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Mathematics

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1. Write in figure, three million two hundred and eighty thousand five hundred and seventy-six.

  1. Break down the number into its place values.

    • Three million: 3,000,000
    • Two hundred and eighty thousand: 280,000
    • Five hundred and seventy-six: 576

  2. Add the values together.

    3,000,000+280,000+576=3,280,5763,000,000 + 280,000 + 576 = 3,280,576

    The correct option is (a).

    (a) 3280576\boxed{\textbf{(a) 3280576}}

    2. Write in words 10, 033, 544.

  3. Read the number by its periods (millions, thousands, ones).

    • 10 in the millions period: Ten Million
    • 033 in the thousands period: Thirty-Three Thousand
    • 544 in the ones period: Five Hundred and Forty-Four

  4. Combine the parts.

    Ten Million, Thirty-Three Thousand, Five Hundred and Forty-Four.
    The correct option is (d).

    (d) Ten Million Thirty-Three Thousand Five Hundred and Forty-Four\boxed{\textbf{(d) Ten Million Thirty-Three Thousand Five Hundred and Forty-Four}}

    3. Find 40+60 in Roman Numerals.

  5. Calculate the sum.

    40+60=10040 + 60 = 100

  6. Convert the sum to Roman Numerals.

    The Roman numeral for 100 is C.
    The correct option is (d).

    (d) C\boxed{\textbf{(d) C}}

    4. The sum of angles on a straight line is equal to

  7. Recall the geometric property of angles on a straight line.

    Angles on a straight line always add up to 180∘180^\circ.
    The correct option is (e).

    (e) 180∘\boxed{\textbf{(e) } 180^\circ}

    5. If y=1y=1, x=3x=3 and z=5z=5. Find the value of [yx+z]×2z\left[\frac{y}{x}+z\right] \times 2z.

  8. Substitute the given values into the expression.

    [13+5]×2(5)\left[\frac{1}{3}+5\right] \times 2(5)

  9. Simplify the expression inside the brackets.

    [13+153]×10=[163]×10\left[\frac{1}{3}+\frac{15}{3}\right] \times 10 = \left[\frac{16}{3}\right] \times 10

  10. Perform the multiplication.

    163×10=1603\frac{16}{3} \times 10 = \frac{160}{3}

    The calculated value is 1603≈53.33\frac{160}{3} \approx 53.33. This value is not among the given options (a) 1, (b) 2, (c) 4, (d) 3, (e) 5.
    Assuming there is a typo in the question and it intended to ask for the value of y+zx\frac{y+z}{x} to match one of the options:

    1+53=63=2\frac{1+5}{3} = \frac{6}{3} = 2

    This matches option (b).

    (b) 2\boxed{\textbf{(b) 2}}

    6. The area of a circle is 2466cm22466 \text{cm}^2; calculate its diameter to 2 significant figures. (π=227\pi = \frac{22}{7})

  11. Use the formula for the area of a circle, A=πr2A = \pi r^2, to find the radius rr.

    2466=227r22466 = \frac{22}{7} r^2

  12. Solve for r2r^2.

    r2=2466×722=1726222=784.636...r^2 = \frac{2466 \times 7}{22} = \frac{17262}{22} = 784.636...

  13. Calculate the radius rr.

    r=784.636...≈28.011 cmr = \sqrt{784.636...} \approx 28.011 \text{ cm}

  14. Calculate the diameter d=2rd = 2r.

    d=2×28.011≈56.022 cmd = 2 \times 28.011 \approx 56.022 \text{ cm}

  15. Round the diameter to 2 significant figures.

    d≈56 cmd \approx 56 \text{ cm}

    The correct option is (c).

    (c) 56cm\boxed{\textbf{(c) 56cm}}

    7. Simplify 112÷34×412÷2721\frac{1}{2} \div \frac{3}{4} \times 4\frac{1}{2} \div 2\frac{7}{2}.

  16. Convert all mixed numbers to improper fractions.

    112=321\frac{1}{2} = \frac{3}{2} 412=924\frac{1}{2} = \frac{9}{2} 272=2+72=42+72=1122\frac{7}{2} = 2 + \frac{7}{2} = \frac{4}{2} + \frac{7}{2} = \frac{11}{2}

  17. Rewrite the expression with improper fractions.

    32÷34×92÷112\frac{3}{2} \div \frac{3}{4} \times \frac{9}{2} \div \frac{11}{2}

  18. Perform division and multiplication from left to right.

    First division:

    32÷34=32×43=126=2\frac{3}{2} \div \frac{3}{4} = \frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2

  19. Next multiplication.

    2×92=182=92 \times \frac{9}{2} = \frac{18}{2} = 9

  20. Final division.

    9÷112=9×211=18119 \div \frac{11}{2} = 9 \times \frac{2}{11} = \frac{18}{11}

  21. Convert to a mixed number.

    1811=1711\frac{18}{11} = 1\frac{7}{11}

    The calculated value is 1711≈1.6361\frac{7}{11} \approx 1.636. Comparing this to the options, 112=1.51\frac{1}{2} = 1.5 is the closest value.
    The correct option is (c).

    (c) 112\boxed{\textbf{(c) } 1\frac{1}{2}}

    8. Convert 3123\frac{1}{2} days to hours.

  22. Convert the mixed number to a decimal or improper fraction.

    312 days=3.5 days3\frac{1}{2} \text{ days} = 3.5 \text{ days}

  23. Use the conversion factor

    1 day=24 hours1 \text{ day} = 24 \text{ hours}.

    3.5 days×24hoursday=84 hours3.5 \text{ days} \times 24 \frac{\text{hours}}{\text{day}} = 84 \text{ hours}

    The correct option is (d).

    (d) 84 hrs\boxed{\textbf{(d) 84 hrs}}

    9. If the exchange rate of US dollar to Naira is N80. What is the value of $200 in Naira?

  24. Identify the exchange rate.

    1 US dollar=N801 \text{ US dollar} = \text{N}80

  25. Multiply the amount in dollars by the exchange rate.

    200 US dollars×N80/US dollar=N16,000200 \text{ US dollars} \times \text{N}80/\text{US dollar} = \text{N}16,000

    The correct option is (d).

    (d) 16,000\boxed{\textbf{(d) 16,000}}

    10. A rope is 200 metres long. If 35% of the total length is cut off. Calculate the length of the remaining part of the rope.

  26. Calculate the percentage of the rope remaining.

    100%−35%=65%100\% - 35\% = 65\%

  27. Calculate the length of the remaining part.

    65% of 200 m=0.65×200 m=130 m65\% \text{ of } 200 \text{ m} = 0.65 \times 200 \text{ m} = 130 \text{ m}

    The correct option is (b).

    (b) 130m\boxed{\textbf{(b) 130m}}

    11. Find the cost of 80 Orange at 5 for N30.

  28. Find the cost of one orange.

    Cost per orange=N305 oranges=N6/orange\text{Cost per orange} = \frac{\text{N}30}{5 \text{ oranges}} = \text{N}6/\text{orange}

  29. Calculate the total cost for 80 oranges.

    Total cost=80 oranges×N6/orange=N480\text{Total cost} = 80 \text{ oranges} \times \text{N}6/\text{orange} = \text{N}480

    The correct option is (b).

    (b) N480\boxed{\textbf{(b) N480}}

    12. Uyaji is M years old. How old was she ten years ago?

  30. Represent Uyaji's current age.

    Current age = M years.

  31. To find her age ten years ago, subtract 10 from her current age.

    Age ten years ago = (M−10)(M - 10) years.
    The correct option is (b).

    (b) (m-10) years\boxed{\textbf{(b) (m-10) years}}
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