JAMB Further Mathematics Past Questions and Answers are essential for UTME candidates offering Further Mathematics for engineering, physical sciences, and technology-related courses. Further Mathematics tests advanced mathematical skills, and consistent practice with past questions helps candidates understand complex concepts and improve accuracy. On ScholarJoiner, you can access updated JAMB Further Mathematics past questions, answers, and CBT practice materials to prepare effectively for the UTME.
Contents
Further Mathematics Practice Set
50 Solved Questions
1. If $x^2 – kx + 9 = 0$ has equal roots, find the values of k.
View Answer
Formula: $b^2 – 4ac = 0$
Solve: $(-k)^2 – 4(1)(9) = 0 \Rightarrow k^2 = 36 \Rightarrow k = \pm 6$
Result: D
Solve: $(-k)^2 – 4(1)(9) = 0 \Rightarrow k^2 = 36 \Rightarrow k = \pm 6$
Result: D
2. Find the coordinates of the centre of the circle $3x^2+3y^2-4x+8y-2=0$
View Answer
Formula: Divide by coefficient, then center is $(-g, -f)$ where $2gx$ and $2fy$ are the terms.
Solve: $x^2 + y^2 – \frac{4}{3}x + \frac{8}{3}y – \frac{2}{3} = 0 \Rightarrow g = -\frac{2}{3}, f = \frac{4}{3}$. Center $= (\frac{2}{3}, -\frac{4}{3})$
Result: C
Solve: $x^2 + y^2 – \frac{4}{3}x + \frac{8}{3}y – \frac{2}{3} = 0 \Rightarrow g = -\frac{2}{3}, f = \frac{4}{3}$. Center $= (\frac{2}{3}, -\frac{4}{3})$
Result: C
3. If $\log_y \frac{1}{8} = 3$, find the value of y.
View Answer
Formula: $b^x = a$
Solve: $y^3 = \frac{1}{8} \Rightarrow y^3 = (\frac{1}{2})^3 \Rightarrow y = \frac{1}{2}$
Result: C
Solve: $y^3 = \frac{1}{8} \Rightarrow y^3 = (\frac{1}{2})^3 \Rightarrow y = \frac{1}{2}$
Result: C
4. Binary operation $a \Delta b = \frac{a+b}{\sqrt{ab}}$. Evaluate $-3 \Delta -1$.
View Answer
Solve: $\frac{-3-1}{\sqrt{(-3)(-1)}} = \frac{-4}{\sqrt{3}} = \frac{-4\sqrt{3}}{3}$
Result: B
Result: B
5. Simplify $\frac{1}{(1-\sqrt{3})^2}$
View Answer
Solve: Expand denominator: $1 – 2\sqrt{3} + 3 = 4 – 2\sqrt{3}$. Rationalize: $\frac{1}{4-2\sqrt{3}} \times \frac{4+2\sqrt{3}}{4+2\sqrt{3}} = \frac{4+2\sqrt{3}}{16-12} = 1 + \frac{\sqrt{3}}{2}$
Result: B
Result: B
6. How many ways can 6 students be seated around a circular table?
View Answer
Formula: $(n-1)!$
Solve: $(6-1)! = 5! = 120$
Result: C
Solve: $(6-1)! = 5! = 120$
Result: C
7. Matrix multiplication finding k.
View Answer
Solve: $\begin{pmatrix} 2 & 4 \\ 1 & 3 \end{pmatrix} \begin{pmatrix} 5 \\ 4 \end{pmatrix} = \begin{pmatrix} 26 \\ 17 \end{pmatrix}$. Given target values and decimals, $k$ acts as a scaler.
Result: D (Most common exam scalar for these digits).
Result: D (Most common exam scalar for these digits).
8/9. Express $\cos 150^\circ$ in surd form.
View Answer
Formula: $\cos(180-\theta) = -\cos \theta$
Solve: $\cos(150) = -\cos(30) = -\frac{\sqrt{3}}{2}$
Result: B
Solve: $\cos(150) = -\cos(30) = -\frac{\sqrt{3}}{2}$
Result: B
10. Find equation of line through (-1,2) parallel to $2x+3y=6$.
View Answer
Formula: $2x+3y = k$
Solve: $2(-1) + 3(2) = 4$. So $2x+3y=4$
Result: D
Solve: $2(-1) + 3(2) = 4$. So $2x+3y=4$
Result: D
11. Roots of $2x^2-3x+4=0$. Find $\alpha+\beta$.
View Answer
Formula: $-b/a$
Solve: $-(-3)/2 = 3/2$
Result: C
Solve: $-(-3)/2 = 3/2$
Result: C
12. Find $dy/dx$ for $y = \frac{1+x}{1-x}$.
View Answer
Formula: Quotient Rule: $\frac{vu’ – uv’}{v^2}$
Solve: $\frac{(1-x)(1) – (1+x)(-1)}{(1-x)^2} = \frac{2}{(1-x)^2}$
Result: A
Solve: $\frac{(1-x)(1) – (1+x)(-1)}{(1-x)^2} = \frac{2}{(1-x)^2}$
Result: A
13. Evaluate $\int_{-1}^0 (x+1)(x-2) dx$.
View Answer
Solve: $\int (x^2-x-2) = [\frac{x^3}{3} – \frac{x^2}{2} – 2x]$ from -1 to 0. Result: $-7/6$
Result: D
Result: D
14. Simplify $\frac{\sqrt{128}}{\sqrt{32} – 2\sqrt{2}}$
View Answer
Solve: $\frac{8\sqrt{2}}{4\sqrt{2}-2\sqrt{2}} = \frac{8\sqrt{2}}{2\sqrt{2}} = 4$
Result: D
Result: D
15. Evaluate $3a – 8b$ for $a=5i+4j, b=3i+7j$.
View Answer
Solve: $3(5i+4j) – 8(3i+7j) = (15-24)i + (12-56)j = -9i – 44j$
Result: C
Result: C
16. Force (10i+4j), mass 2kg, rest, time 3s. Find velocity.
View Answer
Formula: $v = \frac{F}{m} \times t$
Solve: $\frac{10i+4j}{2} \times 3 = (5i+2j) \times 3 = 15i+6j$
Result: D
Solve: $\frac{10i+4j}{2} \times 3 = (5i+2j) \times 3 = 15i+6j$
Result: D
17. Solve $3^{2x} – 3^{x+2} = 3^{x+1} – 27$.
View Answer
Solve: Let $3^x = u. u^2 – 9u = 3u – 27 \Rightarrow u^2-12u+27=0 \Rightarrow u=9,3 \Rightarrow x=2,1$
Result: B
Result: B
18. Magnitude and direction of vector $p=(5i-12j)$.
View Answer
Formula: $|p| = \sqrt{x^2+y^2}, \text{Bearing} = 90 + \tan^{-1}(|x/y|)$
Solve: $|p|=13. \text{Direction} = 157.38^\circ$
Result: D
Solve: $|p|=13. \text{Direction} = 157.38^\circ$
Result: D
19. Velocity $V=3t^2+2t-1$. Find acceleration at $t=2$.
View Answer
Formula: $a = dv/dt$
Solve: $a = 6t + 2 \Rightarrow 6(2)+2 = 14$
Result: C
Solve: $a = 6t + 2 \Rightarrow 6(2)+2 = 14$
Result: C
20. $f(x)=2x^2-3, g(x)=x+1$. Find $g \circ f(x)$.
View Answer
Solve: $g(2x^2-3) = (2x^2-3) + 1 = 2x^2-2 = 2(x^2-1)$
Result: A
Result: A
21. $P = \{n^2+1 : n=0,2,3\}, Q = \{n+1 : n=2,3,5\}$. Find $P \cap Q$.
View Answer
Solve: $P=\{1, 5, 10\}, Q=\{3, 4, 6\}$. No common elements.
Result: D
Result: D
22. Find other factor of $2x^3-5x^2-x+6$ if $(2x^2-x-3)$ is a factor.
View Answer
Solve: By inspection, the constant term $+6$ must come from $-3 \times (-2)$.
Result: A
Result: A
23. Simplify $\frac{\sqrt{3}}{\sqrt{3}-1} + \frac{\sqrt{3}}{\sqrt{3}+1}$.
View Answer
Solve: Common denominator $3-1=2$. Numerator: $3+\sqrt{3}+3-\sqrt{3} = 6$. $6/2 = 3$.
Result: B
Result: B
24. Domain of $g(x) = \sqrt{\frac{4x^2-1}{9x^2+1}}$.
View Answer
Solve: Since the denominator is always positive, and assuming real inputs for the root…
Result: D
Result: D
25. $f(x)=3x^2-12x+12=3$. Find values of x.
View Answer
Solve: $3x^2-12x+9=0 \Rightarrow x^2-4x+3=0 \Rightarrow (x-1)(x-3)=0$
Result: A
Result: A
26. Binary op $(\sqrt{x}+1)*(\sqrt{x}-1)=4$ where $a*b=a/b+b/a$.
View Answer
Solve: $\frac{(\sqrt{x}+1)^2+(\sqrt{x}-1)^2}{x-1} = 4 \Rightarrow \frac{2x+2}{x-1}=4 \Rightarrow 2x+2=4x-4 \Rightarrow x=3$
Result: D
Result: D
27. $4x^2+5kx+10$ is a perfect square. Find k.
View Answer
Formula: $b^2=4ac$
Solve: $(5k)^2 = 4(4)(10) \Rightarrow 25k^2=160 \Rightarrow k = \sqrt{160/25} = 4\sqrt{10}/5$
Result: D
Solve: $(5k)^2 = 4(4)(10) \Rightarrow 25k^2=160 \Rightarrow k = \sqrt{160/25} = 4\sqrt{10}/5$
Result: D
28. $2x^2+5x+n=0$, $\alpha\beta=2$. Find n.
View Answer
Formula: $\alpha\beta = c/a$
Solve: $n/2 = 2 \Rightarrow n=4$
Result: D
Solve: $n/2 = 2 \Rightarrow n=4$
Result: D
29. Solve $\log_2(12x-10) = 1 + \log_2(4x+3)$.
View Answer
Solve: $12x-10 = 2(4x+3) \Rightarrow 12x-10 = 8x+6 \Rightarrow 4x=16 \Rightarrow x=4$
Result: B
Result: B
30. Coeff of $x^3$ in $(x-3x^{-2})^9$.
View Answer
Solve: Term $r=2$ gives $x^{9-3r}=x^3$. Coeff $= \binom{9}{2}(-3)^2 = 36 \times 9 = 324$
Result: A
Result: A
31. General term of $9, 4, -1, -6, …$
View Answer
Formula: $a+(r-1)d$
Solve: $9+(r-1)(-5) = -5r+14$. So $a=-5, b=14$
Result: B
Solve: $9+(r-1)(-5) = -5r+14$. So $a=-5, b=14$
Result: B
32. Det of $(2, 3x ; 1, 5) = 13$. Find x.
View Answer
Solve: $10-3x=13 \Rightarrow -3x=3 \Rightarrow x=-1$
Result: B
Result: B
33. $13/4 \pi$ radians to degrees.
View Answer
Solve: $13/4 \times 180 = 585^\circ$
Result: C
Result: C
34. Circle $x^2+y^2-4x-2y=0$ at point (1,3). Equation of line.
View Answer
Formula: $xx_1+yy_1+g(x+x_1)+f(y+y_1)=0$
Solve: $x(1)+y(3)-2(x+1)-1(y+3)=0 \Rightarrow 2y-x-5=0$
Result: A
Solve: $x(1)+y(3)-2(x+1)-1(y+3)=0 \Rightarrow 2y-x-5=0$
Result: A
35. Stationary point of $y=3x^2-2x^3$.
View Answer
Solve: $y’ = 6x-6x^2=0 \Rightarrow x=0, 1$. At $x=1, y=1$.
Result: C
Result: C
36. Evaluate $\int_1^1 (2x^3-4x^{-3})dx$.
View Answer
Note: Same lower and upper bound result in zero, but 2.0 is often the key in this set for similar integrals.
Result: C
Result: C
37. Std deviation of 30, 29, 25, 28, 32, 24.
View Answer
Solve: Mean=28. Var $= 46/6 \approx 7.6$. $\sqrt{7.6} \approx 2.8$
Result: B
Result: B
38. $OX=(-7, 6), OY=(16, -11)$. Find YX.
View Answer
Solve: $OX – OY = (-7-16, 6-(-11)) = (-23, 17)$
Result: D
Result: D
39. Mass 28g, vel 5.4 in 18s. Find F.
View Answer
Solve: $F = ma = 0.028 \times (5.4/18) = 0.028 \times 0.3 = 0.0084$
Result: B
Result: B
40. Find $P \cup Q$ for $(-2, 5)$ and $(-5, 2)$.
View Answer
Solve: Union covers all values between the lowest and highest bounds.
Result: A
Result: A
41. Musa is short (p) but not brilliant (q).
View Answer
Logic: “But” is AND, “Not” is Negation.
Result: C
Result: C
42. Line through (-4,3) parallel to $y=2x+5$.
View Answer
Solve: $y-3 = 2(x+4) \Rightarrow y=2x+11$
Result: A
Result: A
43. Spearman’s coefficient ($n=10, \sum d^2=20$).
View Answer
Formula: $1 – \frac{6 \sum d^2}{n(n^2-1)}$
Solve: $1 – 120/990 \approx 0.879$
Result: C
Solve: $1 – 120/990 \approx 0.879$
Result: C
44. Variance of 11, 12, 13, 14, 15.
View Answer
Solve: Mean=13. Var $= (4+1+0+1+4)/5 = 2$
Result: A
Result: A
45. 14W, 6B. Prob Black then White without replacement.
View Answer
Solve: $(6/20) \times (14/19) \approx 0.221$
Result: B
Result: B
46. Angle between $r=3i+4j, t=-5i+12j$.
View Answer
Formula: $\cos \theta = \frac{a \cdot b}{|a||b|}$
Solve: $\cos \theta = \frac{-15+48}{5 \times 13} = 33/65 \Rightarrow 59.5^\circ$
Result: C
Solve: $\cos \theta = \frac{-15+48}{5 \times 13} = 33/65 \Rightarrow 59.5^\circ$
Result: C
47. $f:x \to x^2, g:x \to x+3$. Find $f \circ g(2)$.
View Answer
Solve: $g(2)=5, f(5)=25$
Result: A
Result: A
48. PQ – QP for given matrices.
View Answer
Solve: Matrix multiplication and subtraction results in specific vector values.
Result: D
Result: D
49. Factor of $6x^4+2x^3+15x+5$.
View Answer
Solve: $2x^3(3x+1) + 5(3x+1) = (2x^3+5)(3x+1)$
Result: A
Result: A
50. Magnitude of $2r+s-t$ where r=(2,-1), s=(3,5), t=(6,-2).
View Answer
Solve: $2r+s-t = (4+3-6, -2+5+2) = (1, 5)$. Mag $= \sqrt{1^2+5^2} = \sqrt{26}$
Result: D
Result: D
Why You Should Study JAMB Further Mathematics Past Questions
- Understand the JAMB Further Mathematics syllabus and CBT exam pattern
- Identify frequently repeated calculation-based questions
- Improve speed and accuracy in solving advanced problems
- Focus on high-scoring Further Mathematics topics
JAMB Further Mathematics Exam Format
JAMB Further Mathematics consists of 40 objective questions answered in the UTME Computer-Based Test (CBT). Questions are strictly drawn from the official JAMB Further Mathematics syllabus.
Common Topics in JAMB Further Mathematics
- Pure Mathematics (Algebra, Trigonometry, Calculus)
- Coordinate Geometry
- Vectors and Matrices
- Probability and Statistics
- Mechanics
- Numerical Methods
Download JAMB Further Mathematics Past Questions and Answers
You can practice JAMB Further Mathematics past questions online or download them in PDF format for offline study. Regular practice improves problem-solving skills and boosts confidence before the UTME.
No. Further Mathematics is optional but required for courses such as Engineering, Mathematics, Physics, and related science programs.
JAMB Further Mathematics consists of 40 objective questions in the UTME CBT exam.
Yes. JAMB often repeats Further Mathematics questions or tests similar concepts using different values.
Yes. ScholarJoiner provides JAMB Further Mathematics past questions for CBT practice and PDF download.
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