Mathematics 2017 Jamb Examination

Convert both numbers to standard form first: \[ 0.00000231 = 2.31 \times 10^{-6} \] \[ 0.007 = 7 \times 10^{-3} \] Now divide: \[ \frac{2.31 \times 10^{-6}}{7 \times 10^{-3}} = \frac{2.31}{7} \times 10^{-6 - (-3)} \] \[ = 0.33 \times 10^{-3} = 3.3 \times 10^{-4} \]

Percentage error is calculated as: \[ \frac{\text{Error}}{\text{Actual Value}} \times 100 \] \[ \text{Error} = |10.5 - 10| = 0.5 \] \[ \text{Percentage Error} = \frac{0.5}{10} \times 100 = 5\% \]

Amount \( (A) = Principal (P) + Interest (I) \). Simple Interest \( I = \frac{PRT}{100} \). \[ A = P + \frac{PRT}{100} = P(1 + \frac{RT}{100}) \] Given \( A = 5500, R = 2, T = 5 \): \[ 5500 = P(1 + \frac{2 \times 5}{100}) = P(1 + 0.1) \] \[ 5500 = 1.1P \implies P = \frac{5500}{1.1} = 5000 \]

From the pie chart, the angle for fertilizer is \( 90^\circ \) (indicated by the right-angle symbol). \[ \text{Amount} = \frac{\text{Angle}}{360^\circ} \times \text{Total Amount} \] \[ = \frac{90}{360} \times 80,000 = \frac{1}{4} \times 80,000 = 20,000 \]

The word MATHEMATICS has 11 letters. We identify the repeating letters: - M appears 2 times - A appears 2 times - T appears 2 times Using the formula for permutations of multi-sets: \[ \text{Total arrangements} = \frac{11!}{2!2!2!} \]

The word MACICITA consists of 8 letters. We check for repeated letters: - A appears 2 times - C appears 2 times - I appears 2 times The number of arrangements is calculated using the formula for permutations of identical objects: \[ \frac{8!}{2! 2! 2!} \]

For inverse proportion, the relationship is \( y = \frac{k}{x} \), where \( k \) is the constant of variation. Rearranging for \( k \): \[ k = y \times x \] \[ k = 6 \times 7 = 42 \]

The locus of a point equidistant from two fixed points is the perpendicular bisector of the line joining those points. We set the squared distances equal: \[ (x - 1)^2 + (y - 1)^2 = (x - 3)^2 + (y - 5)^2 \] \[ x^2 - 2x + 1 + y^2 - 2y + 1 \]\[= x^2 - 6x + 9 + y^2 - 10y + 25 \] \[ -2x - 2y + 2 = -6x - 10y + 34 \] \[ 4x + 8y = 32 \] Divide through by 4: \[ x + 2y = 8 \]

Use the power rule for integration \( \int x^n dx = \frac{x^{n+1}}{n+1} \): \[ \int x^2 dx = \frac{x^3}{3} \] \[ \int 3x dx = \frac{3x^2}{2} \] \[ \int -5 dx = -5x \] Adding the constant of integration \( k \), we get: \[ \frac{x^3}{3} + \frac{3x^2}{2} - 5x + k \]

To find the chord length \( L \), use the formula \( L = 2r \sin(\frac{\theta}{2}) \), where \( r = 10 \) and \( \theta = 140^\circ \): \[ MN = 2(10) \sin(70^\circ) \] \[ MN = 20 \times 0.9397 \approx 18.79 \] To the nearest cm, the length is 19cm.