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Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the center of the circle
A
2.5cm
B
3.0cm
C
3.5cm
D
4.0cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(5^{2}=3^{2}+x^{2}\)
25 - 9 = x\(^2\)
16 = x\(^2\)
x = 4
Source: Myschool Past Questions Archive (Record #26731)
Mathematics
WAEC / WASSCE 2007
Mensuration (Areas, Perimeters & Volumes)
Solution
A sector of a circle of radius 14cm containing an angle 60o is folded to form a cone. Calculate the radius of the base of the cone.
A
\(5\frac{1}{2}cm\)
B
\(4\frac{2}{3}cm\)
C
\(3\frac{1}{2}cm\)
D
\(2\frac{1}{3}cm\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(r=\frac{\theta \times l}{360^{\circ }}\\
r=?, \theta =60^{\circ }\), l = radius of the orginal sector of a circle = 14cm
\(r=\frac{60\times 14}{360}=\frac{7}{3}=2\frac{1}{3}cm\)
Source: Myschool Past Questions Archive (Record #26732)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
IN the diagram, |LN| = 4cm, LNM = 90o and tan y = 2/3. What is the area of the ∆LMN?
Attached Figure / Diagram
A
24cm2
B
12cm2
C
10cm2
D
6cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(tan \hspace{1mm}y = \frac{opp}{adj}=\frac{2}{3}\Rightarrow \frac{2}{3}=\frac{
LN}{MN}=\frac{4}{MN}\\
∴ MN = \frac{12}{2}=6\\
Area \hspace{1mm}of \hspace{1mm}\Delta LMN = \frac{1}{2}\times MN\times LN=\frac{1}{2}\times 6\times 4=12cm\)
Source: Myschool Past Questions Archive (Record #26733)
Mathematics
UTME / JAMB 2007
Differentiation & Applications
Solution
If y = (1 + x)2, find \(\frac{dy}{dx}\)
A
x - 1
B
2 + 2x
C
1 + 2x
D
2x - 1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If y = (1 + x)2, find \(\frac{dy}{dx}\)
y = (1 + x)2
\(\frac{dy}{dx}\) = 2(1 + x)
= 2 + 2x
Source: Myschool Past Questions Archive (Record #30081)
Mathematics
UTME / JAMB 2007
Fractions, Decimals, Percentages & Approximations
Solution
The sum of the ages of Musa and Lawal is 28 years. After sharing a certain sum of money in the ratio of their ages, Musa gets N600 and Lawal N800. How old is Lawal?
A
14 years
B
20 years
C
12 years
D
16 years
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
M + L = 28,
M : L = 600 : 800
= 3 : 4
\(\frac{M}{L}\) = \(\frac{3}{4}\) \(\to\) M = \(\frac{3}{4}\)L
\(\frac{3}{4}\)L + L = 28
\(\frac{7L}{4}\) = 28
L = \(\frac{4 \times 28}{7}\)
= 16
Source: Myschool Past Questions Archive (Record #30393)
Mathematics
WAEC / WASSCE 2007
Number Bases & Modular Arithmetic
Solution
Evaluate(111two)\(^2\) and leave your answer in base 2.
A
111001two
B
110001two
C
101001two
D
10010two
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(111two)\(^2\) change to base 10
(111two)\(^2\) = 1 x 2\(^2\) + 1 x 2\(^1\) + 1 x 2\(^0\) = 4 + 2 + 1 = 7
(111two)\(^2\) = 7\(^2\) = 49 in base 10
convert 49 in base 10 to base 2
2
49
2
24 R 1
2
12 R 0
2
6 R 0
2
3 R 0
2
1 R 1
2
0 R 1
Therefore (111two)\(^2\) = 110001\(_2\)
Or solve by direct multiplication.
Source: Myschool Past Questions Archive (Record #36226)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Find the LCM of 2\(^3\) x 3 x 5\(^2\), 2 x 3\(^2\) x 5 and 2\(^3\) x 3\(^3\) x 5
A
22 x 33 x 52
B
23 x 33 x 5
C
22 x 32 x 52
D
23 x 33 x 52
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2\(^3\) x 3 x 5\(^2\)
2 x 3\(^2\) x 5
2\(^2\) x 3\(^3\) x 5
The L.C.M = 2\(^2\) x 3\(^3\) x 5\(^2\)
Source: Myschool Past Questions Archive (Record #36227)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Simplify(0.3 x 105) \(\div\) (0.4 \(\times\) 107), leaving you answer in the standard form.
A
7.5 x 10-4
B
7.5 x 10-3
C
7.5 x 10-2
D
7.5 x 10-1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{0.3 \times 10^5}{0.4 \times 10^7} = \frac{3 \times 10^{-1} \times 10^{5}}{4 \times 10^{-1} \times 10^7}\)
\(\frac{3 x 10^4}{4 x 10^4}\)
\(\frac{3}{4}\) x 104-6 = 0.75 x 10-2
= 7.5 x 10-3
Source: Myschool Past Questions Archive (Record #36231)
Mathematics
WAEC / WASSCE 2007
Linear, Simultaneous & Quadratic Equations
Solution
If p \(\alpha \frac{I}{Q}\) which of the following is true?
A
q \(\alpha p^2\)
B
q \(\alpha \frac{1}{p^2}\)
C
q \(\alpha \sqrt{p}\)
D
q \(\alpha \frac{1}{p}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
p \(\alpha \frac{I}{Q}\); p \(\frac{k}{q}\) (where k is constant)
q = \(\frac{k}{p}\)
q \(\alpha \frac{1}{p}\)
Source: Myschool Past Questions Archive (Record #36232)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Simplify 3\(\sqrt{45} - 12\sqrt{5} + 16\sqrt{20}\), leaving your answer in surd form.
A
29\(\sqrt{5}\)
B
14\(\sqrt{15}\)
C
12\(\sqrt{15}\)
D
11\(\sqrt{15}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3 \(\sqrt{45} - 12\sqrt{5} + 16\sqrt{20}\)
= 3 x \(\sqrt{9 \times 5} - 12 \times \sqrt{5} + 16 \times \sqrt{4 \times 5}\)
= 3 x 3 x \(\sqrt{5} - 12 \times \sqrt{5} + 16 \times 2 \times \sqrt{5}\)
= 9\(\sqrt{5} - 2 \sqrt{5} + 32 \sqrt{5}\)
= 9\(\sqrt{5} + 32\sqrt{5} - 12\sqrt{5}\)
= 29\(\sqrt{5}\)
Source: Myschool Past Questions Archive (Record #36233)
Mathematics
WAEC / WASSCE 2007
Inequalities & Linear Programming
Solution
Which of the following statement is true for the ste P = {-3.2 \(\leq\) x < 5} where x is an integer?
A
least value of x is -3.2
B
least value of x is -3
C
greatest value of x is 4.9
D
greatest value of x is 5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
p = {-3.2.....4.9}; Since x is an integer
least value of x is -3
Source: Myschool Past Questions Archive (Record #36234)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Simplify \(\frac{3x^3}{(3x)^3}\)
A
1
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
\(\frac{1}{27}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3x^3}{(3x)^3}\) = \(\frac{3 \times x^3}{3^3 \times x^3}\)
= \(\frac{3 \times x^3}{3 \times 3 \times 3 \times x^3}\)
= \(\frac{1}{3^2}\)
= \(\frac{1}{9}\)
Source: Myschool Past Questions Archive (Record #36235)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode and Kayode has twice as much as Uche. What is Kayode'sshare?
A
N80,000
B
N40,000
C
N2,000
D
10,000
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let Abu's share = 2x;
Kayode's = x
Uche's share = \(\frac{x}{2}\)
Total: 2x + x + \(\frac{x}{2}\) = N140,000
\(\frac{7x}{2}\) = N140,000
x = \(\frac{280,000}{7}\) = N40,000
Kayode's share = N40,000
Source: Myschool Past Questions Archive (Record #36236)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
I am x years old and my brother is 3 years older. How old was my brother last year?
A
(x - 4)years
B
(x + 2) years
C
(3x - 10years
D
(3x + 1)years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
I am x years old; My brother = 3 + x; My brother
last year = (3 + x) - 1 = x + 3 - 1
= (x + 2) years
Source: Myschool Past Questions Archive (Record #36237)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
For what value of x is the expression \(\frac{2x - 1}{x + 3}\) not defined?
A
3
B
2
C
\(\frac{1}{2}\)
D
-3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{2x - 1}{x + 3}\) not defined
x + 3 = 0
x = -3
Source: Myschool Past Questions Archive (Record #36238)