AS Integration Silver

Question 1 of 30

1. Question

To 3DP, find the value of: \({\int }_{1}^{4}\frac{7}{x}dx\)

\(9.704\)
\(-4.852\)
\(-1.892\)
\(-4.257\)

Question 2 of 30

2. Question

To 3DP, find the value of: \({\int }_{1}^{4}\frac{5}{x}dx\)

\(6.931\)
\(16.094\)
\(-8.047\)
\(-12.071\)

Question 3 of 30

3. Question

To 3DP, find the value of: \({\int }_{3}^{5}\frac{6}{x}dx\)

\(3.065\)
\(2.291\)
\(3.054\)
\(-2.291\)

Question 4 of 30

4. Question

To 3DP, find the value of: \({\int }_{2}^{5}\frac{1}{x}dx\)

\(0.916\)
\(-0.462\)
\(0.346\)
\(-1.386\)

Question 5 of 30

5. Question

To 3DP, find the value of: \({\int }_{2}^{5}\frac{4}{x}dx\)

\(3.665\)
\(-8.788\)
\(-2.197\)
\(8.788\)

Question 6 of 30

6. Question

\({f}^{\prime }\left(x\right)=8x\text{ at }\left(4,2\right)\)

\(f\left(x\right)=4{x}^{2}-62\)
\(f\left(x\right)=6x-61\)
\(f\left(x\right)=6x-\frac{1}{61}\)
\(f\left(x\right)=3{x}^{2}-62\)

Question 7 of 30

7. Question

\({f}^{\prime }\left(x\right)=4x\text{ at }\left(6,2\right)\)

\(f\left(x\right)=2{x}^{2}-70\)
\(f\left(x\right)={x}^{2}+\frac{1}{96}\)
\(f\left(x\right)=2x+70\)
\(f\left(x\right)={x}^{2}-\frac{1}{96}\)

Question 8 of 30

8. Question

\({f}^{\prime }\left(x\right)=7\text{ at }\left(2,2\right)\)

\(f\left(x\right)=7x-12\)
\(f\left(x\right)=7x-11\)
\(f\left(x\right)=7x-\frac{1}{12}\)
\(f\left(x\right)=7x+\frac{1}{11}\)

Question 9 of 30

9. Question

\({f}^{\prime }\left(x\right)=8{x}^{2}\text{ at }\left(3,5\right)\)

\(f\left(x\right)=\frac{8}{3}{x}^{3}-67\)
\(f\left(x\right)=\frac{8}{3}{x}^{3}-67\)
\(f\left(x\right)=4{x}^{2}-\frac{1}{67}\)
\(f\left(x\right)=4{x}^{2}+\frac{1}{67}\)

Question 10 of 30

10. Question

\({f}^{\prime }\left(x\right)=x\text{ at }\left(0,6\right)\)

\(f\left(x\right)=\frac{1}{2}{x}^{2}+6\)
\(f\left(x\right)=\frac{1}{2}{x}^{2}-6\)
\(f\left(x\right)=\frac{1}{2}{x}^{2}+\frac{1}{6}\)
\(f\left(x\right)=\frac{1}{2}{x}^{2}-\frac{1}{6}\)

Question 11 of 30

11. Question

\({f}^{\prime }\left(x\right)=7{x}^{\frac{2}{3}}\text{ at }\left(8,2\right)\)

\(f\left(x\right)=\frac{21}{5}{x}^{\frac{5}{3}}-132\frac{2}{5}\)
\(f\left(x\right)=\frac{21}{2}{x}^{\frac{2}{3}}+\frac{1}{132}\)
\(f\left(x\right)=\frac{21}{2}{x}^{\frac{2}{3}}-\frac{1}{131}\)
\(f\left(x\right)=3{x}^{\frac{5}{3}}+\frac{1}{131}\)

Question 12 of 30

12. Question

\({f}^{\prime }\left(x\right)=3{x}^{\frac{1}{6}}\text{ at }\left(0,7\right)\)

\(f\left(x\right)=\frac{18}{7}{x}^{\frac{7}{6}}+7\)
\(f\left(x\right)=18{x}^{\frac{1}{6}}+\frac{1}{7}\)
\(f\left(x\right)=18{x}^{\frac{1}{6}}-\frac{1}{7}\)
\(f\left(x\right)=18{x}^{\frac{1}{6}}+7\)

Question 13 of 30

13. Question

\({f}^{\prime }\left(x\right)=3{x}^{\frac{5}{6}}\text{ at }\left(0,8\right)\)

\(f\left(x\right)=\frac{18}{11}{x}^{\frac{11}{6}}+8\)
\(f\left(x\right)=\frac{18}{11}{x}^{\frac{11}{6}}-\frac{1}{8}\)
\(f\left(x\right)=\frac{18}{11}{x}^{\frac{11}{6}}-8\)
\(f\left(x\right)=\frac{18}{11}{x}^{\frac{11}{6}}+\frac{1}{8}\)

Question 14 of 30

14. Question

\({f}^{\prime }\left(x\right)=12{x}^{\frac{1}{4}}\text{ at }\left(0,3\right)\)

\(f\left(x\right)=\frac{48}{5}{x}^{\frac{5}{4}}+3\)
\(f\left(x\right)=\frac{48}{5}{x}^{\frac{5}{4}}-\frac{1}{3}\)
\(f\left(x\right)=\frac{48}{5}{x}^{\frac{5}{4}}-3\)
\(f\left(x\right)=48{x}^{\frac{1}{4}}+3\)

Question 15 of 30

15. Question

\({f}^{\prime }\left(x\right)={x}^{\frac{3}{5}}\text{ at }\left(1,4\right)\)

\(f\left(x\right)=\frac{5}{8}{x}^{\frac{8}{5}}+3\frac{3}{8}\)
\(f\left(x\right)=\frac{5}{8}{x}^{\frac{8}{5}}-3\frac{2}{8}\)
\(f\left(x\right)=\frac{5}{8}{x}^{\frac{8}{5}}-\frac{7}{23}\)
\(f\left(x\right)=\frac{5}{3}{x}^{\frac{3}{5}}+\frac{7}{23}\)

Question 16 of 30

16. Question

\({f}^{\prime }\left(x\right)=\sqrt[5]{{x}^{3}}\text{ at }\left(0,9\right)\)

\(f\left(x\right)=\frac{5}{8}{x}^{\frac{8}{5}}+9\)
\(f\left(x\right)=\frac{5}{3}{x}^{\frac{3}{5}}+9\)
\(f\left(x\right)=\frac{5}{3}{x}^{\frac{3}{5}}-\frac{1}{9}\)
\(f\left(x\right)=\frac{5}{8}{x}^{\frac{8}{5}}-\frac{1}{9}\)

Question 17 of 30

17. Question

\({f}^{\prime }\left(x\right)=\sqrt[3]{{x}^{2}}\text{ at }\left(8,6\right)\)

\(f\left(x\right)=\frac{3}{5}{x}^{\frac{5}{3}}-13\frac{1}{5}\)
\(f\left(x\right)=\frac{3}{2}{x}^{\frac{2}{3}}-\frac{5}{66}\)
\(f\left(x\right)=\frac{3}{5}{x}^{\frac{5}{3}}+\frac{5}{66}\)
\(f\left(x\right)=\frac{3}{2}{x}^{\frac{2}{3}}+13\frac{1}{5}\)

Question 18 of 30

18. Question

\({f}^{\prime }\left(x\right)=\sqrt[3]{{x}^{2}}\text{ at }\left(8,8\right)\)

\(f\left(x\right)=\frac{3}{5}{x}^{\frac{5}{3}}-11\frac{1}{5}\)
\(f\left(x\right)=\frac{3}{5}{x}^{\frac{5}{3}}-\frac{5}{56}\)
\(f\left(x\right)=\frac{3}{2}{x}^{\frac{2}{3}}-11\frac{1}{5}\)
\(f\left(x\right)=\frac{3}{5}{x}^{\frac{5}{3}}+\frac{5}{56}\)

Question 19 of 30

19. Question

\({f}^{\prime }\left(x\right)=\sqrt[5]{{x}^{2}}\text{ at }\left(0,3\right)\)

\(f\left(x\right)=\frac{5}{7}{x}^{\frac{7}{5}}+3\)
\(f\left(x\right)=\frac{5}{2}{x}^{\frac{2}{5}}-3\)
\(f\left(x\right)=\frac{5}{7}{x}^{\frac{7}{5}}-3\)
\(f\left(x\right)=\frac{5}{2}{x}^{\frac{2}{5}}+3\)

Question 20 of 30

20. Question

\({f}^{\prime }\left(x\right)=\sqrt[4]{{x}^{3}}\text{ at }\left(0,8\right)\)

\(f\left(x\right)=\frac{4}{7}{x}^{\frac{7}{4}}+8\)
\(f\left(x\right)=\frac{4}{7}{x}^{\frac{7}{4}}-\frac{1}{8}\)
\(f\left(x\right)=\frac{4}{7}{x}^{\frac{7}{4}}+\frac{1}{8}\)
\(f\left(x\right)=\frac{4}{3}{x}^{\frac{3}{4}}+\frac{1}{8}\)

Question 21 of 30

21. Question

\({f}^{\prime }\left(x\right)=\frac{4}{{x}^{3}}\text{ at }\left(2,7\right)\)

\(f\left(x\right)=-2{x}^{-2}+7\frac{1}{2}\)
\(f\left(x\right)=-2{x}^{-2}+\frac{2}{15}\)
\(f\left(x\right)=-2{x}^{-2}-\frac{2}{15}\)
\(f\left(x\right)=-\frac{4}{3}{x}^{-3}+\frac{2}{15}\)

Question 22 of 30

22. Question

\({f}^{\prime }\left(x\right)=\frac{5}{{x}^{3}}\text{ at }\left(4,7\right)\)

\(f\left(x\right)=-\frac{5}{2}{x}^{-2}+7\frac{5}{32}\)
\(f\left(x\right)=-\frac{5}{2}{x}^{-2}-\frac{32}{229}\)
\(f\left(x\right)=-\frac{5}{3}{x}^{-3}+7\frac{5}{32}\)
\(f\left(x\right)=-\frac{5}{3}{x}^{-3}-7\frac{5}{32}\)

Question 23 of 30

23. Question

\({f}^{\prime }\left(x\right)=\frac{6}{{x}^{4}}\text{ at }\left(6,2\right)\)

\(f\left(x\right)=-2{x}^{-3}+2\frac{1}{108}\)
\(f\left(x\right)=-\frac{3}{2}{x}^{-4}+\frac{108}{217}\)
\(f\left(x\right)=-\frac{3}{2}{x}^{-4}-2\frac{1}{108}\)
\(f\left(x\right)=-\frac{3}{2}{x}^{-4}+2\frac{1}{108}\)

Question 24 of 30

24. Question

\({f}^{\prime }\left(x\right)=\frac{5}{{x}^{4}}\text{ at }\left(2,2\right)\)

\(f\left(x\right)=-\frac{5}{3}{x}^{-3}+2\frac{5}{24}\)
\(f\left(x\right)=-\frac{5}{4}{x}^{-4}-2\frac{5}{24}\)
\(f\left(x\right)=-\frac{5}{3}{x}^{-3}-2\frac{5}{24}\)
\(f\left(x\right)=-\frac{5}{4}{x}^{-4}+\frac{24}{53}\)

Question 25 of 30

25. Question

\({f}^{\prime }\left(x\right)=\frac{1}{{x}^{3}}\text{ at }\left(6,6\right)\)

\(f\left(x\right)=-\frac{1}{2}{x}^{-2}+6\frac{1}{72}\)
\(f\left(x\right)=-\frac{1}{3}{x}^{-3}-6\)
\(f\left(x\right)=-\frac{1}{3}{x}^{-3}+6\)
\(f\left(x\right)=-\frac{1}{2}{x}^{-2}-\frac{1}{2}\)

Question 26 of 30

26. Question

\({f}^{\prime }\left(x\right)=\frac{6}{\sqrt{{x}^{4}}}\text{ at }\left(8,3\right)\)

\(f\left(x\right)=-6{x}^{-1}+3\frac{3}{4}\)
\(f\left(x\right)=-6{x}^{-1}-\frac{4}{15}\)
\(f\left(x\right)=-3{x}^{-2}+3\frac{3}{4}\)
\(f\left(x\right)=-3{x}^{-2}-3\frac{3}{4}\)

Question 27 of 30

27. Question

\({f}^{\prime }\left(x\right)=\frac{6}{\sqrt{{x}^{3}}}\text{ at }\left(1,3\right)\)

\(f\left(x\right)=-12{x}^{\frac{-1}{2}}+15\)
\(f\left(x\right)=-4{x}^{\frac{-3}{2}}-\frac{1}{15}\)
\(f\left(x\right)=-4{x}^{\frac{-3}{2}}+15\)
\(f\left(x\right)=-4{x}^{\frac{-3}{2}}-15\)

Question 28 of 30

28. Question

\({f}^{\prime }\left(x\right)=\frac{7}{\sqrt{{x}^{7}}}\text{ at }\left(1,3\right)\)

\(f\left(x\right)=-\frac{14}{5}{x}^{\frac{-5}{2}}+5\frac{4}{5}\)
\(f\left(x\right)=-2{x}^{\frac{-7}{2}}+5\frac{4}{5}\)
\(f\left(x\right)=-2{x}^{\frac{-7}{2}}-\frac{5}{29}\)
\(f\left(x\right)=-\frac{14}{5}{x}^{\frac{-5}{2}}+\frac{5}{29}\)

Question 29 of 30

29. Question

\({f}^{\prime }\left(x\right)=\frac{2}{\sqrt{{x}^{8}}}\text{ at }\left(1,5\right)\)

\(f\left(x\right)=-\frac{2}{3}{x}^{-3}+5\frac{2}{3}\)
\(f\left(x\right)=-\frac{1}{2}{x}^{-4}-5\frac{2}{3}\)
\(f\left(x\right)=-\frac{1}{2}{x}^{-4}+5\frac{2}{3}\)
\(f\left(x\right)=-\frac{2}{3}{x}^{-3}+\frac{3}{17}\)

Question 30 of 30

30. Question

\({f}^{\prime }\left(x\right)=\frac{8}{\sqrt{{x}^{4}}}\text{ at }\left(2,9\right)\)

\(f\left(x\right)=-8{x}^{-1}+13\)
\(f\left(x\right)=-4{x}^{-2}-13\)
\(f\left(x\right)=-4{x}^{-2}+\frac{1}{13}\)
\(f\left(x\right)=-8{x}^{-1}-\frac{1}{13}\)

AQA A level

Get video help

Quiz Summary

Information

Results