2017 - JAMB Mathematics Past Questions and Answers - page 5

41
The operation * on the set R of real number is defined by x * y = 3x + 2y − 1, find 3* − 1
A
9
B
- 9
C
6
D
- 6
correct option: c

x * y is an operation on 3x + 2y − 1

Find 3A − 1

x = 3, y = −1

3 * − 1 on 3x + 2y − 1

3(3) + 2(−1) −1

= 9 − 2 − 1

= 6

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42
Find the gradient of the line joining the points (3, 2) and (1, 4)
A
3/2
B
2/1
C
-1
D
3/2
correct option: c

Gradient of line joining points (3, 2), (1, 4)

Gradient = (\frac{\text{Change in Y}}{\text{Change in X}})

= (\frac{y_2 - Y_1}{x_2 - x_1}))

(X1, Y1) = (3, 2)

(X2, Y2) = (1, 4)

Gradient = (\frac{4 − 2}{1 + 3})

= (\frac{2}{-2})

= −1

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43
Simplify (3√64a3)\(^{−1}\)
A
4a
B
\(\frac{1}{8a}\)
C
8a
D
\(\frac{1}{4a}\)
correct option: d

(3√64a3)(^{-1})

(\frac{1}{(3√64a^3)

= (\frac{1}{4a})

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44
If \(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) = m + n √ 6,

find the values of m and n respectively
A
1, − 2
B
− 2, n = 1
C
\(\frac{-2}{5}\), 1
D
\(\frac{2}{3}\)
correct option: b

(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}})= m + n√6

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


(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})})

(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2})

= (\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8})

= (\frac{0 - 4 \sqrt{6} - 6}{5})

= (\frac{10 - 5 \sqrt{6}}{5})

= − 2 + √6

∴ m + n(\sqrt{6}) = − 2 + √6

m = − 2, n = 1

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45
If α and β are the roots of the equation 3x2 + bx − 2 = 0. Find the value of \(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\)
A
\(\frac{-5}{3}\)
B
\(\frac{-2}{3}\)
C
\(\frac{1}{2}\)
D
\(\frac{5}{2}\)
correct option: d

(\frac{1}{\alpha}) + (\frac{1}{\beta}) = (\frac{\beta -\alpha}{\alpha \beta})

3x2 + 5x + 5x − 2 = 0.

Sum of root = α + β

Product of root = αβ

x2 + (\frac{5x}{3}) − (\frac{2}{3}) = 0

αβ = − (\frac{-2}{3})

α + β = (\frac{5}{3})

∴ (\frac{\alpha + \beta}{\alpha \beta}) = − (\frac{\frac{5}{3}}{\frac{2}{3}}})


= − (\frac{2}{3}) × (\frac{3}{3})

= (\frac{5}{2})

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46
Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2
A
1.03
B
0.07
C
0.03
D
1.0
correct option: d

0.4, −0.4, 0.3, 0.47, −0.53, 0.2, −0.2

Range is the difference between the highest and lowest value

i.e Highest − Lowest

− 0.53, −0.4, −0.2, 0.2, 0.3, 0.4, 0.47

0.47 is the highest

− 0.53 is the lowest

∴ = 0.47 − (− 0.53)

∴0.47 + 0.53

= 1.0

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47
Evaluate 1 − (\(\frac{1}{5}\) + 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\))
A
4
B
3
C
2\(\frac{2}{3}\)
D
3 \(\frac{2}{3}\)
correct option: d

1 − ((\frac{1}{5}) + 1(\frac{2}{3})) + (5 + 1(\frac{2}{3}))

1 − ((\frac{1}{5}) × (\frac{5}{3})) + (5 + (\frac{5}{3}))

1 − (\frac{1}{3}) + (\frac{20}{3})

= (\frac{22}{3})

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48
What is the product of 2x2 − x + 1 and 3 − 2x
A
4x3 − 8x2 + 5x + 3
B
−4x3 + 8x2 − 5x + 3
C
−4x3 − 8x2 + 5x + 3
D
4x3 + 8x2 − 5x + 3
correct option: b

(2x2 - x + 1) × (3 - 2x);

3(2x2 - x + 1) - 2x (2x2 - x + 1)

6x2 - 3x + 3 - 4x3 + 2x2 - 2x

-4x3 + 8x2 -5x + 3

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