A 2:3 ratio means for every 2 boys there are 3 girls, so there are more girls than boys, and a class of 20 could have 8 boys and 12 girls (which is 2:3). The class total must be a multiple of 5, so 12 students total is impossible.