# 2000 JAMB Mathematics Past Questions & Answers - page 1

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1
Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}.

Determine (P-Q) ∩ R
A {1, x}
B {x y}
C {x}
D ɸ

Correct Option: C

Solution
P = {1,2,u,v,w,x}
Q = {2,3,u,v,w,5,6,y}
R = {2,3,4,v,x,y}

P - Q = {1,x}
(P - Q) ∩ R = {1,x} ∩ {2,3,4,v,x,y} = {x}

2
If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000?
A 480,000
B 249,696
C 249,600
D 244,800

Correct Option: B

Solution
1st year, Population = 240,000 x (2/100) = 4800.
Being the 2nd year population = 240,000 x 4800 = 244800.
Increase in Pop. in 2nd year = 244800 x (2/100) = 4896
Jan 2000, Pop. = 244800 + 4896 = 249,696

3
If $$\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}$$, find the values of m and n respectively.
A 1, -2
B -2, 1
C $$\frac{-2}{5}$$, 1
D 2, 3/5

Correct Option: B

Solution
Rationalize $$\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}$$ and equate to $$m +n\sqrt{6}$$. Such that m = -2, and n = 1.

4
In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?
A 8
B 24
C 62
D 86

Correct Option: C

Solution
Use a venn diagram:

60-3x+3x+50-3x = 94-x.
110-3x+x = 94
-2x = 94-110

=>-2x = -16, this x = -8.

Members that like only one game:
= 60 - 3x + 50 - 3x
= 60 - 3x8 + 50 - 3x8
= 60 - 24 + 50 - 24
= 36 + 26 = 62

5
Evaluate (2.813 x 10-3 x 1.063) (5.637 x 10-2)
A 0.056
B 0.055
C 0.054
D 0.54

Correct Option: B

6
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit?
A N112,000.50
B N96,000.00
C N85,714.28
D N76,800.00

Correct Option: D

Solution
Amount A = P(1+r)n;
A = N150,000, r = 25%, n = 3.
150,000 = P(1+0.25)3 = P(1.25)3

P = 150,000/1.253 =N76,800.00

7
If 31410 - 2567 = 340x, find x.
A 7
B 8
C 9
D 10

Correct Option: A

Solution
31410 - 2567 = 340x,
Convert 2567 and 340x to base 10, such that:
314 - 139 = 3x2 + 4x
=> 3x2 + 4x - 175 = 0 (quadratic)
Factorising, (x - 7) (3x + 25) = 0,
either x = 7 or x = -25/3 ( but x cannot be negative)

Therefore, x = 7.

8
Simplify 3(2n+1) - 4(2n-1) 2n+1 - 2n
A 2n+1
B 2n-1
C 4
D 1/4

Correct Option: C

Solution
Start by expanding 3(2n+1) - 4(2n-1) 2n+1 - 2n:

3 x 2n x 21 - 22 x 2n x 2-1 2n x 2 -2n

Solving the equation above gives;
2n x 21 x 2 2n = 2 x 2 = 4

9
If P3446 - 23P26 = 2PP26, find the value of the digit P.
A 2
B 3
C 4
D 5

Correct Option: D

Solution
Covert everything to base 10 and collect like terms, such that:
210P - 42P = 434 + 406
168P = 840
P = 840/168 = 5

10
A binary operation * is defined by a*b = ab. If a*2 = 2-a, find the possible values of a.
A 1, -1
B 1, 2
C 2, -2
D 1, -2

Correct Option: D

Solution
a * b = ab
a * 2 = a2 = 2 - a
a2 + 2a - a - 2 = 0
a(a+2) - 1(a+2) = 0
(a-1)(a+2) = 0
a = 1, -2

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