The gradient of a line joining (x,4) and (1,2) is \(\frac{1}{2}\). Find the value of x
5
3
-3
-5
Correct answer is A
\(\text{Gradient m} = \frac{y_2 - y_1}{x_2 - x_1}\)
\(\frac{1}{2} = \frac{2 - 4}{1 - x}\)
1 - x = 2(2 - 4)
1 - x = 4 - 8
1 - x = -4
-x = -4 - 1
x = 5
Find the mid point of S(-5, 4) and T(-3, -2)
-4, 2
4, -2
-4, 1
4, -1
Correct answer is C
Mid point of S(-5, 4) and T(-3, -2) is
\([\frac{1}{2}(-5 + -3), \frac{1}{2}(4 + 2)]\)
\([\frac{1}{2}(x_1 + x_2), \frac{1}{2}(y_1 + y_2)]\)
\([\frac{1}{2}(-8), \frac{1}{2}(2)]\)
\([-4, 1]\)
8.0m
7.5m
5.0m
2.5m
Correct answer is D
Using \(V = \pi r^2 h\)
6160 = 22/7 x 28 x 28 x h
\(h = \frac{6160}{22 \times 4 \times 28} \)
\(h = 2.5m \)
How many sides has a regular polygon whose interior angle is 135°?
12
10
9
8
Correct answer is D
p>If each interior angle of the polygon is 135°, then each exterior angle is 180° - 135° = 45°.
Hence, number of sides =
\(\frac{360°}{\text{one exterior angle}}\)
\(\frac{360°}{45°}\)
= 8
Find the value of \(\begin{vmatrix}0 & 3 & 2 \\1 & 7 & 8 \\0 & 5 & 4\end{vmatrix}\).
12
10
-1
-2
Correct answer is D
\(0 \begin{vmatrix}7 & 8 \\5 & 4\end{vmatrix} -3 \begin{vmatrix}1 & 8 \\0 & 4\end{vmatrix} +2 \begin{vmatrix}1 & 7 \\0 & 5\end{vmatrix}\)
= 0(28 - 40) - 3(4 - 0) + 2(5 - 0)
= 0(-12) - 3(4) + 2(5)
= 0 - 12 + 10
= -2