Question 1
Multiple ChoiceSolve the system of equations:
Explanation
Substitute y = -2x + 5 into 3x + 2y = 1 to get 3x + 2(-2x + 5) = 1 → -x + 10 = 1 → x = 9, then y = -18 + 5 = -13.
Question 2
Multiple ChoiceAnna can paint a room in 4 hours and Ben can paint the same room in 6 hours. How long will it take them working together?
Explanation
Rates add: 1/4 + 1/6 = 5/12 rooms/hour, so time = 1 ÷ (5/12) = 12/5 hours = 2.4 hours = 2 hours 24 minutes.
Question 3
Multiple ChoiceSolve the rational equation:
Explanation
Multiply by x(x+1): 2(x+1)+3x = x(x+1) → 5x+2 = x^2 + x → x^2 -4x -2 = 0 → x = 2 ± √6, both valid since they are not 0 or -1.
Question 4
Multiple ChoiceFactor completely:
Explanation
Factor out 4x: 12x^3 -8x^2 -32x = 4x(3x^2 -2x -8) and 3x^2 -2x -8 = (3x+4)(x-2).
Question 5
Multiple ChoiceSolve the quadratic equation:
Explanation
Quadratic formula: x = [7 ± √(49 + 24)]/4 = [7 ± √73]/4.
Question 6
Multiple ChoiceWhat number should be added to both sides to complete the square for ?
Explanation
Half of 10 is 5 and 5^2 = 25, so add 25 to both sides to form (x+5)^2.
Question 7
Multiple ChoiceFind the vertical asymptotes of the function .
Explanation
Denominator factors to (x-3)(x+2); numerator is (x-3)(x+3) so (x-3) cancels (hole at x=3) and a vertical asymptote remains at x = -2.
Question 8
Multiple ChoiceTwo cars travel along the same road. The lead car goes 30 mph and left 2 hours earlier. A faster car follows at 50 mph. How many hours after the faster car leaves will it catch the lead car?
Explanation
Let t be hours after the faster car leaves: 30(t+2)=50t → 30t+60=50t → 20t=60 → t=3 hours.
Question 9
Multiple ChoiceWhat is the domain of the function ?
Explanation
Inside the square root must be nonnegative: 5 - x ≥ 0 → x ≤ 5, so the domain is all x less than or equal to 5.
Question 10
Multiple ChoiceSolve for x:
Explanation
Rewrite in exponential form: x+1 = 3^4 = 81, so x = 80.