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JAMB Mathematics Past Questions & Answers - Page 203

1,011.

If the quadratic function 3x² - 7x + R is a perfect square, find R

$\frac{49}{24}$

$\frac{49}{12}$

$\frac{49}{13}$

$\frac{49}{3}$

$\frac{49}{36}$

View answer & explanation

Correct answer is B

3x² - 7x + R. Computing the square, we have
x² - $\frac{7}{3}$ = - $\frac{R}{3}$

( $\frac{x}{1} - \frac{7}{6}$ )² = - $\frac{R}{3}$ + $\frac{49}{36}$

$\frac{-R}{3}$ + $\frac{49}{36}$ = 0

R = $\frac{49}{36}$ x $\frac{3}{1}$

= $\frac{49}{12}$

1,012.

At what real value of x do the curves whose equations are y = x³ + x and y = x² + 1 intersect?

-2

-1

View answer & explanation

Correct answer is E

y = x³ + x and y = x² + 1
$\begin{array}{c|c} x & -2 & -1 & 0 & 1 & 2 \\ \hline Y = x^3 + x & -10 & -2 & 0 & 2 & 10 \\ \hline y = x^2 + 1 & 5 & 2 & 1 & 2 & 5\end{array}$
The curves intersect at x = 1

1,013.

Factorize abx² + 8y - 4bx - 2axy

(ax - 4)(bx - 2y)

(ax + b)(x - 8y)

(ax - 2y)(bx - 4)

(bx - 4)(ax - 2y)

(abx - 4)(x - 2y)

View answer & explanation

Correct answer is A

abx² + 8y - 4bx - 2axy = (abx² - 4bx) + (8y - 2axy)

= bx(ax - 4) 2y(ax - 4) 2y(ax - 4)

= (bx - 2y)(ax - 4)

1,014.

If 3^2y + 6(3^y) = 27. Find y

-1

-3

View answer & explanation

Correct answer is E

3^2y + 6(3^y) = 27

This can be rewritten as (3^y)² + 6(3^y) = 27

Let 3^y = x

x² + 6x - 27 = 0

(x + 9)(x - 3) = 0

when x - 3 = 0, x = 3

sub. for x in 3y = x

3^y = 3

log₃3 = y

y = 1

1,015.

The factors of 9 - (x² - 3x - 1)² are

-(x - 4)(x + 1) (x - 1)(x - 2)

(x - 4)(x - 2) (x - 1)(x + 1)

-(x - 2)(x + 1) (x - 2) (x - 1)

(x - 2)(x + 2) (x - 1)(x + 1)

View answer & explanation

Correct answer is A

9 - (x² - 3x - 1)² = [3 - (x² - 3x - 1)] [3 + (x² - 3x - 1)]

= (3 - x² + 3x + 1)(3 + x² - 3x - 1)

= (4 + 3x - x²)(x² - 3x + 2)

= (4 - x)(1 + x)(x - 1)(x - 2)

= -(x - 4)(x + 1) (x - 1)(x - 2)