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

= \(\frac{11!}{2!2!2!}\)

MACICITA is an eight letter word = 8!

Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I

∴ \(\frac{8!}{2! 2! 2!}\)

Y ∝ \(\frac{1}{2}\)

Y = 6, X = 7

Y = \(\frac{k}{x}\) where k is constant

6 = \(\frac{k}{7}\)

k = 42

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

The 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

∫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

Find the diagram
Sin 70^o

x = 10 Sin 70^o

= 9.3969

Hence, length of chord MN = 2x

= 2 × 9.3969

= 18.79

= 19cm (nearest cm)

m * n = \(\frac{m}{n}\) - \(\frac{m}{n}\)

m = − 3

n = 4

∴ − 3 × 4 = \(\frac{-3}{4}\) - \(\frac{-4}{-3}\)

= \(\frac{3(−3) − (− 4 × 4)}{12}\)

= \(\frac{− 9 + 16}{12}\)

= \(\frac{7}{12}\)

x + 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)

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 = \(\frac{nrp}{nr + m^2}\)