Solve the quadratic inequalities x\(^2\) - 5x + 6 ≥ 0
x ≤ 2, x ≥ 3
x ≤ 3, x ≥ 2
x ≤ -2, x ≥ -3
x ≤-3, x ≥ 2
Correct answer is B
x\(^2\) - 5x + 6 = 0
(X-2)(X-3) = 0
X-2 = 0 implies X = 2
X-3 = 0 implies X = 3
∴ x ≤ 3, x ≥ 2
-4 \(\leq\) x \(\leq\) 7
-7 \(\leq\) x \(\leq\) 4
x \(\geq\) -7
-7 \(\leq\) x \(\leq\) 6
Correct answer is A
4X - 7 \(\leq\) 3X and 3X - 4 \(\leq\) 4X
4X - 3X \(\leq\) 7 and 3X - 4X \(\leq\) 4
X \(\leq\) 7 and -X \(\leq\) 4 = X \(\geq\) -4
Range -4 \(\leq\) x \(\leq\) 7
If p varies inversely as the square of q and p=8 when q=4, find q when p =32
\(\pm\)16
\(\pm\)8
\(\pm\)4
\(\pm\)2
Correct answer is D
p ∝ 1/q
p = k/q
K = q\(^2\)p
= 4\(^2\)(8)
∴p = 128/q
32 = 128/q
q\(^2\) = 128/32
q\(^2\) = 4
q = √4 = \(\pm\) 2
If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6.
30
21
16
12
Correct answer is B
(x – 3) ∝ y2
X-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2 (6)2
X-3 = 1/2 x 36/1
X-3 = 18
X = 21
Factorize completely; (4x+3y)\(^2\) - (3x-2y)\(^2\)
(x+5y)(7x+y)
(x+5y)(7x-y)
(x-5y)(7x+y)
(x-5y)(7x-y)
Correct answer is A
(4x+3y)\(^2\) - (3x-2y)\(^2\)
Using the differences of two squares:
(4x+3y+3x-2y)(4x+3y-(3x-2y))
(4x+3y+3x-2y)(4x+3y-3x+2y)
(x+5y)(7x+y)