2012 JAMB Mathematics Past Questions

Questions

1. 1.

   Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5

   1. A.9
   2. B.8
   3. C.7
   4. D.4

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   Answer: D. 4

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2. 2.

   Evaluate $\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta$

   1. A.1
   2. B.2
   3. C.3
   4. D.4

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   Answer: A. 1

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3. 3.

   In how many ways can the letters of the word TOTALITY be arranged?

   1. A.6720
   2. B.6270
   3. C.6207
   4. D.6027

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   Answer: A. 6720

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4. 4.

   Calculate the volume of a cuboid of length 0.76cm, breadth 2.6cm and height 0.82cm.

   1. A.3.92cm3
   2. B.2.13cm3
   3. C.1.97cm3
   4. D.1.62cm3

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   Answer: D. 1.62cm3

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5. 5.

   If $\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix}$ = $\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}$, find the value of x

   1. A.3
   2. B.4
   3. C.5
   4. D.7

   Show answer

   Answer: C. 5

   AI explanation

   1. Analyze the Question

   We are given an equation involving the determinants of two $2 \times 2$ matrices. We need to calculate the determinant of both sides and solve the resulting linear equation for the unknown variable $x$.

   2. Explain the Concept

   The determinant of a $2 \times 2$ matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is calculated using the formula:

   $\text{Determinant} = (ad) - (bc)$

   This means you multiply the elements of the leading diagonal and subtract the product of the elements of the other diagonal.

   3. Show the Solution

   Step 1: Calculate the determinant of the left-hand side (LHS).

   $\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix} = (5 \times 2) - (3 \times x)$

   $= 10 - 3x$

   Step 2: Calculate the determinant of the right-hand side (RHS).

   $\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix} = (3 \times 5) - (5 \times 4)$

   $= 15 - 20$

   $= -5$

   Step 3: Equate the two results and solve for $x$.

   $10 - 3x = -5$

   Subtract 10 from both sides:

   $-3x = -5 - 10$

   $-3x = -15$

   Divide both sides by -3:

   $x = \frac{-15}{-3}$

   $x = 5$

   4. Identify the Answer

   Comparing our result to the given options: A. 3 B. 4 C. 5 D. 7

   The correct option is C.

   5. Tip

   When dealing with determinants, always remember the "cross-multiplication" rule: (Top-Left $\times$ Bottom-Right) minus (Top-Right $\times$ Bottom-Left). A common mistake students make is forgetting the minus sign between the two products—don't let that happen to you!

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6. 6.

   The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.

   1. A.24o
   2. B.30o
   3. C.33o
   4. D.36o

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   Answer: D. 36o

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7. 7.

   Find the range of 4,9,6,3,2,8,10 and 11

   1. A.11
   2. B.9
   3. C.8
   4. D.4

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   Answer: B. 9

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8. 8.

   Simply $\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}$

   1. A.$1\frac{1}{4}$
   2. B.$1\frac{1}{6}$
   3. C.$\frac{5}{6}$
   4. D.$\frac{4}{5}$

   Show answer

   Answer: C. $\frac{5}{6}$

   AI explanation

   To solve this expression, we need to convert the mixed fractions into improper fractions, perform the multiplication, and then divide by the denominator.

   1. Analyze the question

   We are given the expression:

   $\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}$

   2. Explain the concept

   To work with mixed fractions, follow these steps:

   • Convert to improper fractions: Multiply the whole number by the denominator and add the numerator. Place this over the original denominator.
   • Multiply fractions: Multiply the numerators together and the denominators together.
   • Divide fractions: Multiply the first fraction by the reciprocal (flipped version) of the second fraction.

   3. Show the solution

   Step 1: Convert all mixed fractions to improper fractions.

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

   Step 2: Substitute these into the expression.

   $\frac{\frac{8}{3} \times \frac{3}{2}}{\frac{24}{5}}$

   Step 3: Simplify the numerator.

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

   Step 4: Divide by the denominator. Now we have:

   $\frac{4}{\frac{24}{5}}$

   To divide by a fraction, multiply by its reciprocal:

   $4 \times \frac{5}{24}$

   $\frac{4 \times 5}{24} = \frac{20}{24}$

   Step 5: Reduce the fraction to its simplest form. Divide both the numerator and denominator by their highest common factor, which is 4:

   $\frac{20 \div 4}{24 \div 4} = \frac{5}{6}$

   4. Identify the answer

   Comparing our result to the given options, we find that $\frac{5}{6}$ matches option C.

   5. Exam Tip

   When multiplying fractions, always look for common factors in the numerators and denominators to cancel them out before you multiply. For example, in Step 3, you could have cancelled the '3's immediately, leaving you with $\frac{8}{2} = 4$. This saves time and reduces the risk of calculation errors!

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9. 9.

   If log3x2 = -8, what is x?

   1. A.$\frac{1}{3}$
   2. B.$\frac{1}{9}$
   3. C.$\frac{1}{27}$
   4. D.$\frac{1}{81}$

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   Answer: D. $\frac{1}{81}$

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10. 10.

    If angle $\theta$ is 135o, evaluate cos$\theta$

    1. A.$\frac{1}{2}$
    2. B.$\frac{\sqrt{2}}{2}$
    3. C.$-\frac{\sqrt{2}}{2}$
    4. D.$-\frac{1}{2}$

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    Answer: C. $-\frac{\sqrt{2}}{2}$

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11. 11.

    Solve for x and y in the equations below x2 - y2 = 4 x + y = 2

    1. A.x = 0, y = -2
    2. B.x = 0, y = 2
    3. C.x = 2, y = 0
    4. D.x = -2, y = 0

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    Answer: C. x = 2, y = 0

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12. 12.

    The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is

    1. A.$\sqrt{13}$
    2. B.$3\sqrt{2}$
    3. C.$\sqrt{26}$
    4. D.$10\sqrt{5}$

    Show answer

    Answer: B. $3\sqrt{2}$

    AI explanation

    1. Analyze the question

    We need to find the distance between a fixed point $(4, 3)$ and the point where two lines, $y = 2x + 4$ and $y = 7 - x$, intersect.

    2. Explain the concept

    • Intersection of lines: To find the point of intersection, we solve the two equations simultaneously.
    • Distance formula: The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

    3. Show the solution

    Step 1: Find the point of intersection. Set the two equations equal to each other since both are equal to $y$: $2x + 4 = 7 - x$

    Add $x$ to both sides: $3x + 4 = 7$

    Subtract 4 from both sides: $3x = 3$

    Divide by 3: $x = 1$

    Now, substitute $x = 1$ into either equation to find $y$: $y = 7 - (1) = 6$ The point of intersection is (1, 6).

    Step 2: Calculate the distance between (4, 3) and (1, 6). Using the distance formula where $(x_1, y_1) = (4, 3)$ and $(x_2, y_2) = (1, 6)$: $d = \sqrt{(1 - 4)^2 + (6 - 3)^2}$ $d = \sqrt{(-3)^2 + (3)^2}$ $d = \sqrt{9 + 9}$ $d = \sqrt{18}$

    Step 3: Simplify the radical. $\sqrt{18} = \sqrt{9 \times 2}$ $d = 3\sqrt{2}$

    4. Identify the answer

    Comparing our result $3\sqrt{2}$ to the given options, it matches option B.

    5. Tip

    When solving for the intersection of two lines, always double-check your coordinates by plugging them back into both original equations. If the values satisfy both, you are guaranteed to have the correct point before calculating the distance!

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13. 13.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

14. 14.

    The shaded region above is represented by the equation

    1. A.y ≤ 4x + 2
    2. B.y ≥ 4x + 2
    3. C.y ≤ -4x + 4
    4. D.y ≤ 4x + 4

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    Answer: C. y ≤ -4x + 4

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15. 15.

    Evaluate n+1Cn-2 If n =15

    1. A.3630
    2. B.3360
    3. C.1120
    4. D.560

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    Answer: D. 560

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16. 16.

    Make 'n' the subject of the formula if w = $\frac{v(2 + cn)}{1 - cn}$

    1. A.$\frac{1}{c}(\frac{w - 2v}{v + w})$
    2. B.$\frac{1}{c}(\frac{w - 2v}{v - w})$
    3. C.$\frac{1}{c}(\frac{w + 2v}{v - w})$
    4. D.$\frac{1}{c}(\frac{w + 2v}{v + w})$

    Show answer

    Answer: A. $\frac{1}{c}(\frac{w - 2v}{v + w})$

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17. 17.

    A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.

    1. A.52 cm
    2. B.43 cm
    3. C.40 cm
    4. D.15 cm

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    Answer: B. 43 cm

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18. 18.

    The binary operation * is defined on the set of integers such that p * q = pq + p - q. Find 2 * (3 * 4)

    1. A.11
    2. B.13
    3. C.15
    4. D.22

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    Answer: B. 13

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19. 19.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

20. 20.

    Find the range of values of m which satisfy (m - 3)(m - 4) < 0

    1. A.2 < m < 5
    2. B.-3 < m < 4
    3. C.3 < m < 4
    4. D.-4 < m < 3

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    Answer: C. 3 < m < 4

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21. 21.

    The nth term of a sequence is n2 - 6n - 4. Find the sum of the 3rd and 4th terms.

    1. A.24
    2. B.23
    3. C.-24
    4. D.-25

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    Answer: D. -25

    AI explanation

    1. Analyze the question

    We are given a formula for the $n^{th}$ term of a sequence: $T_n = n^2 - 6n - 4$. We need to find the sum of the 3rd term ($T_3$) and the 4th term ($T_4$).

    2. Explain the concept

    To find any specific term in a sequence when given the general formula, we simply substitute the value of $n$ (the position of the term) into the expression. Once we calculate $T_3$ and $T_4$ individually, we add them together to get the final result.

    3. Show the solution

    Step 1: Find the 3rd term ($T_3$) Substitute $n = 3$ into the formula $n^2 - 6n - 4$: $T_3 = (3)^2 - 6(3) - 4$ $T_3 = 9 - 18 - 4$ $T_3 = -9 - 4$ $T_3 = -13$

    Step 2: Find the 4th term ($T_4$) Substitute $n = 4$ into the formula $n^2 - 6n - 4$: $T_4 = (4)^2 - 6(4) - 4$ $T_4 = 16 - 24 - 4$ $T_4 = -8 - 4$ $T_4 = -12$

    Step 3: Find the sum of the 3rd and 4th terms Sum $= T_3 + T_4$ Sum $= (-13) + (-12)$ Sum $= -25$

    4. Identify the answer

    Comparing our result to the given options: A. 24 B. 23 C. -24 D. -25

    The correct option is D.

    5. Tip

    When dealing with sequences involving negative numbers, always be careful with your signs during subtraction. A common mistake is to calculate $9 - 18$ as $9$ instead of $-9$. Always perform the operations from left to right to stay organized!

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22. 22.

    The value of y for which $\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}$ is

    1. A.$y > \frac{2}{3}$
    2. B.$y < \frac{2}{3}$
    3. C.$y > -\frac{2}{3}$
    4. D.$y < -\frac{2}{3}$

    Show answer

    Answer: C. $y > -\frac{2}{3}$

    AI explanation

    To solve the inequality $\frac{1}{5}y + \frac{1}{5} < \frac{1}{2}y + \frac{2}{5}$, follow these steps:

    1. Analyze the inequality

    We have a linear inequality with fractions. To make the calculation easier, we should eliminate the fractions by multiplying the entire inequality by the Least Common Multiple (LCM) of the denominators (5, 5, 2, 5). The LCM is 10.

    2. Clear the fractions

    Multiply every term on both sides by 10: $10 \left( \frac{1}{5}y \right) + 10 \left( \frac{1}{5} \right) < 10 \left( \frac{1}{2}y \right) + 10 \left( \frac{2}{5} \right)$

    Simplify each term: $2y + 2 < 5y + 4$

    3. Solve for $y$

    Group the $y$ terms on one side and the constants on the other. Let's move $2y$ to the right and $4$ to the left: $2 - 4 < 5y - 2y$

    Simplify: $-2 < 3y$

    Now, divide both sides by 3 to isolate $y$: $-\frac{2}{3} < y$

    This can also be written as: $y > -\frac{2}{3}$

    4. Conclusion

    Comparing our result to the given options, we find that $y > -\frac{2}{3}$ matches option C.

    Exam Tip: When working with inequalities, remember that if you multiply or divide by a negative number, you must flip the inequality sign. In this problem, we kept the coefficients positive by moving terms strategically, which helped us avoid that common pitfall!

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23. 23.

    A circular arc subtends angle 150° at the centre of a circle of radius 12cm. Calculate the area of the sector of the arc.

    1. A.30$\pi$ cm$^2$
    2. B.60$\pi$ cm$^2$
    3. C.120$\pi$ cm$^2$
    4. D.150$\pi$ cm$^2$

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    Answer: B. 60$\pi$ cm$^2$

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24. 24.

    The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is

    1. A.$\frac{1}{2}$
    2. B.$\frac{2}{5}$
    3. C.$-\frac{4}{7}$
    4. D.$-\frac{2}{3}$

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    Answer: C. $-\frac{4}{7}$

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25. 25.

    Find the remainder when 2x3 - 11x2 + 8x - 1 is divided by x + 3

    1. A.-871
    2. B.-781
    3. C.-187
    4. D.-178

    Show answer

    Answer: D. -178

    AI explanation

    1. Analyze the Question

    We are asked to find the remainder when the polynomial $P(x) = 2x^3 - 11x^2 + 8x - 1$ is divided by the linear factor $(x + 3)$.

    2. Explain the Concept: The Remainder Theorem

    The Remainder Theorem states that if a polynomial $P(x)$ is divided by $(x - a)$, the remainder is simply $P(a)$.

    In this case, we are dividing by $(x + 3)$. To find the value of $a$, we set the divisor to zero: $x + 3 = 0$ $x = -3$

    Therefore, the remainder is equal to $P(-3)$.

    3. Show the Solution

    Substitute $x = -3$ into the polynomial $P(x) = 2x^3 - 11x^2 + 8x - 1$:

    Step 1: Substitute -3 for x $P(-3) = 2(-3)^3 - 11(-3)^2 + 8(-3) - 1$

    Step 2: Evaluate the powers $(-3)^3 = -27$ $(-3)^2 = 9$

    Step 3: Multiply the terms $P(-3) = 2(-27) - 11(9) + 8(-3) - 1$ $P(-3) = -54 - 99 - 24 - 1$

    Step 4: Combine the values $-54 - 99 = -153$ $-153 - 24 = -177$ $-177 - 1 = -178$

    The remainder is -178.

    4. Identify the Answer

    Comparing our result to the given options: A. -871 B. -781 C. -187 D. -178

    The correct option is D.

    5. Exam Tip

    When using the Remainder Theorem, be extremely careful with negative signs! Students often make mistakes when squaring or cubing negative numbers. Remember:

    • A negative number raised to an even power becomes positive.
    • A negative number raised to an odd power remains negative.
    • Always write out the substitution clearly in brackets to avoid sign errors.

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26. 26.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

27. 27.

    If y = x2 - $\frac{1}{x}$, find $\frac{\delta y}{\delta x}$

    1. A.2x - $\frac{1}{x^2}$
    2. B.2x + x2
    3. C.2x - x2
    4. D.2x + $\frac{1}{x^2}$

    Show answer

    Answer: D. 2x + $\frac{1}{x^2}$

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28. 28.

    Find the standard deviation of 2,3,8,10 and 12

    1. A.3.9
    2. B.4.9
    3. C.5.9
    4. D.6.9

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    Answer: A. 3.9

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29. 29.

    Given that I3 is a unit matrix of order 3, find |I3|

    1. A.-1
    2. B.O
    3. C.1
    4. D.2

    Show answer

    Answer: C. 1

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30. 30.

    Find the equation of the line through the points (-2, 1) and (-$\frac{1}{2}$, 4)

    1. A.y = 2x - 3
    2. B.y = 2x + 5
    3. C.y = 3x - 2
    4. D.y = 2x + 1

    Show answer

    Answer: B. y = 2x + 5

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31. 31.

    The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.

    1. A.126
    2. B.180
    3. C.216
    4. D.224

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    Answer: D. 224

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32. 32.

    Evaluate $\int^2_1(x^2 - 4x)dx$

    1. A.$\frac{11}{3}$
    2. B.$\frac{3}{11}$
    3. C.$-\frac{3}{11}$
    4. D.$-\frac{11}{3}$

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    Answer: D. $-\frac{11}{3}$

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33. 33.

    Find $\frac{\mathrm d y}{\mathrm d x}$ if $y = \cos x$.

    1. A.$\sin x$
    2. B.$- \sin x$
    3. C.$\tan x$
    4. D.$- \tan x$

    Show answer

    Answer: B. $- \sin x$

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34. 34.

    If y varies directly as $\sqrt{n}$ and y = 4 when n = 4, find y when n = 1$\frac{7}{9}$

    1. A.$\sqrt{17}$
    2. B.$\frac{4}{3}$
    3. C.$\frac{8}{3}$
    4. D.$\frac{2}{3}$

    Show answer

    Answer: C. $\frac{8}{3}$

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35. 35.

    A man earns N3,500 per month out of which he spends 15% on his children's education. If he spends additional N1,950 on food, how much does he have left?

    1. A.N525
    2. B.N1,025
    3. C.N1,950
    4. D.N2,975

    Show answer

    Answer: B. N1,025

    AI explanation

    Analysis

    To solve this problem, we need to calculate the total amount the man spends from his monthly salary and subtract that total from his initial earnings to find the remainder.

    Concept

    1. Percentage Calculation: To find a percentage of a number, multiply the number by the percentage (expressed as a fraction or decimal). • Formula: $\text{Amount} = (\text{Percentage} / 100) \times \text{Total Salary}$
    2. Subtraction: Subtract all expenses from the total income to find the balance.

    Step-by-Step Solution

    Step 1: Calculate the amount spent on education. The man spends 15% of N3,500 on his children's education.

    • $\text{Education Expense} = \frac{15}{100} \times 3500$
    • $\text{Education Expense} = 0.15 \times 3500$
    • $\text{Education Expense} = N525$

    Step 2: Calculate the total expenditure. The man also spends N1,950 on food. Add this to the education expense.

    • $\text{Total Expenditure} = \text{Education Expense} + \text{Food Expense}$
    • $\text{Total Expenditure} = N525 + N1,950$
    • $\text{Total Expenditure} = N2,475$

    Step 3: Calculate the balance left. Subtract the total expenditure from the monthly salary.

    • $\text{Balance} = \text{Total Salary} - \text{Total Expenditure}$
    • $\text{Balance} = N3,500 - N2,475$
    • $\text{Balance} = N1,025$

    Conclusion

    After spending 15% on education and N1,950 on food, the man is left with N1,025.

    Exam Tip: When dealing with percentage problems in JAMB, always convert the percentage to a decimal first (e.g., 15% = 0.15). This makes multiplication much faster and reduces errors when working with large numbers like 3,500.

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36. 36.

    In a class of 46 students, 22 play football and 26 play volleyball. If 3 students play both games, how many play neither?

    1. A.1
    2. B.2
    3. C.3
    4. D.4

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    Answer: A. 1

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37. 37.

    Simplify $(\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2$

    1. A.$2\sqrt{6}$
    2. B.$4\sqrt{6}$
    3. C.$8\sqrt{6}$
    4. D.$16\sqrt{6}$

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    Answer: C. $8\sqrt{6}$

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38. 38.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

39. 39.

    The binary operation on the set of real numbers is defined by m*n = $\frac{mn}{2}$ for all m, n $\in$ R. If the identity element is 2, find the inverse of -5

    1. A.$-\frac{4}{5}$
    2. B.$-\frac{2}{5}$
    3. C.4
    4. D.5

    Show answer

    Answer: A. $-\frac{4}{5}$

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40. 40.

    U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

    1. A.24
    2. B.27
    3. C.32
    4. D.36

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    Answer: A. 24

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41. 41.

    The probability that a student passes a physics test is $\frac{2}{3}$. If he takes three physics tests, what is the probability that he passes two of the tests?

    1. A.$\frac{2}{27}$
    2. B.$\frac{3}{27}$
    3. C.$\frac{4}{27}$
    4. D.$\frac{5}{3}$

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    Answer: C. $\frac{4}{27}$

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42. 42.

    If 27$^{x + 2}$ $\div$ 9$^{x + 1}$ = 3$^{2x}$, find x.

    1. A.3
    2. B.4
    3. C.5
    4. D.6

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    Answer: B. 4

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43. 43.

    Evaluate $\frac{21}{9}$ to 3 significant figures

    1. A.2.30
    2. B.2.31
    3. C.2.32
    4. D.2.33

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    Answer: D. 2.33

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44. 44.

    Convert 112$_6$ to a number in base three

    1. A.2211
    2. B.2121
    3. C.1212
    4. D.1122

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    Answer: D. 1122

    AI explanation

    1. Analyze the question

    We are asked to convert a number given in base six ($112_6$) into base three. Since there is no direct way to convert between base six and base three, we must use Base 10 as an intermediary.

    2. Explain the concept

    • Step 1: Convert the number from base six to base ten by multiplying each digit by its corresponding power of 6.
    • Step 2: Convert the resulting base ten number to base three by using the method of successive division (dividing by 3 and keeping track of the remainders).

    3. Show the solution

    Step 1: Convert $112_6$ to base 10 $112_6 = (1 \times 6^2) + (1 \times 6^1) + (2 \times 6^0)$ $112_6 = (1 \times 36) + (1 \times 6) + (2 \times 1)$ $112_6 = 36 + 6 + 2$ $112_6 = 44_{10}$

    Step 2: Convert $44_{10}$ to base 3 We divide 44 by 3 repeatedly and record the remainders:

    • $44 \div 3 = 14$ remainder 2
    • $14 \div 3 = 4$ remainder 2
    • $4 \div 3 = 1$ remainder 1
    • $1 \div 3 = 0$ remainder 1

    Reading the remainders from the bottom to the top, we get 1122.

    4. Identify the answer

    Comparing our result ($1122_3$) to the given options, it matches option D.

    5. Tip

    When converting from base 10 to any other base, always remember to read your remainders from the last one obtained (bottom) to the first one obtained (top). A common mistake students make is reading them from top to bottom, which will give you the wrong answer!

    AI can make mistakes. Report anything that looks wrong.

45. 45.

    The sum to infinity of a geometric progression is $-\frac{1}{10}$ and the first term is $-\frac{1}{8}$. Find the common ratio of the progression.

    1. A.$-\frac{1}{5}$
    2. B.$-\frac{1}{4}$
    3. C.$-\frac{1}{3}$
    4. D.$-\frac{1}{2}$

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    Answer: B. $-\frac{1}{4}$

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46. 46.

    The probabilities that a man and his wife live for 80 years are $\frac{2}{3}$ and $\frac{3}{5}$ respectively. Find the probability that at least one of them will live up to 80 years

    1. A.$\frac{2}{15}$
    2. B.$\frac{3}{15}$
    3. C.$\frac{7}{15}$
    4. D.$\frac{13}{15}$

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    Answer: D. $\frac{13}{15}$

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47. 47.

    If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P $\cap$ Q

    1. A.{3}
    2. B.{2,3}
    3. C.{2,3,5}
    4. D.{1,2}

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    Answer: B. {2,3}

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48. 48.

    Find the area of the trapezium above.

    1. A.91 cm2
    2. B.78 cm2
    3. C.60 cm2
    4. D.19 cm2

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    Answer: B. 78 cm2

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