2024 - JAMB Mathematics Past Questions and Answers - page 1

To convert the base-ten number 27 to base three, we repeatedly divide by 3 and record the remainders. 1. 27 ÷ 3 = 9, remainder 0 2. 9 ÷ 3 = 3, remainder 0 3. 3 ÷ 3 = 1, remainder 0 4. 1 ÷ 3 = 0, remainder 1 Reading the remainders from bottom to top gives us 1000. So, $27_{10} = 1000_3$ Looking at the options, there seems to be an error as we should be expecting 10003 as the answer. However, since we need to pick from the options given, and 1000

To find the number of arrangements of the word MATHEMATICIAN, we use the formula for permutations with repetitions. 1. **Count the letters:** The word MATHEMATICIAN has 13 letters. 2. **Identify repetitions:** * M appears 2 times * A appears 3 times * T appears 2 times * I appears 2 times * C, E, and N each appear once. 3. **Apply the formula:** The number of arrangements is given by: $$\frac{13!}{2! \times 3! \times 2! \times 2! \times 1! \times 1! \times 1!} = \frac{13!}{2!

Here's how to solve this problem: 1. **Find the diagonal of the floor:** * The floor is a rectangle with length 12m and width 9m. * Use the Pythagorean theorem: diagonal = \(\\sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15\) m 2. **Find the diagonal of the room:** * Consider a right-angled triangle formed by the height of the room (8m), the floor diagonal (15m), and the room diagonal (the hypotenuse). * Use the Pythagorean theorem: room diagonal = \(\\sqrt{8^2 + 15^

1. **Calculate the determinant of the left-hand side (LHS):** The determinant of \\(\\begin{vmatrix} 5 & 3 \\ x & 2 \\end{vmatrix}\\) is (5 \* 2) - (3 \* x) = 10 - 3x. 2. **Calculate the determinant of the right-hand side (RHS):** The determinant of \\(\\begin{vmatrix} 3 & 5 \\ 4 & 5 \\end{vmatrix}\\) is (3 \* 5) - (5 \* 4) = 15 - 20 = -5. 3. **Equate the determinants and solve for x:** We have 10 -

The total surface area of an open-ended cylinder is given by the formula: Total Surface Area = Curved Surface Area + Area of the base 1. **Identify the values:** * Length (h) = 50 cm = 0.5 m * Radius (r) = 7 m 2. **Calculate the Curved Surface Area:** * Curved Surface Area = 2πrh * Curved Surface Area = 2 * π * 7 m * 0.5 m = 7π m² 3. **Calculate the Area of the base:** * Area of the base = πr² * Area of the base = π * (7 m)² = 49π m²

\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)

\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)

= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)

= \(\frac{1 - \sqrt5}{4}\)

Here's how to calculate the standard deviation: 1. **Calculate the mean (average):** Mean = (2 + 3 + 8 + 10 + 12) / 5 = 35 / 5 = 7 2. **Calculate the deviations from the mean:** * 2 - 7 = -5 * 3 - 7 = -4 * 8 - 7 = 1 * 10 - 7 = 3 * 12 - 7 = 5 3. **Square the deviations:** * (-5)^2 = 25 * (-4)^2 = 16 * 1^2 = 1

To find the derivative of y = (2x + 1)³, we can use the chain rule. The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x). Here's how to apply the chain rule: 1. **Identify the outer function and inner function:** * Outer function: f(u) = u³ * Inner function: g(x) = 2x + 1 2. **Find the derivatives of the outer and inner functions:** * f'(u) = 3u² * g'(x) = 2 3. **Apply the chain rule:** * dy/dx = f'(g

The quadratic equation can be solved using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Where $a = 3$, $b = -4$, and $c = -5$ in the equation $3x^2 - 4x - 5 = 0$. 1. Substitute the values into the formula: $x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(3)(-5)}}{2(3)}$ 2. Simplify the expression: $x = \frac{4 \pm \sqrt{16 + 60}}{6}$ $x = \frac{4 \pm \sqrt{76}}{6}$

To calculate the volume of a cuboid, we use the formula: Volume = length × breadth × height. 1. **Identify the given values:** * length = 0.76 cm * breadth = 2.6 cm * height = 0.82 cm 2. **Apply the formula:** Volume = 0.76 cm × 2.6 cm × 0.82 cm 3. **Calculate the volume:** Volume ≈ 1.61632 cm³ 4. **Round to the correct number of significant figures:** Volume ≈ 1.62 cm³