Gabrielle’s Exercises
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Gabrielle Exercise 14
15-Jun-2023 to ?-Jun-2023
1. 5, 8, 15, 26, 41 ... is a sequence with nth term 2n2 − 3n + c.
Find the value of c.
2. 4, 7, 14, 25, 40 ... is a sequence with nth term 2n2 − 3n + c.
Find the value of c.
3. 12, 26, 46, 72, 104 ... is a sequence with nth term 3n2 +5n+c.
Find the value of c.
4. 8, 20, 40, 68, 104 ... is a sequence with nth term 4n2 +bn+4.
Find the value of b.
5. 1, 8, 21, 40, 65 ... is a sequence with nth term 3n2 + bn.
Find the value of b.
Gabrielle’s Exercises
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Gabrielle’s Exercises
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6. The diagram shows a sector of a circle, centre O.
The angle of the sector is 306o .
The radius of the sector is 30.5 cm.
Find the area of sector. Give your answer correct to 3 significant figures
A
306o
O
30.5 cm
B
7. The diagram shows a sector of a circle, centre O.
The angle of the sector is 69o .
The radius of the sector is 4.5 cm.
Find the area of sector. Give your answer correct to 3 significant figures
B
69o
A
O
4.5 cm
Gabrielle’s Exercises
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Gabrielle’s Exercises
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8. The diagram shows a sector of a circle, centre O.
The angle of the sector is 64o .
The radius of the sector is 38.5 cm.
Find the area of sector. Give your answer correct to 3 significant figures
B
64o
O
A
38.5 cm
9. Find the length of x. Express your answer as surd if necessary.
x−8
x−4
x
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10. Find the length of t. Express your answer as surd if necessary.
t−4
t−8
t
11. Find the length of t. Express your answer as surd if necessary.
t−4
t−8
t
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Gabrielle’s Exercises
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12. Find the length of k. Express your answer as surd if necessary.
15
12
k
13. Find the length of f . Express your answer as surd if necessary.
15
f
12
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Gabrielle’s Exercises
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14. Find the length of y. Express your answer as surd if necessary.
20
y
12
15. Factorize x2 + 4x − 21
16. Factorize x2 + x − 6
17. Factorize x2 + x − 6
18. Factorize x2 + 9x + 14
19. Factorize x2 − 10x + 21
20. Solve 2x2 − 2 = 0.
21. Solve 4x2 − 1 = 0.
22. Solve 35x2 − 2x − 1 = 0.
23. Solve 3x2 + 6x + 3 = 0.
24. Solve 10x2 + 3x − 1 = 0.
Gabrielle’s Exercises
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Gabrielle’s Exercises
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25. Solve 7x2 = −9x − 2
26. Solve 5x2 − 2 = −3x
27. Solve 3x2 + 3 = −6x
28. Solve 7x2 = −2x + 5
29. Solve 3x2 − 4x = 7
30. 5, 8, 15, 26, 41 ... is a sequence with nth term 2n2 − 3n + c.
Find the value of c.
31. 4, 7, 14, 25, 40 ... is a sequence with nth term 2n2 − 3n + c.
Find the value of c.
32. 8, 20, 40, 68, 104 ... is a sequence with nth term 4n2 +bn+4.
Find the value of b.
33. 12, 26, 46, 72, 104 ... is a sequence with nth term 3n2 +5n+c.
Find the value of c.
34. 1, 8, 21, 40, 65 ... is a sequence with nth term 3n2 + bn.
Find the value of b.
Gabrielle’s Exercises
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Gabrielle’s Exercises
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35. Plot the points A(21, 200), B(9, 20), C(0, −180) and
D(−24, 0) on the following graph.
200
100
−30
−15
15
30
−100
−200
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Gabrielle’s Exercises
36. Find
the
coordinates
400
of
points
A
Page 9
to
D
B
A
200
C
−20
−10
D
10
20
−200
−400
37. Find the length of a. Express your answer as surd if necessary.
√
61
a
5
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38. Find the length of w. Express your answer as surd if necessary.
2
√
w
29
39. Find the length of m. Express your answer as surd if necessary.
3
m
√
45
40. Find the length of n. Express your answer as surd if necessary.
5
n
√
125
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41. Find the length of e. Express your answer as surd if necessary.
√
58
e
3
r
42. Make q the subject of f =
g−q
.
x3
43. Expand (2b + 2)(7b − 2)
44. Expand (7 − 3y)(3 + 7y)
45. Rewrite −2r2 as product with no power (exponent).
Answer for some questions
Gabrielle’s Exercises
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