How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
If the quadratic function 3x2 - 7x + R is a perfect square, find R
\(\frac{49}{24}\)
\(\frac{49}{12}\)
\(\frac{49}{13}\)
\(\frac{49}{3}\)
\(\frac{49}{36}\)
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 \(\frac{3}{1}\)
= \(\frac{49}{12}\)
At what real value of x do the curves whose equations are y = x3 + x and y = x2 + 1 intersect?
-2
2
-1
9
1
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
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)
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)
3
-1
2
-3
1
Correct answer is E
32y + 6(3y) = 27
This can be rewritten as (3y)2 + 6(3y) = 27
Let 3y = x
x2 + 6x - 27 = 0
(x + 9)(x - 3) = 0
when x - 3 = 0, x = 3
sub. for x in 3y = x
3y = 3
log33 = y
y = 1
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)
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)