Further Mathematics Questions and Answers
Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.
Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.
The equation of a circle is 3x2+3y2+6x−12y+6=0. Find its radius
1
√3
√11
√6
Correct answer is B
The equation of a circle is given as (x−a)2+(y−b)2=r2
Expanding this, we have x2+y2−2ax−2by+a2+b2=r2
Comparing with the given equation, 3x2+3y2+6x−12y+6=0≡x2+y2+2x−4y+2=0 (making the coefficients of x2 and y2 = 1 , we get that
−2a=2⟹a=−1
2b=4⟹b=2
r2−a2−b2=−2
∴
r = \sqrt{3}
x < -1, x < -\frac{1}{3}
x > -1, x > -\frac{1}{3}
x > \frac{1}{3}, x < -1
x < \frac{1}{3}, x > -1
Correct answer is B
3x^{2} + 4x + 1 > 0
3x^{2} + 3x + x + 1 > 0
3x(x + 1) + 1(x + 1) > 0
(3x + 1)(x + 1) > 0
3x + 1 > 0 \implies 3x > -1
x > -\frac{1}{3}
x + 1 > 0 \implies x > -1
x > -1, x > -\frac{1}{3}
Simplify \sqrt[3]{\frac{8}{27}} - (\frac{4}{9})^{-\frac{1}{2}}
\frac{-5}{6}
-\frac{4}{27}
0
\frac{2}{9}
Correct answer is A
\sqrt[3]{\frac{8}{27}} - (\frac{4}{9})^{\frac{-1}{2}}
\frac{2}{3} - (\frac{9}{4})^{\frac{1}{2}}
= \frac{2}{3} - \frac{3}{2}
= \frac{-5}{6}
A function is defined by f(x) = \frac{3x + 1}{x^{2} - 1}, x \neq \pm 1. Find f(-3).
-1\frac{1}{4}
-1
\frac{4}{5}
1
Correct answer is B
f(x) = \frac{3x + 1}{x^{2} - 1}
f(-3) = \frac{3(-3) + 1}{(-3)^{2} - 1} = \frac{-8}{8} = -1
Find the remainder when 5x^{3} + 2x^{2} - 7x - 5 is divided by (x - 2).
-51
-23
29
49
Correct answer is C
Using remainder theorem, the remainder when 5x^{3} + 2x^{2} - 7x -5 is divided by (x - 2) = f(2)
f(2) = 5(2^{3}) + 2(2^{2}) - 7(2) -5 = 40 + 8 - 14 - 5
= 29