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Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged?
A
\(2\frac{1}{4}\)%
B
4%
C
5%
D
6%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(I = \frac{PRT}{100}\)
\(R = \frac{100I}{PT}\)
\(R = \frac{100 \times 60}{2000 \times \frac{3}{4}}\)
\(R = \frac{6000}{1500}\)
= 4%
Source: WAEC / JAMB / NECO Classroom Archive (Record #26471)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
If x varies inversely as y and \(x = \frac{2}{3}\) when y = 9, find the value of y when \(x=\frac{3}{4}\)
A
\(\frac{1}{18}\)
B
\(\frac{8}{81}\)
C
\(\frac{9}{2}\)
D
8
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(x \propto \frac{1}{y}\)
\(x = \frac{k}{y}\)
\(\frac{2}{3} = \frac{k}{9}\)
\(3k = 18 \implies k = 6\)
\(x = \frac{6}{y}\)
When y = \(\frac{3}{4}\),
x = \(\frac{6}{\frac{3}{4}}\)
= \(\frac{6 \times 4}{3}\)
= 8
Source: WAEC / JAMB / NECO Classroom Archive (Record #26452)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
Given that x = -\(\frac{1}{2}\) and y = 4 evaluate 3x\(^2y+xy^2\)
A
-5
B
-1
C
4
D
11
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(x = -\frac{1}{2}\), y = 4
3x\(^2\)y + xy\(^2\)
3\(\left[-\frac{1}{2}\right]^2 \times 4 + \left(\frac{-1}{2}\right)(4)^2\)
3\(\times \frac{1}{4} \times 4 -\frac{1}{2} \times 16\)
3 - 8 = -5
Source: WAEC / JAMB / NECO Classroom Archive (Record #26450)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
Make t the subject of formula \(k = m\sqrt{\frac{t-p}{r}}\)
A
\(\frac{rk^2 + p}{m^2}\)
B
\(\frac{rk^2+pm^2}{m^2}\)
C
\(\frac{rk^2-p}{m^2}\)
D
\(\frac{rk^2-p^2}{m^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(k = m\sqrt{\frac{t - p}{r}}\)
\(\frac{k}{m} = \sqrt{\frac{t - p}{r}}\)
\((\frac{k}{m})^2 = \frac{t - p}{r}\)
\(rk^2 = m^2 (t - p)\)
\(\therefore m^2 t = rk^2 + m^2 p\)
\(t = \frac{rk^2 + m^2 p}{m^2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26457)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
Simplify \(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\)
A
\(\frac{x-1}{x-3}\)
B
\(\frac{-2}{x+3}\)
C
\(\frac{x-1}{x+3}\)
D
\(\frac{4x}{x^2-9}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{x-3}-\frac{3(x-1)}{x^2 - 9}\)
\(\frac{1}{x-3}-\frac{3(x-1)}{(x-3)(x+3)}\)
\(\frac{x+3-3x+3}{(x-3)(x+3)};\frac{-2x+6}{(x-3)(x+3)}\)
\(\frac{-2(x-3)}{(x-3)(x+3)}=\frac{-2}{x+3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26454)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
Find the value of x such that the expression \(\frac{1}{x}+\frac{4}{3x}-\frac{5}{6x}+1\) equals zero
A
\(\frac{1}{6}\)
B
\(\frac{1}{4}\)
C
\(\frac{-3}{2}\)
D
\(\frac{-7}{6}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{x} + \frac{4}{3x} - \frac{5}{6x} + 1 = 0\)
\(\frac{6 + 8 - 5 + 6x}{6x} = 0\)
\(\frac{9 + 6x}{6x} = 0 \implies 9 + 6x = 0\)
\(6x = -9 \implies x = \frac{-3}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26459)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
The height of a pyramid on square base is 15cm. if the volume is 80cm^3, find the area of the square base.
A
8cm2
B
9.6cm2
C
16cm2
D
25cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of pyramid with square base = \(\frac{\text{base area} \times height}{3}\)
\(80 = \frac{\text{base area} \times 15}{3}\)
\(80 = 5 \times \text{base area}\)
\(\text{Base area} = 16 cm^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26463)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Diagram
Solution
Find the volume (in cm\(^3\)) of the solid shown above
Attached Figure / Diagram
A
100cm3
B
150cm3
C
175cm3
D
250cm3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total volume = (5 x 5) x 5 + (5 x 5) x 2
= 125 + 50
= 175 cm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26469)
Mathematics
UTME / JAMB 2000
Number and Numeration
Diagram
Solution
If the diagram is the graph of y = x\(^2\), the shaded area is
Attached Figure / Diagram
A
64 square units
B
\(\frac{128}{3}\) square units
C
32 square units
D
\(\frac{64}{3}\) square units
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
A = \(\int^{x = 4}_{x = 0}\) ydx = \(\int^{4}_{0}\)16 - x\(^2\)dx = [16 - \(\frac{x^3}{3} + c]^{4}_{0}\)
= \(\frac{128}{3}\) square units
Source: WAEC / JAMB / NECO Classroom Archive (Record #33093)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Diagram
Solution
The bar chart shows the distribution of marks scored by a group of students in a test. Use the chart to answer the question below
How many students scored 4 marks and above?
Attached Figure / Diagram
A
15
B
11
C
10
D
17
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Students that scored 4 and above = 5 + 3 + 3 + 0 + 2 + 2 + 2
= 17
Source: WAEC / JAMB / NECO Classroom Archive (Record #26441)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Diagram
Solution
The bar chart shows the distribution of marks scored by a group of students in a test. Use the chart to answer the question below
How many students took the test?
Attached Figure / Diagram
A
38
B
32
C
15
D
11
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2 + 3 + 4 + 5 + 6 + 3 +3 + 0 + 2 + 2 + 2 = 32
Source: WAEC / JAMB / NECO Classroom Archive (Record #26442)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
Given that \(27^{(1+x)}=9,)\ find x
A
-3
B
\(\frac{-1}{3}\)
C
\(\frac{5}{3}\)
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(27^{(1+x)}\) = 9
\(3^{3(1+x)} = 3^2\)
3(1+x) = 2
3 + 3x = 2
3x = -1
x = \(\frac{-1}{3}\)
Source: Myschool Past Questions Archive (Record #26451)
Mathematics
WAEC / WASSCE 2000
Number and Numeration
Solution
Given that (2x + 7) is a factor of \(2x^2 + 3x - 14\), find the other factor
A
x + 2
B
2 - x
C
x - 2
D
x + 1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(2x^2 + 3x - 14\)
\(2x^2 + 7x - 4x - 14\)
\(x(2x + 7) - 2(2x + 7)\)
= \((x - 2)(2x + 7)\)
The other factor = (x - 2).
Source: Myschool Past Questions Archive (Record #26453)
Mathematics
UTME / JAMB 1999
Number and Numeration
Solution
A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?
A
25
B
19
C
18
D
17
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
Source: Myschool Past Questions Archive (Record #6)
Mathematics
UTME / JAMB 1999
Number and Numeration
Solution
If log\(_810\) = X, evaluate log\(_85\) in terms of X.
A
\(\frac{1}{2}\)X
B
X-\(\frac{1}{4}\)
C
X-\(\frac{1}{3}\)
D
X-\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(log_810\) = X = \(log_8{2 x 5}\)
\(log_82\) + \(log_85\) = X
Base 8 can be written as \(2^3\)
\(log_82 = y\)
therefore \(2 = 8^y\)
\(y = \frac{1}{3}\)
\(\frac{1}{3} = log_82\)
taking \(\frac{1}{3}\) to the other side of the original equation
\(log_85 = X-\frac{1}{3}\)
explanation courtesy of Oluteyu and Ifechuks
OR
Given \(\log_8 10 = X\), we can express \(\log_8 5\) as follows:
\(\log_8 5 = \log_8 \left( \frac{10}{2} \right) = \log_8 10 - \log_8 2\)
Using the change of base formula, we find:
\(\log_8 2 = \frac{\log 2}{\log 8} = \frac{1}{3}\)
Thus, substituting back, we get: \(\log_8 5 = X - \log_8 2 = X - \frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #9)