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Algebra Level 1 Test 6

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Question 1
Find the value of p3 + q3, given pq = 900, (p+ q) = 60
A
36000
B
54000
C
48000
D
60000
Question 1 Explanation: 
p + q = 60
Cubing both sides
p3 + q3 + 3pq (p + q) = 216000
p3 + q3 + 3 ´ 900(60) = 216000.
(Replacing the variables by two values given)
p3 + q3 = 216000 – 162000 = 54000.
Question 2
If x2 + 1/x2 = 66, what is the value of x - 1/x?
A
8
B
+ 8 , -8
C
-8
D
9
Question 2 Explanation: 
x2 + 1/x2 = 66,
Subtract 2 from both sides
x2 + 1/x2 -2 = 66 – 2
(x - 1/x)2 = 64
Hence x - 1/x = +8,-8
Question 3
Find the range of : x2 – 7x – 8 < 0
A
-1 < x < 8.
B
-8 < x < 1
C
-1 < x < 1
D
-8 < x < 8
Question 3 Explanation: 
x2 – 7x – 8 < 0
(x-8)(x+1) < 0
x <8 ,x > -1
Hence answer = -1 < x < 8
Question 4
If P+Q = 54 and PQ = 9, find 1/P+ 1/Q.
A
9
B
6
C
18
D
12
Question 4 Explanation: 
1/P+1/Q = P+Q/ PQ = 54/9 = 6
Question 5
Find the value of (0.512 + 0.216) /(0.64+ 0.36+0.48)
A
1.4
B
0.8
C
0.2
D
2
Question 5 Explanation: 
The equation is: a3+b3 = (a+b)
(a2−ab+b2)
Hence the value should be = 1.4
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