2017 - JAMB Mathematics Past Questions and Answers - page 4
MATHEMATICS is an eleven letter word = 11!
There are 2Ms and 2As and 2Es
Divide the number of repeating letters
= (\frac{11!}{2!2!2!})
Users' Answers & CommentsMACICITA is an eight letter word = 8!
Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I
∴ (\frac{8!}{2! 2! 2!})
Users' Answers & CommentsY ∝ (\frac{1}{2})
Y = 6, X = 7
Y = (\frac{k}{x}) where k is constant
6 = (\frac{k}{7})
k = 42
Users' Answers & Comments
MN || PQ || RS
MN = PQ = RS (parallel lines)
Label the angle in the lines
a = i (corresponding angles are equal)
b = x (corresponding angles are equal)
If |MN| = |RS|
If a = i
and a = 63 = i
a + b = 180 (Adjacent interior angles are supplementary i.e add to 180)
∴ i + x = 180
63 + x = 180
x = 180 - 63
x = 1170
Users' Answers & CommentsThe locus of a point p(x, y) such that pv = pw where v = (1, 1)
and w = (3, 5). This means that the point p moves so that its distance from v and w are equidistance
(\sqrt{(x − x_1)^2 + (y − y_1)^2}) = (\sqrt{(x − x_2)^2 + (y − y_2)^2})
(\sqrt{(x -1)^2 + (y - 1)^2}) = (\sqrt{(x - 3)^2 + (y - 5)^2})
square both sides
(x - 1)2 + (y - 1)2 = (x - 3)2 + (y - 5)2
x2 - 2x + 1 + y2 - 2y + 1 = x2 - 6x + 9 + y2 - 10y + 25
x2 + y2 -2x -2y + 2 = x2 + y2 - 6x - 10y + 34
Collecting like terms
x2 - x2 + y2 - y2 - 2x + 6x -2y + 10y = 34 - 2
4x + 8y = 32
Divide through by 4
x + 2y = 8
Users' Answers & Comments∫xndx = (\frac{x_{n + 1}}{n + 1})
∫dx = x + k
where k is constant
∫(x2 + 3x − 5)dx
∫x2 dx + ∫3xdx − ∫5dx
(\frac{2_{2 + 1}}{2 + 1}) + (\frac{3x^{1 + 1}}{1 + 1}) − 5x + k
(\frac{x_3}{3}) + (\frac{3x_2}{2}) − 5x + k
Users' Answers & CommentsFind the diagram
Sin 70o
x = 10 Sin 70o
= 9.3969
Hence, length of chord MN = 2x
= 2 × 9.3969
= 18.79
= 19cm (nearest cm)
Users' Answers & Commentsm * n = (\frac{m}{n}) - (\frac{m}{n})
m = − 3
n = 4
∴ − 3 × 4 = (\frac{-3}{4}) - (\frac{-4}{-3})
= (\frac{3(−3) − (− 4 × 4)}{12})
= (\frac{− 9 + 16}{12})
= (\frac{7}{12})
Users' Answers & Commentsx + 2xy + y + 3x + 3y - 18
x + 2xy + 3x + y + 3y -18
x + 2xy - 3x + 6x + y -3y + 6y -18
x + 2xy -3x + y -3y + 6x + 6y -18
x + xy -3x + xy + y - 3y + 6x + 6y -18
x(x + y - 3) + y(x + y - 3) + 6(x + y - 3)
= (x + y - 3)(x + y + 6)
= (x + y + 6)(x + y -3)
Users' Answers & Commentsp = s + \(\frac{sm^2}{nr}\)
p = s + (\frac{sm^2}{nr})
p = s + ( 1 + (\frac{m^2}{nr}))
p = s (1 + (\frac{nr + m^2}{nr}))
nr × p = s (nr + m2)
s = (\frac{nrp}{nr + m^2})
Users' Answers & Comments