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Mathematics
WAEC / WASSCE 2005
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
A car dealer sells a car and makes a profit of 15%. If the car costs N320,000.00, how much did he sell the car?
A
N272,000.00
B
N296,000.00
C
N300,000.00
D
N368,000.00
E
N400,000.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #42379)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
A flagpole is placed at the top of a tower. The angles of elevation of the bottom and top of the flagpole from a point on the ground 10m away are 40° and 50° respectively. Find the length of the flagpole.
A
1.8m
B
3.5m
C
8.4m
D
11.9m
E
17.3m
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 #42391)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
A ship sails 6km from a port on a bearing 070° and then 8km on a bearing of 040°. Find the distance from the port.
A
7.21km
B
13.53km
C
16.86km
D
44.57km
E
67.17km
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 #42431)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
Calculate without using tables Tan 45° + Cos 60°
A
\(\sqrt{\frac{3}{2}}\) - 1
B
\(\frac{1}{2}\)
C
1\(\frac{1}{2}\)
D
\(\sqrt{\frac{3}{2}}\) + 1
E
2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #42438)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
A is at 50°N and B is at 10°N, If A and B are on the same longitude, find the distance AS. Correct your answer to Four significant figures. (Earth radius = 6400km)
A
6468km
B
5469km
C
4470km
D
3470km
E
2488km
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #42441)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
Solution
Find the standard deviation of the numbers 6, 9, 10, 8 and 7
A
1.4
B
2
C
2.4
D
5
E
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
6, 9, 10, 8 and 7
S.D = \(\sqrt{V}\)
S.D = standard deviation, V = variance
V = \(\frac{\sum({x - \overline{x})^2}}{n}\)
Mean(\(\overline{x}\)) = \(\frac{6 + 9 + 10 + 8 + 7}{5}\) = 8
x
x - \(\overline{x}\)
(x - \(\overline{x}\))\(^2\)
6
6 - 8 = -2
4
9
9 - 8 = 1
1
10
10 - 8 = 2
4
8
8 - 8 = 0
0
7
7 - 8 = -1
1
TOTAL = 10
V = \(\frac{\sum({x - \overline{x})^2}}{n}\) = \(\frac{10}{5}\) = 2
S.D = \(\sqrt{V}\) = \(\sqrt{2}\) = 1.414 ≈ 1.4
Source: Myschool Past Questions Archive (Record #42451)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
A chord 20cm long subtends an angle of 60° at the circumference of a circle, what is the diameter of the circle the nearest cm?
A
12cm
B
20cm
C
23cm
D
60cm
E
80cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #42458)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.
A
5cm
B
6cm
C
7cm
D
10cm
E
12cm
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 #42462)
Mathematics
WAEC / WASSCE 2005
Geometry and Trigonometry
Solution
(a) Two fair die are thrown once. Find the probabitlity of getting : (i) the same digit ; (ii) a total score greater than 5.
(b) Given that \(x = \cos 30^\circ\) and \(y = \sin 30^\circ\), evaluate without using a mathematical table or calculator : \(\frac{x^{2} + y^{2}}{y^{2} - x^{2}}\).
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) Sample - space
1
2
3
4
5
6
1
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
3
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
4
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
5
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6
6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6
(i) Same digit = {(1,1), (2,2),(3,3), (4,4),(5,5), (6,6)}
P(same digit) = \(\frac{6}{36}\)
(ii) P(total score greater than 5) = \(\frac{26}{36}\)
= \(\frac{13}{18}\)
(b) \(\frac{x^{2} + y^{2}}{y^{2} - x^{2}} = \frac{(\cos 30)^{2} + (\sin 30)^{2}}{(\sin 30)^{2} - (\cos 30)^{2}}\)
= \(\frac{(\frac{\sqrt{3}}{2})^{2} + (\frac{1}{2})^{2}}{(\frac{1}{2})^{2} - (\frac{\sqrt{3}}{2})^{2}}\)
= \(\frac{\frac{3}{4} + \frac{1}{4}}{\frac{1}{4} - \frac{3}{4}}\)
= \(\frac{1}{-\frac{1}{2}}\)
= \(-2\).
Source: Myschool Past Questions Archive (Record #53072)