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Mathematics
UTME / JAMB 1999
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
The table above shows the frequency distribution of the ages (in years) of pupils in a certain secondary school. What percentage of the total number of pupils is over 15 years but less than 21 years?
Attached Figure / Diagram
A
35%
B
45%
C
50%
D
60%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
% of those above 15 but less than 21 years
age = \(\frac{25}{50}\) x \(\frac{100}{1}\)
= 50%
Source: Myschool Past Questions Archive (Record #10420)
Mathematics
WAEC / WASSCE 1999
Inequalities & Linear Programming
Solution
The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?
A
39cm ≤ P ≤41cm
B
38cm ≤ P < 42cm
C
38.5 ≤ P ≤ 41.5cm
D
38.5 ≤ P ≤ 40cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If the side = 10 cm, correct to the nearest whole number, then
The side ranges from 9.5 cm to 10.5 cm. (9.5 \(\leq\) s < 10.5)
Perimeter of a rhombus = 4 x side
\(\therefore\) 4 x 9.5 \(\leq\) perimeter < 4 x 10.5
= 38 cm \(\leq\) P < 42 cm
Source: Myschool Past Questions Archive (Record #26380)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.
A
0
B
\(2log_7 2\)
C
\(3log_7 2\)
D
\(4log_7 2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4
= log\(_7\) (8/2 x 4)
= log\(_7\) 16
= 4 log\(_7\) 2
Source: Myschool Past Questions Archive (Record #26381)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.
A
-2
B
-1
C
1
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\\
2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0\\
2K\sqrt{7}=-2\sqrt{7}\\
K=\frac{-2\sqrt{7}}{2\sqrt{7}}\\
K=-1\)
Source: Myschool Past Questions Archive (Record #26382)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number
A
\(\frac{1}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{3}{5}\)
D
\(\frac{4}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(A = {3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}}\)
n(A) = 5
Let the rational nos = R
n(R) = 2 (3, \(\sqrt{9}\))
P(R) = 2/5
Source: Myschool Past Questions Archive (Record #26383)
Mathematics
WAEC / WASSCE 1999
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
Find the value of K
Attached Figure / Diagram
A
15o
B
30o
C
60o
D
90o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total angle in a circle = 360^\circ
\(\therefore\) 105 + 75 + 2k + k + 3k = 360^\circ
6k = 360 - 180 = 180
k = 180/6 = 30^\circ
Source: Myschool Past Questions Archive (Record #26384)
Mathematics
WAEC / WASSCE 1999
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week
A
\(3\frac{1}{3}\) hours
B
5 hours
C
8 hours
D
12 hours
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let x represent the total number of hours spent per week
∴ \(\frac{75}{360} \times x = \frac{5}{2}\)
∴ x =\(\frac{360 \times 5}{725 \times 2}\) =12 hours
Source: Myschool Past Questions Archive (Record #26385)
Mathematics
WAEC / WASSCE 1999
Permutations, Combinations & Probability
Solution
A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?
A
\(\frac{2}{11}\)
B
\(\frac{4}{11}\)
C
\(\frac{5}{11}\)
D
\(\frac{11}{13}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let the number of people that speak both English and French = x
Then (7 - x) + x + (6 - x) = 11
13 - x = 11 \(\implies\) x = 2.
\(\therefore\) P(picking a person that speaks both languages) = 2/11
Source: Myschool Past Questions Archive (Record #26386)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Solution
The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?
A
5
B
6
C
8
D
9
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let the exterior angle = d
Note: Exterior angle + Interior angle = 180^\circ
\(\implies\) d + 2d = 180^\circ
3d = 180^\circ \(\implies\) d = 60^\circ
Recall, exterior angle = \(\frac{360}{\text{no of sides}}\)
\(\therefore \text{No of sides} = \frac{360}{60}\)
= 6 sides
Source: Myschool Past Questions Archive (Record #26387)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Solution
Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite
A
I and II only
B
II and III only
C
I and III only
D
I, II, and III
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Isosceles triangle and Kite shapes have 1 line of symmetry each while the rhombus has 2 lines of symmetry.
Source: Myschool Past Questions Archive (Record #26388)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Calculate the value of Y in the diagram
Attached Figure / Diagram
A
18o
B
42o
C
48o
D
132o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x = 180^\circ - 123^\circ = 57^\circ
z = 180^\circ - 105^\circ = 75^\circ
y = 180^\circ - 57^\circ - 75^\circ = 48^\circ
Source: Myschool Past Questions Archive (Record #26391)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, POR is a circle with center O. ∠QPR = 50^\circ, ∠PQO = 30^\circ and ∠ORP = m. Find m.
Attached Figure / Diagram
A
20o
B
25o
C
30o
D
50o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
< QOR = 50^\circ x 2 = 100^\circ
Reflex < QOR = 360^\circ - 100^\circ = 260^\circ
\(\therefore\) 30^\circ + 50^\circ + 260^\circ + m = (4 - 2) x 180^\circ
340^\circ + m = 360^\circ
m = 360^\circ - 340^\circ = 20^\circ
Source: Myschool Past Questions Archive (Record #26392)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Solution
Given that m = -3 and n = 2 find the value of \(\frac{3n^2 - 2m^3}{m}\)
A
-22
B
-14
C
14
D
22
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given that m = -3, n = 2, the value of
\(\frac{3n^2 - 2m^3}{m}\)
\(\frac{3(2)^2 -2(-3)^3}{-3} = \frac{12+54}{-3}\) = -22
Source: Myschool Past Questions Archive (Record #26393)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{2-18m^2}{1+3m}\)
A
\(2(1+3m)\)
B
\(2(1+3m^2)\)
C
\(2(1-3m)\)
D
\(2(1-3m^2)\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{2-18m^2}{1+3m}=\frac{2(1-(3m)^2)}{1+3m}\\
\frac{2(1-(3m)(1+3m)}{1+3m}=2(1-3m)\)
Source: Myschool Past Questions Archive (Record #26394)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Solution
If \(y = \sqrt{ax-b}\) express x in terms of y, a and b
A
\(x = \frac{y^2-b}{a}\)
B
\(x = \frac{y+b}{a}\)
C
\(x = \frac{y-b}{a}\)
D
\(x = \frac{y^2 + b}{a}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(y = \sqrt{ax-b}\)
\(y^2 = ax-b\)
\(y^2 +b = ax\)
\(x = \frac{y^2 + b}{a}\)
Source: Myschool Past Questions Archive (Record #26395)