2018 - JAMB Mathematics Past Questions and Answers - page 5
Express 495g as a percentage of 16.5kg
First, express the two numbers in the same unit.
To convert 495g to kg, divide it by 1000
495g = \(\frac{495}{1000}\)
= 0.495kg
To express in percentage, 0.495 will be divided by 16.5 and then multiplied by 100
% will be added to the answer \(\frac{0.4950}{16.5}\) x 100
= 3%
Evaluate (2√3 - 4) (2√3 + 4)
Find the equation of the tangent at the point (2, 0) to the curve y = x\(^2\) - 2x
To find the gradient to the curve, we differentiate the equation of the curve with respect to x
\(\frac{dy}{dx}\) 2x - 2
The gradient of the curve is the same with that of the tangent.
At point (2, 0) \(\frac{dy}{dx}\) = 2(2) - 2
= 4 – 2 = 2
The equation of the tangent is given by (y - y1) \(\frac{dy}{dx}\) (x – x1)
At point (x1, y1) = (2, 0)
y - 0 = 2(x - 2)
y = 2x - 4
Use the quadratic equation curve to answer this questions
What is the 80th percentile?
The minimum value is the lowest value of the curve on y axis which gives a value of -5.3
Evaluate log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\)
log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\)
= log \(_2\) 2\(^3\) – log\(_3\) 9\(^{-1}\)
= log\(_2\) 2\(^3\) – log\(_3\) 3\(^{-2}\)
Based on law of logarithm
= 3 log\(_2\) 2 – (-2 log\(_3\) 3)
But log\(_2\) 2 = 1,
log\(_3\) 3 = 1
So, = 3 + 2
= 5
Tanθ is positive and Sinθ is negative. In which quadrant does θ lies
The correct option is the third quadrant only where Tanθ is positive and Sinθ is negative
How many children are in the hospital
The total number of students is ∑ f = 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4
= 40
The figure below is a Venn diagram showing the elements arranged within sets A,B,C,ε.
Use the figure to answer this question
What is n(A U B)1 ?
A = (p, q, r, t, u, v)
B = (r, s, t, u)
A U B = Elements in both A and B = (p, q, r, s, t, u, v)
(A U B)1 = elements in the universal set E but not in (A U B)= (w, x, y, z)
n(A U B) 1 = number of the elements in (A U B)1 = 4
What is the loci of a distance 4cm from a given point P?
Locus is the path traced at by a point which moves in accordance with a certain law. It is also the set of all possible position occupied by an object The path traced from all possible location of 4cm from a given point P form a circle of radius 4cm with centre P.
Given that Sin (5\(_x\) − 28)\(^o\) = Cos(3\(_x\) − 50)\(^o\), O\(_x\) < 90\(^o\)
Find the value of x
Sin(5x - 28) = Cos(3x - 50)………..i
But Sinα = Cos(90 - α)
So Sin(5x - 28) = Cos(90 - [5x - 28])
Sin(5x - 28) = Cos(90 - 5x + 28)
Sin(5x - 28) = Cos(118 - 5x)………ii
Combining i and ii
Cos(3x - 50) = Cos(118 - 5x)
3x - 50 = 118 - 5x
Collecting the like terms
3x + 5x = 118 + 50
8x = 168
x = \(\frac{168}{8}\)
x = 21\(^o\)
Answer is B