2024 - JAMB Mathematics Past Questions and Answers - page 2

The word 'LEADER' has 6 letters, with 2 repeating letters (E appears twice). The number of ways to arrange the letters is given by the formula: ( \frac{6!}{2!} = \frac{720}{2} = 360 ).

To find the median, we first need to organise the data from the table. The table gives us the scores and their corresponding frequencies:

Now, we need to list all the data points based on their frequency:

• Score 3 appears 2 times: 3, 3
• Score 6 appears 3 times: 6, 6, 6
• Score 5 appears 4 times: 5, 5, 5, 5
• Score 2 appears 6 times: 2, 2, 2, 2, 2, 2

The ordered data is:

2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 5, 6, 6, 6

There are 15 data points in total. The median is the middle value. Since the total number of data points is odd (15), the position of the median is:

\(\frac{15 + 1}{2} = 8\)

The 8th value in the ordered list is 3.

Thus, the median is 3.

The probability of selecting a fruit that is neither an apple nor an orange is calculated as follows: P(neither apple nor orange) = ( \frac{8}{24} = \frac{1}{3} ).

We are tasked with finding the equation of a line that is perpendicular to the line given by 4y = 7x + 3 and passes through the point (-3, 1).

Step 1: Rewrite the given line in slope-intercept form (y = mx + c)

Start by dividing through by 4 to isolate y:

\( 4y = 7x + 3 \)

\( y = \frac{7}{4}x + \frac{3}{4} \)

From this, the slope \( m_1 \) of the given line is \( \frac{7}{4} \).

Step 2: Find the slope of the perpendicular line

The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope \( m_2 \) of the perpendicular line is:

\( m_2 = -\frac{1}{m_1} = -\frac{1}{\frac{7}{4}} = -\frac{4}{7} \).

Step 3: Use the point-slope form of a line equation

The equation of a line with slope \( m \) passing through a point \((x_1, y_1)\) is:

\( y - y_1 = m(x - x_1) \)

Substitute \( m_2 = -\frac{4}{7} \) and the point (-3, 1):

\( y - 1 = -\frac{4}{7}(x + 3) \)

Step 4: Simplify the equation

Expand the right-hand side:

\( y - 1 = -\frac{4}{7}x - \frac{12}{7} \)

Combine like terms:

\( y = -\frac{4}{7}x - \frac{12}{7} + 1 \)

\( y = -\frac{4}{7}x - \frac{12}{7} + \frac{7}{7} \)

\( y = -\frac{4}{7}x - \frac{5}{7} \)

Step 5: Eliminate fractions to write in general form

Multiply through by 7 to eliminate fractions:

\( 7y = -4x - 5 \)

Rearrange to general form:

\( 4x + 7y + 5 = 0 \)

Final Answer: 7y + 4x + 5 = 0

(\frac{1}{2})x + (\frac{1}{4}) > (\frac{1}{3})x + (\frac{1}{2})

Multiply through by through by the LCM of 2, 3 and 4

12 x (\frac{1}{2})x + 12 x (\frac{1}{4}) > 12 x (\frac{1}{3})x + 12 x (\frac{1}{2})

6x + 3 > 4x + 6

6x - 4x > 6 - 3

2x > 3

(\frac{2x}{2}) > (\frac{3}{2})

x > (\frac{3}{2})

We are tasked with finding the depth of a cylindrical tank given that its capacity (volume) is \( 3080 \, \text{m}^3 \), and the diameter of its base is \( 14 \, \text{m} \). We are to take \( \pi = \frac{22}{7} \).

Step 1: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by:

\( V = \pi r^2 h \)

Where:

• \( r \) is the radius of the base
• \( h \) is the height (or depth in this case)
• \( \pi = \frac{22}{7} \)

Step 2: Calculate the radius

The diameter of the base is \( 14 \, \text{m} \). Therefore, the radius \( r \) is:

\( r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \, \text{m} \)

Step 3: Substitute known values into the formula

Substitute \( V = 3080 \, \text{m}^3 \), \( r = 7 \, \text{m} \), and \( \pi = \frac{22}{7} \) into the formula:

\( 3080 = \frac{22}{7} \times (7)^2 \times h \)

Step 4: Simplify the equation

\( 3080 = \frac{22}{7} \times 49 \times h \)

\( 3080 = 22 \times 7 \times h \)

\( 3080 = 154h \)

Step 5: Solve for \( h \)

Divide both sides by 154:

\( h = \frac{3080}{154} \)

\( h = 20 \, \text{m} \)

 Answer:  20m

We are tasked with simplifying the expression:

\(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)

Step 1: Convert all mixed fractions to improper fractions

• \(2\frac{2}{3} = \frac{(3 \times 2) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}\)
• \(1\frac{1}{2} = \frac{(2 \times 1) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}\)
• \(4\frac{4}{5} = \frac{(5 \times 4) + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5}\)

The expression becomes:

\(\frac{\frac{8}{3} \times \frac{3}{2}}{\frac{24}{5}}\)

Step 2: Simplify the numerator

\(\frac{8}{3} \times \frac{3}{2} = \frac{8 \times 3}{3 \times 2} = \frac{24}{6} = 4\)

So the expression becomes:

\(\frac{4}{\frac{24}{5}}\)

Step 3: Simplify the division of fractions

Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:

\(\frac{4}{\frac{24}{5}} = 4 \times \frac{5}{24}\)

\(= \frac{4 \times 5}{24} = \frac{20}{24}\)

Step 4: Simplify the fraction

\(\frac{20}{24}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:

\(\frac{20}{24} = \frac{20 \div 4}{24 \div 4} = \frac{5}{6}\)

Answer: \(\frac{5}{6}\)

The length of an arc can be calculated using the formula:

\(L = \frac{\theta}{360} \times 2\pi r\)

where:

• \(\theta\) is the angle subtended by the arc at the center of the circle (in degrees).
• \(r\) is the radius of the circle.

Step 1: Substitute the given values into the formula

Given:

• \(\theta = 30^\circ\)
• \(r = 12 \, \text{cm}\)

\(L = \frac{30}{360} \times 2\pi \times 12\)

Step 2: Simplify the fraction

\(\frac{30}{360} = \frac{1}{12}\)

So:

\(L = \frac{1}{12} \times 2\pi \times 12\)

Step 3: Simplify further

\(L = 2\pi \, \text{cm}\)

The total surface area of the cupboard is calculated by summing the areas of all six faces: 2lw + 2lh + 2wh, where l = 12, w = 10, and h = 8. The total surface area is 592 cm².

The set P of all prime factors of 30 is {2, 3, 5}, and the set Q of all factors of 18 less than 10 is {1, 2, 3, 6}. The intersection P ∩ Q contains the common elements {2, 3}.