ONDO JOINT MATHS RUNZ
MATHEMATICS-OBJ
1-10: DCCADCBBAB
11-20: DCADBCBDAC
21-30: BDAADBCBBA
31-40: DABDCABDCA
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ONDO-MATHS-ANSWERS-BY-DONIZZY
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VERIFY MATHEMATICS THEORY ANSWER
SECTION A: (30 Marks)
INSTRUCTION:Answer all questions. All Questions carry equal marks.
(1a)
1011.1012= 13021110. 1-10-21-3
= (1*23)+(0*22)+(1*21)+(1*20)+(1*2-1)+(1*2-2)+(1*2-3)
= (1*8) + (0*4) + (1*2) + (1*1) + (1*1/2) + (0*1/4) + (1*1/8)
= 8 + 0 + 2 + 1 + 1/2 + 0 + 1/8
= 11 + 1/2 + 1/8 = 88 + 4 + 1/8 = 93/8 = 11.625
1011.1012= 11.62510
1011.101two= 11.625ten
(b)
Draw The Table in Row & Column Like The Question..
|(x)| 0 | 1 | 2 | 3 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 |
| 2 | 0 | 2 | 4 | 1 | 3 |
| 3 | 0 | 3 | 1 | 4 | 2 |
| 4 | 0 | 4 | 3 | 2 | 1 |
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(2a)
Solve 4r – 3/6r + 1 = 2r – 1/3r + 4
Cross Multiply
(4r – 3)(3r + 4) = (2r – 1) (6r + 1)
12r2+ 16r – 9r – 12 = 12r2+ 2r – 6r – 1
12r2+ 7r – 12 = 12r2– 4r -1
12r2– 12r2+ 7r + 4r = -1 + 12
11r = 11
Divide both sides by 11
11r/11 = 11/11
r = 1Ans…
(b)
Sn= n/2 [2a + (n -1)d]
S9= 9/2 [2a + (a-1)d] = 72
S9= 9/2 [2a + 8d] = 72
Next four terms = 71
S13= 13/2 [2a + (13-1)d] = 72 + 71
13/2 [2a + 12d] = 143
S9=> 18a + 72d = 144 ——– (eqn i) a + 4d =8
S13=> 26a + 156d = 286 ——-(eqn ii) a + 6d = 11
Subtract
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(3a)
Solve 9(x-3)= 27(x-5)
32 (x-3)= 33 (x-5)
2(x-3) = 3(x-5)
2x-6 = 3x-15
-6 + 15 = 3x -2x
9 = x
x = 9Ans…
(b)
U = { all integers}. = {…,-3,-2,-1,0,1,2,3,…}
P = {x:x ≤0}. = {…,-3,-2,-1,0}.
R = {x:-2 ≤x <7}. = {-2,-1,0,1,2,3,4,5,6,} pI= {1,2,3,…}, RI= {…,-3,7,8,9,…}
PI⋂ RI= {1,2,3,…] ⋂ {…,-3,7,8,9,…}
= {7,8,9,10,11,…}
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(4a)
Given that P = m/4√a2– x2
to express x in terms of P,m and a
Cross Multiply
4P = m√a2– x2, Divide both sides by m.
4P/m = √a2– x2
square both sides
(4P/m)2= (√a2– x2
)2
(4P/m)2= a2– x2
16P2/m2– a2=-x2
=> x2= 16P2/m2+ a2
x2= a2– 16P2/m2
x=m√a2– 16P2/m2
=a – 4P/m = am – 4P/m
x = am – 4P/m
(b)
True Table for ∽ (P ⋀ ∽ q)
p q ∽q p⋀∽ ∽(p p⋀
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(5)
Let income be = x
1/8 of x = x/8 on tax free
(7/8 * 20/100)x = 7/40x
x/8 + 7x/40 + 49000 = x
5x + 7x + 1,960,000/40 = x
5x + 7x + 1,960,000 = 40x
1,960,000 = 40x – 12x
1,960,000 = 28x
Divide both sides by 28
1,960,000/28 28x/8
x = #70,000
∴ The tax payer`s income is #70,000
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SECTION B: (50 Marks)
INSTRUCTION:Answer any five (5) questions from this section. All Questions carry equal marks.
(6a)
nth term = a + (n-1)d
4th term = a + (4-1)d = a+3d = -3
9th term = a + (9-1)d = a+8d = 12
Let a+3d = -3 —————— (eqn i)
a+8d = 12 —————— (eqn ii)
Subtract eqn ii from eqn i
3d – 8d = -3 – 12
-5d = -15
d = -15/-5
d = 3.
sum of the first seven terms
Snn/2 [2a+(n-1)d]
where n = 7, d = 3, a = -12
Sn7/2 [2(-12) + (7-1)(3)]
= 7/2 [-24 + 18]
= 7/2 [-6] = -42/2 = -21
Sketch the Circle
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(8)
To get the value of n.
543n = 244n + 255n
5*n2 + 4*n + 3*no = 2*n2 + 4*n + 4*no + 2*n2 + 5*n + 5*no
5n2 + 4n + 3 = 2n2 + 4n + 2n2 5n + 5
5n2 + 4n + 3 = 4n2 +9n + 9
5n2 – 4n2 + 4n – 9n + 3 – 9 = 0
n2 – 5n – 6 = 0
n2 + n -6n – 6 = 0
n(n+1) -6 (n+1) = 0
(n+1)(n-6) = 0
n = -1 or 6
n = 6
(b)
Sketch out the Triangle
Cos65o = h/25
=> 25 cos 65o = h
h = 25 (0.4226)
h = 10.5650
h = 10.6 (1 d.p)
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