JAMB Mathematics Past Questions & Answers

1,166.

Express $\frac{1}{x + 1}$ - $\frac{1}{x - 2}$ as a single algebraic fraction

$\frac{-3}{(x + 1)(2 - x)}$

$\frac{3}{(x + 1)(2 - x)}$

$\frac{-1}{(x + 1)}$

$\frac{1}{(x + 1)(x - 2)}$

View answer & explanation

Correct answer is A

$\frac{1}{x + 1}$ - $\frac{1}{x - 2}$ = $\frac{x - 2 - x - 1}{(x + 1)(x - 2)}$

= $\frac{-3}{(x + 1)(2 - x)}$

1,167.

Find the range of values of values of r which satisfies the following inequality, where a, b and c are positive $\frac{r}{a}$ + $\frac{r}{b}$ + $\frac{r}{c}$ > 1

r > $\frac{abc}{bc + ac + ab}$

r < abc

r > $\frac{1}{a}$ + $\frac{1}{b}$ + $\frac{1}{c}$

$\frac{1}{abc}$

View answer & explanation

Correct answer is A

$\frac{r}{a}$ + $\frac{r}{b}$ + $\frac{r}{c}$ > 1 = $\frac{bcr + acr + abr}{abc}$ > 1

r(bc + ac + ba > abc) = r > $\frac{abc}{bc + ac + ab}$

1,168.

What value of Q will make the expression 4x² + 5x + Q a complete square?

$\frac{25}{16}$

$\frac{25}{64}$

$\frac{5}{8}$

$\frac{5}{4}$

View answer & explanation

Correct answer is A

4x² + 5x + Q

To make a complete square, the coefficient of x² must be 1

= x² + $\frac{5x}{4}$ + $\frac{Q}{4}$

Then (half the coefficient of x²) should be added

i.e. x² + $\frac{5x}{4}$ + $\frac{25}{64}$

∴ $\frac{Q}{4}$ = $\frac{25}{64}$

Q = $\frac{4 \times 25}{64}$

= $\frac{25}{16}$

1,169.

Solve the pair of equation for x and y respectively $2x^{-1} - 3y^{-1} = 4; 4x^{-1} + y^{-1} = 1$

-1, 2

1, 2

2, 1

2, -1

View answer & explanation

Correct answer is D

$2x^{-1} - 3y^{-1} = 4; 4x^{-1} + y^{-1} = 1$

Let $x^{-1}$ = a and $y^{-1}$ = b

2a - 3b = 4 .......(i)

4a + b = 1 .........(ii)

(i) x 3 = 12a + 3b = 3........(iii)

2a - 3b = 4 ...........(i)

(i) + (iii) = 14a = 7

∴ a = $\frac{7}{14}$ = $\frac{1}{2}$

From (i), 3b = 2a - 4

3b = 1 - 4

3b = -3

∴ b = -1

From substituting, $2^{-1} = x^{-1}$

∴ x = 2

$y^{-1} = -1, y = -1$

1,170.

What are K and L respectively if $\frac{1}{2}$ (3y - 4x)² = (8x² + kxy + Ly²)

-12, $\frac{9}{2}$

-6, 9

6, 9

12, $\frac{9}{2}$

View answer & explanation

Correct answer is A

$\frac{1}{2}$ (3y - 4x)² = (8x² + kxy + Ly²)

$\frac{1}{2}$ (9y² - 24xy + 16x²) = 8x² + kxy + Ly²

$\frac{9}{2}$ y² - 12xy) = kxy + Ly²

k = -12 ∴ L = $\frac{9}{2}$