If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68
24
22
-12
-21
Correct answer is D
x \(\ast\) y = x + y - xy
(x \(\ast\) 2) + (x \(\ast\) 3) = 68
= x + 2 - 2x + x + 3 - 3x
= 86
3x = 63
x = -21
60
57
54
42
Correct answer is C
m \(\ast\) n = mn - n - 1, m \(\oplus\) n = mn + n - 2
3 \(\oplus\) (4 \(\ast\) 5) = 3 \(\oplus\) (4 x 5 - 5 - 1) = 3 \(\oplus\) 14
3 \(\oplus\) 14 = 3 x 14 + 14 - 2
= 54
The nth term of a sequence is given 31 - n , find the sum of the first terms of the sequence.
\(\frac{13}{9}\)
1
\(\frac{1}{3}\)
\(\frac{1}{9}\)
Correct answer is A
Tn = 31 - n
S3 = 31 - 1 + 31 - 2 + 31 - 3
= 1 + \(\frac{1}{3}\) + \(\frac{1}{9}\)
= \(\frac{13}{9}\)
Sn is the sum of the first n terms of a series given by Sn = n\(^2\) - 1. Find the nth term
4n + 1
4n - 1
2n + 1
2n - 1
Correct answer is D
\(S_{n} = n^{2} - 1\)
\(T_{n} = S_{n} - S_{n - 1}\)
\(S_{n - 1} = (n - 1)^{2} - 1\)
= \(n^{2} - 2n + 1 - 1\)
= \(n^{2} - 2n\)
\(S_{n} - S_{n - 1} = (n^{2} - 1) - (n^{2} - 2n)\)
= \(2n - 1\)
Find the range of values of x which satisfies the inequality 12x2 < x + 1
-\(\frac{1}{4}\) < x < \(\frac{1}{3}\)
\(\frac{1}{4}\) < x < -\(\frac{1}{3}\)
-\(\frac{1}{3}\) < x < \(\frac{1}{4}\)
-\(\frac{1}{4}\) < x < - \(\frac{1}{3}\)
Correct answer is A
12x2 < x + 1
12 - x - 1 < 0
12x2 - 4x + 3x - 1 < 0
4x(3x - 1) + (3x - 1) < 0
Case 1 (+, -)
4x + 1 > 0, 3x - 1 < 0
x > -\(\frac{1}{4}\)x < \(\frac{1}{3}\)
Case 2 (-, +) 4x + 1 < 0, 3x - 1 > 0
-\(\frac{1}{4}\) < x < - \(\frac{1}{3}\)