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Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram PQRS is a circle, |PT| = |QT| and ∠QPT = 70o what is the size of ∠PRS?
Attached Figure / Diagram
A
40o
B
70o
C
80o
D
140o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
∠QPT = ∠QTP = 70o. Since ∠QTR = 140o
∠PRS = TSR = 1/2(180-40) = 70o
Source: Myschool Past Questions Archive (Record #26708)
Mathematics
WAEC / WASSCE 2005
Mensuration (Areas, Perimeters & Volumes)
Solution
XOY is a real sector of a circle center O of radius 3.5cm which subtends an angle of 144o at the center. Calculate, in term of \(\pi\), the area of the sector
A
1.4\(\pi\)cm2
B
2.8\(\pi\)cm2
C
4.9\(\pi\)cm2
D
9.8\(\pi\)cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of a sector \(=\frac{\theta}{360}\times \pi r^2\\
\left(\frac{144}{360}\times \pi \times \frac{3.5}{1} \times 3.5\right)cm^2 = 4.9\pi cm^2\)
Source: Myschool Past Questions Archive (Record #26710)
Mathematics
WAEC / WASSCE 2005
Mensuration (Areas, Perimeters & Volumes)
Solution
A rectangular packet has inner dimension 16cm by 12cm by 6cm. How many cubes of sugar of side 2cm can be neatly packed into the packet?
A
90
B
144
C
150
D
288
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of rectangular packet = (16 x 12 x 6)cm3 = 1152cm3. Volume of cube of sugar = 2 x 2 x 2 = 8cm
∴ The number of cubes f sugar \(=\frac{1152}{8}=144\)
Source: Myschool Past Questions Archive (Record #26711)
Mathematics
WAEC / WASSCE 2005
Linear, Simultaneous & Quadratic Equations
Solution
If y \(\alpha\) x\(^2\) and y = 1\(\frac{1}{4}\) when x = 4, find the value of y when x = \(\frac{1}{2}\)
A
\(2\frac{1}{2}\)
B
5
C
10
D
80
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y \(\propto x^2\), y = 1\(\frac{1}{4}\), x = 4
y = \(\frac{\text{k}}{x^2}\)
k = y x\(^2\) = \(\frac{5}{4}\) x 4\(^2\) = 20
y = \(\frac{20}{x^2}\) = \(\frac{20}{x^2}\) = \(\frac{20}{(\frac{1}{2})^2}\)
= \(\frac{20}{\frac{1}{4}}\) = 20 x 4 = 80
Source: Myschool Past Questions Archive (Record #26712)
Mathematics
WAEC / WASSCE 2005
Fractions, Decimals, Percentages & Approximations
Solution
The monthly salary of a man increased from N2,700 to N3,200. Find the percentage increase
A
10%
B
15%
C
15.6%
D
18.5%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\% increase = \frac{Increase}{initial\hspace{1mm} salary}\times 100\%\)
Increase = N3,200 - N2,700 = N500
Initial \(\hspace{1mm} salary = N2,700.00 = \frac{N500}{N2,700}\times 100\% = 18.5\%\)
Source: Myschool Past Questions Archive (Record #26714)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, O is the center of the circle, ∠MON = 80o, ∠LMO = 10o and ∠LNO = 15o. Calculate the value of x
Attached Figure / Diagram
A
40o
B
50o
C
55o
D
75o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Reflex + ∠OML + ∠ONL + ∠NLM = 360
280o + 10o + 15o + x = 360o => 305o + xo = 360o
x = 360o - 305o = 55o
Source: Myschool Past Questions Archive (Record #26715)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The figure shows a quadrilateral PQRS having equal sides and opposite sides parallel. The diagonals PR and QS intersect perpendicularly at O, Which of the following statements cannot be correct
Attached Figure / Diagram
A
|PO|=|RO|
B
PQR is an equilateral triangle
C
PQRX is a parallelogram
D
There are two lines of symmetry
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Since PQRS is a quadrilateral with equal sides, PQR cannot be an equilateral triangle unless R coincides with S, which is not the case in a quadrilateral.
Source: Myschool Past Questions Archive (Record #26716)
Mathematics
UTME / JAMB 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
in the diagram above, calculate the value of x.
Attached Figure / Diagram
A
60o
B
100o
C
120o
D
140o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
FROM the diagram above
100 + a = 180 (sum of angles on a straight line)
a = 180 - 100 = 80º
Z = 80 + 40 = 120º (exterior angles of a triangle = sum of the two opp. interior angles)
Z = x = 120º (corresponding angles are equal).
Source: Myschool Past Questions Archive (Record #33120)
Mathematics
UTME / JAMB 2005
Trigonometry, Elevation & Bearings
Diagram
Solution
From the diagram given, find the bearing of R from S
Attached Figure / Diagram
A
226o
B
224o
C
136o
D
134o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The bearing of R from S = 180 + 44 = 224º, because
-Following the clockwise movement at 90º:
-NORTH -EAST, EAST-SOUTH, SOUTH - WEST & WEST - NORTH
- It is observed that R is situated between SOUTH - WEST poles on S
Source: Myschool Past Questions Archive (Record #33122)
Mathematics
NECO SSCE 2005
Plane Geometry, Polygons & Circle Theorems
Solution
The diagonals of a rhombus are 6cm and 8cm. Find the area of the rhombus.
A
96cm2
B
48cm2
C
24cm2
D
0.14cm2
E
12cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of a rhombus = \(\frac{pq}{2}\)
where p and q are the two diagonals of the rhombus.
Source: Myschool Past Questions Archive (Record #42350)
Mathematics
NECO SSCE 2005
Plane Geometry, Polygons & Circle Theorems
Mohammed is 8 years older than Joy now. In five years’ time he will be twice as old as Joy. How old is Joy now?
A
1\(\frac{1}{2}\)years
B
3years
C
4\(\frac{1}{2}\)years
D
6 years
E
8 years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42354)
Mathematics
NECO SSCE 2005
Plane Geometry, Polygons & Circle Theorems
If (x - a) is a factor of bx - ax + x2 - ab, what is the other factor?
A
(x + b)
B
(b - a)
C
(x - a)
D
(a + b)
E
(a - b)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #42358)
Mathematics
NECO SSCE 2005
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify (6 - x - x2) \div (x2 - 4)
A
(3 + x) ÷ (x + 2)
B
(x - 3) ÷ (x - 2)
C
(x - 3) ÷ (x + 3)
D
(3 - x) ÷ (x + 2)
E
(3 - x) ÷ (x - 2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(6 - x - x2) = ( 2 - x ) ( 3 + x )
divides
( x^2 - 4 ) = ( -2 - x ) ( 2 - x )
= ( 3 + x ) / ( x + 2)
Source: Myschool Past Questions Archive (Record #42360)
Mathematics
NECO SSCE 2005
Statistics (Data Representation, Central Tendency & Dispersion)
Find the absolute mean deviation of the sample 10, 12, 14, 11, 13.
A
14.6
B
14
C
12
D
6.2
E
1.2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #42362)
Mathematics
NECO SSCE 2005
Plane Geometry, Polygons & Circle Theorems
In Δ ABC, A = 60°, C = 90° and AC = 12m. Find the Length of the hypotenuse.
A
24m
B
14m
C
12m
D
7m
E
6m
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #42364)