Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3
-4
4
1
-1
Correct answer is C
x = -3
substitute x = -3 in 3x3 + 5x2 - 11x + 4
3(-3)3 + 5(-3)2 - 11(-3) + 4
-81 + 45 + 33 + 4
-81 + 82
= 1
8
3
16
4
Correct answer is A
\(P\times Q=\sqrt{PQ}\\4\times(8\times32)=4\times\sqrt{8\times32}\\=4\times\sqrt{256}\\=4\times16\\=\sqrt{4\times16}\\=\sqrt{64}\\=8\)
27
8
78
48
Correct answer is C
\(a=6, U_4 = 162\\U_4 = ar^{4-1}\\U_4 = ar^3\\162 = 6(r)^3\\r^3 = 27\\r=\sqrt[3]{27}\\r=3\\S_4 = \frac{a(r^{n}-1)}{r-1}\\=\frac{6(3^{3}-1)}{3-1}\\=\frac{6(27-1)}{2}\\=3\times26\\=78\)
What are the integer values of x which satisfy the inequality -1 < 3 -2x \(\leq\) 5?
-1. 0, 1, 2
-2, 1, 0 , -1
0, 1, 2
-1, 0, 1
Correct answer is D
-1 < 3 -2x and 3 - 2x \(\leq\) 5
2x < 3 + 1 and -2x \(\leq\) 5 - 3
2x < 4 and -2x \(\leq\) 2
x < 2 and x \(\geq\) 2/-2 = x \(\geq\) -1
If -1 \(\leq\) x < 2
it implies that x = -1, 0, 1
y is inversely proportional to x and y = 4 when x = 1/2. Find x when y = 10.
2.5
10
1/5
1/10
Correct answer is C
y ∝ 1/x
y = K/x
K = xy
K = (1/2) * 4 ( when y = 4 and x = 1/2)
K = 2
∴y = 2/x
10 = 2/x (when y = 10)
10x = 2
x = 2/10
x = 1/5