Waec Gce 2019 Further Mathematics Answers And Questions To Essay/Obj Expo Answer

2019 WAEC GCE FURTHER MATHEMATICS ANSWERS

F/MATHS OBJ
1-10: ABCCBCDBDC
11-20: DBDCADABCD
21-30: BCBBCDCCCD

31-40: CBDABBAACA

(1)
Digits 1,2,4,5,6
The first digit can be formed in 5 ways
The last digit can be formed in 2 ways since no repition take place
The second digit can be formed in 3 ways
The third digit can be formed in 2 ways
The fourth in 1 way
Total ways
53212

Answer= 60 ways

(2)
ar^4-1=54
ar^3=54————(1)
ar^6-1=486
ar^5=486————(2)
Divide equation (2) by (1)
ar^5/ar^3=496/54
r²=9
Square root both sides
r=√9
r=3//
Substitute r=3 on equation (1)
a(3)³=54
a(27)=54
Divide both sides by 27
a=54/27
a=2//
3rd term
ar^n-1
2(3)³–¹
2(3)²
2(9)

18//

(4)
y=3x²+4x–1 —————(1)
y+∆y=3(x+∆x)² + 4(x+∆x) –1 ————(2)
Subtract (1) from (2)
∆y=3(x+∆x)² + 4(x+∆x) –1–(3x²+4x–1)
=3(x²+2x∆x+∆x²) +4(x+∆x) –1–(3x²+4x–1)
=3x²+6x∆x+3∆x²+4x+4∆x–1–3x²–4x+1
∆y=6x∆x+3∆x²+4∆x
∆y/∆x=6x∆x3∆x²+4∆x/∆x
∆y/∆x=(6x+3∆x+4)∆x/∆x
Lim ∆y/∆x=∆y/∆x=6x+3(0)+4
∆x→0

∆y/∆x=6x+4

(5) sample space
TABULATE
★| 1 2 3 4 5 6
1 | 11 12 13 14 15 16
2 | 21 22 23 24 25 26
3 | 31 32 33 34 35 36
4 | 41 42 43 44 45 46
5 | 51 52 53 54 55 56
6 | 61 62 63 64 65 66
TABULATE

• | 1 2 3 4 5 6
  1| 2 (3) 4 5 (6) 7
  2| (3) 4 5 (6) 7 8
  3| 4 5 (6) 7 8 (9)
  4| 5 (6) 7 8 (9) 10
  5| (6) 7 8 (9) 10 11
  6| 7 8 (9) 10 11 (12)

probability of
(a) multiple of 3=12/36=1/3

(b) between 3 and 6 =7/36