2019 MATHEMATICS WAEC GCE

(1a)

Tabulate

X|2|3|4|5|7|

2|4|6|2|6|

3|6|1|7|5|

5|2|7|1|3|

7|6|5|3|1|

(1bi)

n=7,i;e 3 (*)7=5

(1bii)

n(*)n=1, n=3

(2a)

Given; slant height l = 18.7cm

Diameter, d = 24cm

π = 22/7

But, Curved surface area of cone = πrl

=π(d/2)l

= 22/7 × 24/2 × 18.7

# =9873.6/14 = 705cm²

(2b)

128^x × 2/16^(1-x) = 8⅔x

= 2^7x × 2/2^4(1-x) = 2³(⅔x)

= 2^7x + 1/2^4(1-x) = 2^2x

Cross multiply

2^4(1 – x) + 2x = 2^7x + 1

4(1 – x) + 2x = 7x + 1

4 – 4x + 2x = 7x + 1

4 – 2x = 7x + 1

9x = 3

# X = 3/9 = 1/3

(3a)

3√3/2 – 4√2/3 – √24

=3√3/2 – 4√2/√3 -√6*4

=(3√3/√2 × √2/√2) – (4√2/√3 × √3/√3) – 2√6

=3√6/2 – 4√6/3 – 2√6

=(3/2 – 4/3 – 2)√6

=(9 – 8 – 12)√6

= -11/6√6

(3bi) prob(only one passes) = m passes and N fails or M fails and N passes

Prob (M passes) = 2/3; prob(M fails) = 1 – 2/3 = 1/3

Prob(N passes) = 4/5; prob(N fails) = 1 – 4/5 = 1/5

Prob(only one passes) = (2/3 × 1/5) + (1/3 × 4/5)

= 2/15 + 4/15

= 6/15

= 2/15

(3bii)

prob(at least one passes) = prob(only one passes) + prob(both parties)

= 2/5 + (2/3 × 4/5)

= 2/5 + 8/15

= 6/15 + 8/15

# = 14/15

4

tany = √2

Opp = √2 and Adj = 1

hyp = √[2 + 1) = √3

a) cosy = 1/√3 = √3/3

b)

sinx = 1 – √3/3

sinx = (3-√3)/3 = 0.4226

# x = 25°

QUESTION 5

Loop +mop 360 Angle at a pont )

obtuse & Mop +96° = 360°

obtuse < MOP = 360 -1969

But OP = OPM = x Radius of the circle and hence

ome + oem + obtuse mêp = 180° in a triangle )

- tase angles are the same

2x =

150-164

20 – 16

Als MNP

= 32

MRP NMPN?M 80 (h

82 +62+8) + Ctr) = 180

Now

A)

m= iso- 1500

# M =30°

8a)8th term=a+7d

4th term=a+3d

a+7d-a+3d=40

10d=40

d=40/10

d=4..

8aii)a+7d=3/2(a+3d)

2(a+7d)=3(a+2d)

2a + 14d =3a + 6d

Where d=4.

2a+ 14(4)= 3a + 6(4)

2a + 56 = 3a + 24

2a-3a = 24-56

-a = -32

# a= 32.

(9i) DRAW THE DIAGRAM

n (U) = 110

n (P) = 25

n (B) = 45

n (M) = 48

n (Pnm) = 10

n (Bnm) = 8

n (pnBnm) = 5

(9ii) for biology = 45 = 36

(9iii)

x + 14 + 1 + 5 + 5 + 36 + 3 + 35 = 110

x + 25 + 36 + 38 = 110

x = 110 – 99

x = 11

(9b)

15 = 22 + 18 + 2 x 1 + 10 +20/5

15 x 5 = 40 + 2x + 31

45 = 71 + 2x

45 – 71 + 2x

2x/2 = -26/2

X = 13

22, 18, 2x + 1, 10 , 20

For 2x (-B) +1 = -26 +1 = -25

22, 18, -25, 10, 20

-25, 10, 18, 20, 22

The media is 18