Final Skills Check

1: C. Requested object. 4x=20, so x=5. The question asks for 3x−1, not x: 3(5)−1=14. Choice A reports x itself instead of completing the requested value of 3x−1.

2: G. Wrong reference base. (96−120)÷120×100=−20%. Choice H uses 96 as the base instead of the original value 120, giving −24% instead of the correct −20%.

3: D. Sign / direction. −6x≥30, so dividing by a negative flips the inequality: x≤5. Choice A keeps the inequality direction unchanged instead of flipping it when dividing by −6.

4: H. Unit / dimension. 1 square yard=9 square feet; 4×9=36. Choice F uses the linear conversion factor (3) instead of squaring it (9) for a square-unit conversion.

5: B. Restriction / domain. Squaring gives x²−2x−3=0, so x=3 or x=−1. Checking x=3: √9=3, matching. Checking x=−1: √(2(−1)+3)=√1=1, but x=−1, and 1≠−1; rejected. Only x=3 is valid. Choice C reports both candidate solutions without checking that x=−1 is extraneous.

6: F. Method / execution. x²−8x+16 is a perfect square trinomial, (x−4)²=0, giving the single repeated root x=4 directly. Choice G drops the sign on the repeated root, reporting −4 instead of 4.

7: A. Representation switch. Reading the table, the output values are symmetric around x=3, where the minimum value 3 occurs, identifying the vertex without an equation. Choice B reports the x-value one step past the true vertex instead of the point of symmetry itself.

8: G. Wrong reference base. A percentage-point difference is the raw subtraction: 63−45=18, not the 40% relative increase. Choice F computes the percent increase relative to the original rate instead of the raw percentage-point difference.

9: C. Requested object. 300−180=120 people do not own a dog; 180 is the number who do, the opposite of what was asked. Choice A reports the number of dog owners instead of the requested number who do not own a dog.

10: H. Sign / direction. Case 1: x−10=3x+2 gives x=−6, but 3(−6)+2=−16<0, impossible for an absolute value; rejected. Case 2: x−10=−(3x+2) gives x=2, and 3(2)+2=8≥0, matching |2−10|=8. Choice F reports the extraneous solution from the case that fails the nonnegative check.

11: A. Unit / dimension. 22×3,600÷5,280=15 miles per hour. Choice G reports the original value in feet per second, forgetting to convert to miles per hour.

12: F. Restriction / domain. The radical requires 5−x≥0 (x≤5); the denominator requires x≠−2. Both restrictions apply together. Choice G gives the radical restriction but forgets the denominator exclusion x≠−2.

13: B. Wrong measurement role. The radius is half the diameter: 18÷2=9. Area=π(9)²≈254.47. Choice A uses the diameter itself as the radius instead of halving it first.

14: J. Method / execution. Time: 200/40=5 hr and 200/100=2 hr; average speed=400/7≈57.14, not the simple average of 40 and 100. Choice F averages the two speeds directly instead of using total distance divided by total time.