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Grade 11: Math subject test

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Subject practice test

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Subject practice test
1. Find the remainder when P(x)=x²+2x+3 is divided by x−8.
2. Divide x²−64 by x−8. Give the polynomial quotient.
3. P(x)=(x−9)(x−2)(x+2). List all real zeros.
4. For y=(x−8)^2(x+9), what does the graph do at x=8?
5. Simplify √768 exactly.
6. Evaluate 512^(2/3) as a real number.
7. Solve √(x+8)=−9 over the reals.
8. Evaluate (8+i)(8−i), using i²=−1.
9. What inputs are excluded from (x+1)/(x²−64)?
10. Simplify (x²−64)/(x−8) and keep its original domain.
11. Solve 8/x=1/2, retaining the restriction x≠0.
12. A positive inverse-variation rule y=k/x passes through (8,9). Find y at x=16.
13. Evaluate log₂(256).
14. For positive x,y, rewrite log_9(xy).
15. Solve log₃(x−8)=2 over the reals.
16. A model is A(t)=8·2^t. At what t does A(t)=64?
17. An arithmetic sequence has a₁=8, common difference 3. Find a_9.
18. Find the sum of the first three terms of a geometric sequence starting at 8 with ratio 2.
19. Find the sum of the four-term arithmetic sequence 8,10,12,14.
20. A recursive sequence has a₁=8 and a_(n+1)=3a_n+1. Find a₂.
21. Identify center and radius of (x−8)²+(y+9)²=64.
22. For x²=32y, find the focus.
23. For x²/121+y²/64=1, what is the full major-axis length?
24. Find the vertices of x²/64−y²/81=1.
25. From 11 distinct candidates choose a chair and a different recorder. How many assignments are possible?
26. From 11 distinct candidates choose an unordered two-person committee. How many committees are possible?
27. A supplied fictional payoff model gives +32 points with probability 1/4 and −8 points with probability 3/4. Find expected payoff per trial.
28. A fair coin is tossed independently 9 times. Find the probability of exactly one head.
29. Fictional study 8 randomly assigns volunteers to practice A or B, then uses the same test. What does random assignment primarily help address?
30. In fictional simulation 8, repeated random samples of size 100 have means less spread out than samples of size 10. Which interpretation is warranted?
31. A supplied survey report gives estimate 56% with margin ±4 percentage points. What interval is reported?
32. In fictional observational study 8, students choosing a practice app have higher scores. What conclusion fits?

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