32 questions · explained feedback · no signup

Grade 12: Math subject test

Try the supplied cases without hints first. Use paper for calculations, notes or drawings. Check all your answers together, then revisit the lessons you want to practice.

Take breaks when useful. Leaving or reloading clears these answers; download your notes before leaving. This practice test is not a standardized examination, school grade or credential.

Download tests & answer keys

Subject practice test

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

1. Let f(x)=x² and g(x)=2x+1. Find (f∘g)(8).290288578289

2. Let f(u)=√u and g(x)=x−8. What is the real domain of f(g(x))?x≥8x≤8x≠8Every real x

3. Find the inverse of f(x)=3x+8.f⁻¹(x)=1/(3x+8)f⁻¹(x)=(x−8)/3f⁻¹(x)=3x−8f⁻¹(x)=(x+8)/3

4. The function f(x)=x²+8 has domain x≥0. Find its inverse and domain.f⁻¹(x)=±√(x−8), all real xf⁻¹(x)=√(x+8), x≥0f⁻¹(x)=√(x−8), x≥8f⁻¹(x)=x²−8, x≥0

5. Convert 240° to radians exactly.8π8/3π2/3π4/3π

6. Using special-angle triangles, find the unit-circle point at angle 5π/3.(1/2, −√3/2)(√3/2, 1/2)(1/2, √3/2)(−1/2, √3/2)

7. Find tan(7π/6) exactly, using sinθ=−1/2 and cosθ=−√3/2.1√3/3−1√3

8. Angle 600° terminates strictly inside quadrant III. What are the signs of sine and cosine?sin positive, cos positivesin positive, cos negativesin negative, cos negativesin negative, cos positive

9. If sin θ=8/9, find cos²θ exactly.1/964/81145/8117/81

10. If sin θ=12/37 and cos θ=35/37, find sin(2θ).840/136924/3747/37420/1369

11. Find all solutions to sin θ=1/2 on 12π≤θ<14π.73/6π only73/6π and 77/6π73/6π and 79/6π73/3π and 74/3π

12. Two triangle sides are 8 and 9 cm with included angle 60°. Use cos(60°)=1/2 to find the exact opposite side.17 cm√290 cm√73 cm√1 cm

13. Add vectors ⟨8,−9⟩ and ⟨3,2⟩.⟨5,-11⟩⟨24,-18⟩⟨10,-6⟩⟨11,-7⟩

14. Find the magnitude of vector ⟨24,32⟩.40413980

15. Find ⟨8,9⟩·⟨3,−2⟩.76512

16. Eliminate t from x=t+8, y=2t+9, with t any real number.y=2x+25y=x+1y=2x−7y=2x+9

17. Multiply [[1,2],[0,1]] by column [8,9]. What is the first component?27255226

18. Find the determinant of [[8,9],[9,12]].15161430

19. Which matrix is the inverse of [[1,8],[0,1]]?[[1,8],[0,1]][[1,−8],[0,1]][[1,0],[−8,1]][[0,1],[1,8]]

20. In an augmented system, R1=[1,1|8], R2=[2,3|9]. Replace R2 with R2−2R1.R2=[0,1|1]R2=[1,2|1]R2=[0,1|-7]R2=[0,5|25]

21. Find lim as x→8 of (x²−64)/(x−8).17153216

22. Near x=0, f(x)=8 for x<0 and f(x)=9 for x>0; f(0)=18. Find the two-sided limit at 0.The two-sided limit does not existThe limit is 8The limit is 9The limit is 18

23. For x≠8, f(x)=(x²−64)/(x−8); define f(8)=k. What k makes f continuous at 8?17161532

24. Find lim as x→∞ of (8x+1)/(9x−2).9/8-18/90

25. For f(x)=x², find f′(8) from the limit of [f(8+h)−f(8)]/h.17153216

26. For f(x)=x³, find f′(8).192193191384

27. For f(x)=x²(x+1), find f′(8).209208207416

28. For y=x², find the tangent line at x=8.y−64=8(x−8)y=16xy−64=16(x−8)y+64=16(x+8)

29. Approximate accumulation over three equal intervals of width 8 using supplied heights 1,2,3. What is the rectangle sum?49479648

30. Evaluate the definite integral of 2x from 0 to 8.646563128

31. A supplied graph has geometric area 24 above the x-axis and 16 below, over one interval. Find its definite integral.98716

32. Let F(x)=integral from 0 to x of (t²+1) dt. Find F′(8).666465130

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.