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Mathematics
UTME / JAMB 2003
Number and Numeration
Diagram
Solution
In the diagram above, PQR is a straight line and PS is a tangent to the circle QRS with /PS/ = /SR/ and ∠SPR = 40^\circ. Find ∠PSQ
Attached Figure / Diagram
A
40o
B
30o
C
20o
D
10o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
R = P (base ∠s of isc \Delta, ps = RS)
∴R = 40^\circ
∠PSQ = R (∠s in alternate segment)
∴∠PSQ = 40^\circ
Source: Myschool Past Questions Archive (Record #11108)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Simplify \(\left(\frac{3}{4} - \frac{1}{3}\right)\times 4\frac{1}{3}\div 3\frac{1}{4}\)
A
\(\frac{5}{9}\)
B
\(\frac{5}{16}\)
C
\(\frac{8}{13}\)
D
\(\frac{16}{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\((\frac{3}{4} - \frac{1}{3}) \times 4\frac{1}{3} \div 3\frac{1}{4}\)
= \((\frac{9 - 4}{12}) \times \frac{13}{3} \div \frac{13}{4}\)
= \(\frac{5}{12} \times \frac{13}{3} \times \frac{4}{13}\)
= \(\frac{5}{9}\)
Source: Myschool Past Questions Archive (Record #26570)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Diagram
Solution
The table below gives the distribution of marks obtained by a number of pupils in a class test.
How many pupils scored at least 2 marks?
Attached Figure / Diagram
A
12
B
23
C
37
D
49
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
= 12 + 18 + 11 + 8
= 49 students
Source: Myschool Past Questions Archive (Record #26573)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Simplify \(\frac{4\sqrt{18}}{\sqrt{8}}\)
A
2
B
3
C
6
D
12
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{4\sqrt{18}}{\sqrt{8}}\\
= \frac{4\sqrt{9\times 2}}{\sqrt{4 \times 2}} = \frac{12\sqrt{2}}{2\sqrt{2}}=\frac{6\sqrt{2}}{\sqrt{2}}\\
Rationalising \frac{6\sqrt{2}}{\sqrt{2}}\\
=\frac{6\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 6\)
Source: Myschool Past Questions Archive (Record #26577)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Diagram
Solution
In the diagram, PQ/RT /RS/ =/QS/, ∠QST= 70o and ∠PQW = 55o
Find the size of reflex ∠WQS
Attached Figure / Diagram
A
235o
B
290o
C
305o
D
325o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Reflex ∠WQS = 360o - (55o + 70o)
=360o - 125o = 235o
Source: Myschool Past Questions Archive (Record #26578)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Three men, Bedu, Bakre and Kofi shared' N500 in the ratio 3:2: x respectively. If Bedu’s share is N150, find the value of x.
A
1
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(5+x\rightarrow 500\)
3 \(\rightarrow 150\)
∴ 3 \(\times 500 = 150 \times\) (5+x)
1500 = 750 + 150x
x = \(\frac{750}{150}\) = 5
Source: Myschool Past Questions Archive (Record #26579)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Simplify \(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
A
\(2\frac{1}{3}\)
B
\(1\frac{1}{3}\)
C
1
D
\(\frac{3}{7}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2=\left(\frac{5}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
Difference of two squares
\(\left(\frac{5}{3}-\frac{2}{3}\right)\left(\frac{5}{3}+\frac{2}{3}\right)=\left(\frac{3}{3}\right)\left(\frac{7}{3}\right)\\
\frac{7}{3}=2\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #26580)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Evaluate \(\frac{log8}{log\left(\frac{1}{4}\right)}\)
A
-2
B
\(\frac{-3}{2}\)
C
\(\frac{1}{2}\)
D
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{log8}{log\frac{1}{4}}=\frac{log2^3}{log2^{-2}}=\frac{3log2}{-2log2}=-\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #26582)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
A pyramid of volume 120cm3 has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid
A
5cm
B
9cm
C
12cm
D
15cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of pyramid = 120 cm\(^3\)
Base area = 5 cm \times 6 cm = 30 cm\(^2\)
120 = (\(\frac{1}{3}\)) \times 30 \times h
h = 12 cm
Source: Myschool Past Questions Archive (Record #26583)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Given, that \(4P4_5 = 119_{10}\), find the value of P
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(4P4_5 = 119_{10}\)
\(4 \times 5^2 + P \times 5^1 + 4 \times 5^0 = 119\)
\(100 + 5P + 4 = 119\)
\(5P = 119 - 104 = 15\)
\(P = 3\)
Source: Myschool Past Questions Archive (Record #26588)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Find the values of x for which \( \frac{1}{2x^2 - 13x +15} \) is not defined,
A
5 or \( \frac{3}{2} \)
B
1 or \( \frac{15}{13} \)
C
2 or 15
D
13 or 15
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The fraction is undefined when the denominator is equal to zero
\(2x^2 - 13x + 15 = 0\\
2x^2 - 3x - 10x + 15\\
x(2x-3)-5(2x-3) = 0\\
(2x-3)(x-5)=0\\
x = \frac{3}{2} or x = 5\)
Source: Myschool Past Questions Archive (Record #26594)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Evaluate \((111_{two})^2 - (101_{two})^2\)
A
10two
B
100two
C
1100two
D
11000two
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((111_{2})^2 - (101_{2})^2\)
Difference of two squares
\((111 - 101)(111 + 101)\)
= \((10)(1100)\)
= \(11000_{2}\)
Source: Myschool Past Questions Archive (Record #26596)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
Given that x ≅ 0.0102 correct to 3 significant figures, which of the following cannot be the actual value of x?
A
0.01014
B
0.01021
C
0.01015
D
0.01016
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
option A CANNOT BE BECAUSE THE LAST NUMBER BEFORE 1 CAN ONLY BE ROUNDED DOWN TO ZERO.
Source: Myschool Past Questions Archive (Record #26597)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
If \(\frac{3^{(1-n)}}{9^{-2n}}\) = \(\frac{1}{9}\) find n
A
\(-\frac{3}{2}\)
B
\(\frac{1}{3}\)
C
-1
D
-3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3^{(1-n)}}{9^{-2n}}\) =\(\frac{1}{9}\)
3\(^{1-n}\times 3^{-2(-2n)} = 3^{-2}\)
1 - n - 2(-2n) = -2
1 - n + 4n = -2
n = -1
Source: Myschool Past Questions Archive (Record #26598)
Mathematics
WAEC / WASSCE 2003
Number and Numeration
Solution
In a ∆ XYZ, /YZ/ = 6cm YXZ = 60o and XYZ is a right angle. Calculate /XZ/in cm, leaving your answer in surd form
A
2√3
B
4√3
C
6√3
D
12√3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(sin \theta = \frac{opp}{hyp}\)
sin 60^o = \(\frac{|YZ|}{|XZ|}=\frac{6}{P}\)
P sin 60^o = 6
P = \(\frac{6}{sin60^o}\)
=\(\frac{6}{\sqrt{\frac{3}{2}}}=4\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #26600)