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MATHEMATICS AISHK
Stage 5
Number and Algebra
Indices for Advanced year 8
Teacher: Phillip O'Connor
Exam Equivalent Time: 90 minutes (based on allocation ~1.25 min/mark)
Questions
1. Indices (226373)
Which of the following is equal to 32?
A.
B.
C.
D.
2. Indices (025457)
Simplify
A.
B.
C.
D.
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3. Indices (226377)
is equal to which of the following?
A.
B.
C.
D.
4. Indices (226382)
A.
B.
C.
D.
5. Indices (010136)
Simplify
.
A.
B.
C.
D.
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6. Indices (014151)
Which expression is equivalent to
?
A.
B.
C.
D.
7. Indices (226388)
Which expression is equal to
?
A.
B.
C.
D.
8. Indices (226394)
Which of the following has the same value as
A.
B.
C.
D.
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9. Indices (002644)
Which of the following expresses
in its simplest form?
A.
B.
C.
D.
10. Indices (001935)
Which of the following is
in its simplest form?
A.
B.
C.
D.
11. Indices (029205)
Which of the following is
in its simplest form?
A.
B.
C.
D.
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12. Indices (226398)
Select the expression that is equivalent to
A.
B.
C.
D.
13. Indices (137025)
What is the value of
so that
?
A.
B.
C.
D.
14. Indices (226453)
Simplify the expression
. (2 marks)
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15. Indices (226459)
Express
as a fraction. (1 mark)
16. Indices (026665)
Simplify
(2 marks)
17. Indices (226456)
Simplify the expression
. (2 marks)
18. Indices (226450)
Simplify the expression
. (2 marks)
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19. Indices (226447)
Simplify the expression
. (2 marks)
20. Indices (226462)
Simplify the expression
. (1 mark)
21. Indices (226467)
Simplify the expression
. (1 mark)
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22. Indices (061877)
Simplify
. (2 marks)
23. Indices (000474)
Solve
.
(2 marks)
24. Indices (005374)
Fully simplify
. (3 marks)
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25. Indices (226655)
Simplify
. (2 marks)
26. Indices (226472)
Simplify the expression
. (1 mark)
27. Indices (226477)
Simplify the expression
. (1 mark)
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28. Indices (226604)
Simplify
. (2 marks)
29. Indices (003171)
Simplify fully
. (2 marks)
30. Indices (226409)
Solve the equation
for
(2 marks)
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31. Indices (226484)
Express
as a fraction involving non-negative indices only. (1 mark)
32. Indices (226415)
Solve the equation
for . (2 marks)
33. Indices (226421)
Find given
. (2 marks)
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34. Indices (226495)
Simplify
and express as a fraction involving non-negative indices only. (3
marks)
35. Indices (226480)
Express
as a fraction involving non-negative indices only. (1 mark)
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36. Indices (226488)
Simplify
and express as a fraction involving non-negative indices only. (3
marks)
37. Indices (226632)
Find the reciprocal of
. (3 marks)
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Worked Solutions
1. Indices (226373)
2. Indices (025457)
3. Indices (226377)
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4. Indices (226382)
5. Indices (010136)
6. Indices (014151)
7. Indices (226388)
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8. Indices (226394)
9. Indices (002644)
ALGEBRA TIP: When you
divide by a fraction, invert
the divisor and multiply as
shown in the Worked
Solution.
10. Indices (001935)
11. Indices (029205)
♦ Mean mark below 43%. BE
CAREFUL!
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12. Indices (226398)
13. Indices (137025)
14. Indices (226453)
15. Indices (226459)
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16. Indices (026665)
17. Indices (226456)
18. Indices (226450)
19. Indices (226447)
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20. Indices (226462)
21. Indices (226467)
22. Indices (061877)
23. Indices (000474)
MARKER’S COMMENT:
Many students correctly
solved this by taking the
logarithms of both sides.
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24. Indices (005374)
♦♦ Mean mark 33%.
MARKER’S
COMMENT: Remember to
“invert and multiply” when
dividing a fraction by a
fraction (see Worked
Solution).
25. Indices (226655)
26. Indices (226472)
27. Indices (226477)
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28. Indices (226604)
29. Indices (003171)
♦ Mean mark 35%!
30. Indices (226409)
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31. Indices (226484)
32. Indices (226415)
33. Indices (226421)
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34. Indices (226495)
35. Indices (226480)
36. Indices (226488)
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37. Indices (226632)
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