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Mathematics
UTME / JAMB 2005
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The grades of 36 students in a test are shown in the pie chart above. How many students had excellent?
Attached Figure / Diagram
A
7
B
8
C
9
D
12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Angle of Excellence
= 360 - (120+80+90)
= 360 - 290
= 70o
If 360o represents 36 students
1º will represent \(\frac{36}{360}\)
50^\circ will represent \(\frac{36}{360}\) * \(\frac{70}{1}\)
= 7
Source: Myschool Past Questions Archive (Record #8535)
Mathematics
UTME / JAMB 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The table above shows that the scores of a group of students in a test. If the average score is 3.5, find the value of x
Attached Figure / Diagram
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(mean=\frac{60+5x}{18+x}\\3.5=\frac{60+5x}{18+x}\\\frac{7}{2}=\frac{60+5x}{18+x}\)
7(18+x) = 2(60+5x)
126 + 7x = 120 + 10x
10x - 7x = 126 - 120
3x = 6
x = 2
Source: Myschool Past Questions Archive (Record #8609)
Mathematics
UTME / JAMB 2005
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The modal height and range of heights 1.35, 1.25, 1.35, 1.40, 1.35, 1.50, 1.35, 1.50, and 1.20 are m and r, respectively. Find m+2r.
A
1.35
B
1.65
C
1.95
D
3.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1.35, 1.25, 1.35, 1.40, 1.35, 1.50, 1.35, 1.50, and 1.20
Modal height = 1.35
Range (r) = 1.50 - 1.20
= 0.30
∴m + 2r = 1.35 + 2(0.30)
= 1.35 + 0.60
= 1.95
Source: Myschool Past Questions Archive (Record #8610)
Mathematics
UTME / JAMB 2005
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the value of t if the standard deviation of 2t, 3t, 4t, 5t, and 6t is \sqrt2
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(mean(x) = \frac{20t}{5}\)
= S.D = \(\sqrt{\frac{((\overline{x} - x)^2}{\text{n}}}\)
\(\sqrt{2}\) = \(\sqrt{\frac{10t^2}{5}}\)
2 = \(\frac{10t^2}{5}\)
10t\(^2\) = 10
t\(^2\) = 1
t = \(\sqrt{1}\) = 1
Source: Myschool Past Questions Archive (Record #8611)
Mathematics
UTME / JAMB 2005
Permutations, Combinations & Probability
Solution
In how many ways can 6coloured chalks be arranged if 2 are same colour?
A
60
B
120
C
240
D
360
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{6!}{2!} = ways
=\(\frac{6\times5\times4\times3\times2!}{2!}\)
= 6\(\times5\times4\times3\)
= 360ways
Source: Myschool Past Questions Archive (Record #8612)
Mathematics
UTME / JAMB 2005
Permutations, Combinations & Probability
Solution
How many possible ways are there of seating seven people P,Q,R,S,T,U and V at a circular table
A
360
B
720
C
2520
D
5040
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(n - 1)! = (7 - 1)!
= 6!
= 6*5*4*3*2*1
= 720 ways
Source: Myschool Past Questions Archive (Record #8613)
Mathematics
UTME / JAMB 2005
Permutations, Combinations & Probability
Solution
A box contains 5 blue balls, 3 red balls and 2 white balls. Two balls are selected from the box with replacement. Find the probability of obtaining two blue or two red balls
A
\(\frac{17}{50}\)
B
\(\frac{3}{25}\)
C
\(\frac{1}{50}\)
D
\(\frac{3}{250}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Blue balls = 5
Red balls = 3
White balls = 2
Total = 10
P(Two blue) = 5/10 * 5/10 = 25/100
P(Two Red) = 3/10 * 3/10 = 9/100
∴P(Two blue or two red balls)
= 25/100 + 9/100
= 34/100
= 17/50
Source: Myschool Past Questions Archive (Record #8614)
Mathematics
UTME / JAMB 2005
Inequalities & Linear Programming
Solution
What is the probability that an integer x,(1 \(\leq\) x \(\leq\) 20) chosen at random is divisible by both 2 and 3?
A
\(\frac{1}{20}\)
B
\(\frac{1}{3}\)
C
\(\frac{3}{20}\)
D
\(\frac{7}{10}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}
A = {x/x is divisible by 2}
A = {2,4,6,8,10,12,14,16,18,20}
B = {x/x is divisible by 3}
A ∩ B = {6, 12, 18}
P(Number divisible by both 2 and 3)
= 3/20
Source: Myschool Past Questions Archive (Record #8615)
Mathematics
NECO SSCE 2005
Number Bases & Modular Arithmetic
Solution
What is the Value of 11101\(_{two}\)+ 10011\(_{two}\) - 10001\(_{two}\)?
A
10001\(_{two}\)
B
10011\(_{two}\)
C
10111\(_{two}\)
D
11111\(_{two}\)
E
111111\(_{two}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
11101\(_{two}\) → 29
+ 10011\(_{two}\) → 19
- 10001\(_{two}\) → 17
11111 = 31
Source: WAEC / JAMB / NECO Classroom Archive (Record #42425)
Mathematics
WAEC / WASSCE 2005
Fractions, Decimals, Percentages & Approximations
Solution
Correct 0.04945 to two significant figures
A
0.040
B
0.049
C
0.050
D
0.49
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
0.04945 \(\approxeq\) 0.049. (to 2 sig. figs)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26670)
Mathematics
WAEC / WASSCE 2005
Fractions, Decimals, Percentages & Approximations
Solution
Simplify: \(\frac{2}{3xy} - \frac{3}{4yz}\)
A
\(\frac{2-x}{12xyz}\)
B
\(\frac{2z-3x}{12xyz}\)
C
\(\frac{4z-3x}{12xyz}\)
D
\(\frac{8z-9x}{12xyz}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{2}{3xy} - \frac{3}{4yz} = \frac{2(4)-3(3x)}{12xyz} = \frac{8z-9x}{12xyz}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26703)
Mathematics
WAEC / WASSCE 2005
Fractions, Decimals, Percentages & Approximations
Solution
Ladi sold a car for N84,000 at a loss of 4%. How much did ladi buy the car?
A
80,500
B
80,640
C
87,360
D
87,500
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
SP = 84,000
Loss% = 4%
100% = 4% = 96% = \(\frac{96}{100}\)
Reverse \(\frac{96}{100}\) and use it to multiply SP to get the cost price.
CP = 84,000 x \(\frac{100}{96}\) = N 87500.
Source: WAEC / JAMB / NECO Classroom Archive (Record #26713)
Mathematics
WAEC / WASSCE 2005
Trigonometry, Elevation & Bearings
Solution
The angle of elevation of the top of a cliff 15 meters high from a landmark is 60º. How far is the landmark from the foot of the cliff? Leave your answer in surd form
A
\(15\sqrt{3}m\)
B
\(15\sqrt{2}m\)
C
\(10\sqrt{3}m\)
D
\(5\sqrt{3}m\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Tan 60º = \(\frac{15}{x}\)
cross multiply:
x = \(\frac{15}{\sqrt3}\) = 5\(\sqrt3\)m
Source: WAEC / JAMB / NECO Classroom Archive (Record #26709)
Mathematics
WAEC / WASSCE 2005
Indices, Logarithms & Surds
Solution
Simplify \(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}\)
A
\(\frac{1}{6}(5\sqrt{3}-3\sqrt{2}\)
B
\(\frac{1}{6}(15\sqrt{3}-6\sqrt{2}\)
C
\(\frac{1}{6}(3\sqrt{2}-\sqrt{3}\)
D
\(\frac{1}{6}(10\sqrt{3}-9\sqrt{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{5}{\sqrt{3}}-\frac{3}{\sqrt{2}}=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}}\\
=\frac{5\sqrt{2}-3\sqrt{3}}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}}Rationalize\\
\frac{\sqrt{6}(5\sqrt{2}-3\sqrt{3})}{6}\\
\frac{5\sqrt{12}-3\sqrt{18}}{6}=\frac{10\sqrt{3}-9\sqrt{2}}{6}\\
\frac{1}{6}(10\sqrt{3}-9\sqrt{2})\)
Source: Myschool Past Questions Archive (Record #26671)
Mathematics
WAEC / WASSCE 2005
Fractions, Decimals, Percentages & Approximations
Solution
Evaluate, correct to the nearest whole number \(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div\frac{33}{2}\)
A
33
B
8
C
7
D
o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div\frac{33}{2}\\
=\frac{15}{2}-\left(\frac{5}{2}+\frac{3}{1}\right)\times\frac{2}{33}\\
=\frac{15}{2}-\left(\frac{5+6}{2}\right)\times \frac{2}{33}=\frac{15}{2}-\frac{11}{2}\times \frac{2}{33}=\frac{15}{2}-\frac{1}{3}\\
=\frac{45-2}{6}=\frac{43}{6}\)
= 7.1666 ≈ 7
Source: Myschool Past Questions Archive (Record #26672)