JAMB Mathematics Past Questions & Answers

Correct Answer: Option B

Explanation

(x+3y+5)(2x2+5y+2)$(x+3y+5)(2x^2+5y+2)$

= 2x3+5xy+2x+6yx2+15y2+6y+10x2+25y+10$2x^3+5xy+2x+6y{x}^2+15y^2+6y+10x^2+25y+10$

= 2x3+5xy+2x+6yx2+15y2+31y+10x2+10

Correct Answer: Option A

Explanation

Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.

Correct Answer: Option A

Explanation

Area of the rectangular picture = L x B = 8 x 6

= 48 sq.cm.

Area of the whole surface (which is gotten by adding 12

$\frac{1}{2}$

 on every side to the original picture size) is 9 x 7 = 63 sq. cm

area of the frame is 63 - 48

= 15 sq. cm

Correct Answer: Option C

Explanation

Number of oranges = X; Costing N5X.

Number of mangoes = 2X; Costing N8X.

∴65≤5X+8X≤130$\therefore 65\le 5X+8X\le 130$

5≤X≤10

Explanation

To find the values of x

$x$

 where the curve

y=x3+2x2−5x−6

$y=x^3+2x^2-5x-6$

crosses the x-axis, we set y=0

$y=0$

:

x3+2x2−5x−6=0

$x^3+2x^2-5x-6=0$

Testing for rational roots, we find that x=−1

$x=-1$

 is a root. Factoring the polynomial gives:

x3+2x2−5x−6=(x+1)(x2+x−6)

$x^3+2x^2-5x-6=(x+1)(x^2+x-6)$

Solving the quadratic x2+x−6=0

$x^2+x-6=0$

 using the quadratic formula yields:

x=−1±12−4⋅1⋅−6√2⋅1=−1±52

$x=\frac{-1\pm \sqrt{1^2-4\cdot 1\cdot -6}}{2\cdot 1}=\frac{-1\pm 5}{2}$

Thus, the solutions are:

x=−1,x=2,x=−3

$x=-1,x=2,x=-3$

Therefore, the values of x

$x$

 where the curve crosses the x-axis are  x=−1,x=2,x=−3

$x=-1,x=2,x=-3$

.

In the diagram above, PQ¯¯¯¯¯¯¯¯$\overline{PQ}$ || RS¯¯¯¯¯¯¯$\overline{RS}$, ∠$\mathrm{\angle }$WYZ = 44º and ∠$\mathrm{\angle }$WXY = 50º. Find ∠$\mathrm{\angle }$WTX

Explanation

P(2, -8) and Q(1, y)

Gradient of slope(m) = y2−y1x2−x1

$\frac{y_2-y_1}{x_2-x_1}$

- 4 = y−(−8))1−2

$\frac{y-(-8))}{1-2}$

-4 = y+8−1

$\frac{y+8}{-1}$

cross multiplying

4 = y + 8

y = 4 - 8 = -4

Correct Answer: Option C

Explanation

From the diagram on the right-hand side above,

x2

${}^2$

 = 202

${}^2$

 - 192

${}^2$

 = 39 ( from Pythagoras theorem)

x = 39−−√

$\sqrt{39}$

 = 6.245m

As can be seen from  the diagram on the right-hand side above,

h = x + 17 = 6.245 + 17 = 23.245 m ≈ 23 m(to the nearest whole number)

Correct Answer: Option B

Explanation

Vol of cylinder = π

$\pi$

r2

${}^2$

H = vol of cone = 13

$\frac{1}{3}$

π

$\pi$

r2

${}^2$

h

H = height of cylinder and h = height of cone

Let y = radius of cylinder = y, then radius of cone = 2y

π

$\pi$

y2

${}^2$

H = 13

$\frac{1}{3}$

π

$\pi$

(2y)2

${}^2$

h

y2

${}^2$

H  =  13

$\frac{1}{3}$

4y2

${}^2$

h  ( π

$\pi$

 cancels out and cross multiplying)

The ratio of the height of the cylinder to that of the cone = Hh

$\frac{}{}$

 = 4y23y2

$\frac{4y^2}{3y^2}$

= 43

$\frac{4}{3}$

 = 4: 3 (y2

${}^2$

 cancels out )