If angle θ is 135°, evaluate cosθ
12
√22
−√22
−12
Correct answer is C
θ = 135°
Cos 135° = Cos(90 + 45)°
= cos90° cos45° - sin90° sin45°
= 0cos45° - (1 x √22)
= −√22
Find the equation of the line through the points (-2, 1) and (-12, 4)
y = 2x - 3
y = 2x + 5
y = 3x - 2
y = 2x + 1
Correct answer is B
y−y1x−x1 = y2−y1x2−x1
y−1x−−2 = 4−1−12+2
= y−1x+2 = 332
y = 2x + 5
The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is
√13
3√2
√26
10√5
Correct answer is B
P1 (4, 3), P2 (x, y)
y = 2x + 4 .....(1)
y = 7 - x .....(2)
Substitute (2) in (1)
7 - x = 2x + 4
7 - 4 = 2x + x
3 = 3x
x = 1
Substitute in eqn (2)
y = 7 - x
y = 7 - 1
y = 6
P2 (1, 6)
Distance between 2 points is given as
D = √(x2−x1)2+(y2−y1)2
D = √(1−4)2+(6−3)2
D = √(−3)2+(3)2
D = √9+9
D = √18
D = √9×2
D = 3√2
The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is
12
25
−47
−23
Correct answer is C
PQ = y1−y0x1−x0 = −3−(−7)−2−5 = −3+7−2−5 = 4−7
Calculate the volume of a cuboid of length 0.76cm, breadth 2.6cm and height 0.82cm.
3.92cm3
2.13cm3
1.97cm3
1.62cm3
Correct answer is D
Volume of cuboid = L x b x h
= 0.76cm x 2.6cm x 0.82cm
= 1.62cm3