2016 JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS Leave a Comment / Jamb Mathematics / By Jamb Tutor Report a question What’s wrong with this question? You cannot submit an empty report. Please add some details. 0% 0 votes, 0 avg Created by Jamb TutorJAMB Mathematics 2016 JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS 1 / 50 Category: Jamb Mathematics 2016 1. Integrate $\frac{2x^3+2x}{x}$ with respect to x a) $\frac{2x^3}{3}-2x+k$ b) $x^3+2x+k$ c) $\frac{2x^3}{3}+2x+k$ d) $x^3-2x+k$ The question requires simplifying first: $\frac{2x^3+2x}{x} = 2x^2+2$. Then integrate: $\int(2x^2+2)dx = \frac{2x^3}{3}+2x+k$. Option A has the correct form with the constant of integration. 2 / 50 Category: Jamb Mathematics 2016 2. If the mean of 4, y, 8 and 10 is 7. Find Y? a) 6 b) 10 c) 7 d) 9 Using the mean formula: $(4+y+8+10)/4=7$. Multiply both sides by 4: $4+y+8+10=28$. Solve for y: $y=28-22=6$. 3 / 50 Category: Jamb Mathematics 2016 3. Find the derivative of $y=({\frac{1}{3}x+6})^2$ a) $2({\frac{1}{3}x+6})$ b) $\frac{2}{3}({\frac{1}{3}x+6})$ c) $\frac{2}{3}({\frac{1}{3}x+6})^2$ d) $\frac{1}{3}({\frac{1}{3}x+6})^2$ Using chain rule: $\frac{dy}{dx}=2({\frac{1}{3}x+6})\cdot\frac{1}{3}=\frac{2}{3}({\frac{1}{3}x+6})$ 4 / 50 Category: Jamb Mathematics 2016 4. In a school of 150 students, 80 offer French while 60 offer Arabic and 20 offer neither. How many students offer both subjects? a) 45 b) 10 c) 35 d) 30 Let x be students taking both subjects. Using set theory: $80+60-x+20=150$. Solve for x: $140-x=130$, therefore $x=10$. 5 / 50 Category: Jamb Mathematics 2016 5. If the 2nd term of a G.P is $\frac{8}{9}$ and the 6th term is $4\frac{1}{2}$. Find the common ratio. a) $\frac{2}{3}$ b) 3 c) 2 d) $\frac{3}{2}$ Using GP formula: $\frac{t_6}{t_2}=r^4$. Substitute: $\frac{4.5}{8/9}=r^4$. Solve: $r=\frac{3}{2}$ 6 / 50 Category: Jamb Mathematics 2016 6. Find the value of ∠OTQ a) $230°$ b) $55°$ c) $115°$ d) $65°$ Based on the diagram, using angle properties: angle at center is twice angle at circumference. Given inscribed angle, calculate center angle: $115°$ 7 / 50 Category: Jamb Mathematics 2016 7. The sum of the interior angles of a polygon is given as $1080°$. Find the number of the sides of the polygon. a) 5 b) 7 c) 6 d) 8 Using formula: $(n-2)\times180°=1080°$. Solve for n: $n-2=6$, therefore $n=8$ 8 / 50 Category: Jamb Mathematics 2016 8. Find the value of ∠PMT a) $82°$ b) $36°$ c) $72°$ d) $118°$ Using parallel line properties and corresponding angles: Angle PMT = $72°$ 9 / 50 Category: Jamb Mathematics 2016 9. Find the value of ∠ROP a) $110°$ b) $70°$ c) $95°$ d) $85°$ Using properties of circles and inscribed angles: ∠ROP = $70°$ 10 / 50 Category: Jamb Mathematics 2016 10. How many students play only two games? a) 15 b) 16 c) 20 d) 18 From the Venn diagram, sum regions where two sports overlap: $5+6+7=18$ 11 / 50 Category: Jamb Mathematics 2016 11. If line p = 5x + 3 is parallel to line p = wx + 5. Find the value of w. a) 7 b) 3 c) 6 d) 5 For parallel lines, coefficients must be equal: $5=w$ 12 / 50 Category: Jamb Mathematics 2016 12. Evaluate $\int(cos4x + sin3x)dx$ a) $sin4x – cos3x + k$ b) $sin4x + cos3x + k$ c) $\frac{1}{4}sin4x – \frac{1}{3}cos3x + k$ d) $\frac{1}{4}sin4x + \frac{1}{3}cos3x + k$ Using standard integration rules: $\int cos4x dx=\frac{1}{4}sin4x$ and $\int sin3x dx=-\frac{1}{3}cos3x$ 13 / 50 Category: Jamb Mathematics 2016 13. If $x^{10}=2^{35}$. Find x a) 15 b) 12 c) 14 d) 13 Taking $log_2$ of both sides: $10log_2x=35$. Therefore $x=2^{3.5}=14$ 14 / 50 Category: Jamb Mathematics 2016 14. What is the size of the angle of the sector in economics? a) $24°$ b) $39°$ c) $32°$ d) $36°$ Using proportion: $\frac{10}{100}\times360°=36°$ 15 / 50 Category: Jamb Mathematics 2016 15. Calculate the range of 20, -6, 25, 30, 21, 28, 32, 33, 34, 5, 3, 2, and 1. a) 32 b) 36 c) 33 d) 40 Range = Highest value – Lowest value = $34-(-6)=40$ 16 / 50 Category: Jamb Mathematics 2016 16. How many visitors were received on Friday, Tuesday and Sunday? a) 17 b) 22 c) 20 d) 16 Sum the values for specified days: $8+7+7=22$ 17 / 50 Category: Jamb Mathematics 2016 17. Factorize $k^2-2kp+p^2$ a) $(k+p)^2$ b) $(k-p)^2$ c) $k^2+p^2$ d) $k^2-p^2$ This is a perfect square trinomial: $(k-p)^2$ 18 / 50 Category: Jamb Mathematics 2016 18. Calculate the perimeter of a sector of a circle of radius 12cm and angle $60°$ a) $(12+4\pi)$ cm b) $(24+4\pi)$ cm c) $(12+6\pi)$ cm d) $(24+6\pi)$ cm Perimeter = 2r + rθ = $24+12\cdot\frac{\pi}{3}=(24+4\pi)$ cm 19 / 50 Category: Jamb Mathematics 2016 19. Find the value of y when total mark is 48 a) 6 b) 8 c) 7 d) 5 Using equation: $2(4)+3(4)+4(y)=48$. Solve: $8+12+4y=48$, therefore $y=7$ 20 / 50 Category: Jamb Mathematics 2016 20. Find the complement of P a) {1,3,5,7,9,11,13,15} b) {2,3,5,7,9,11,13} c) {1,3,5,7,9,11,13} d) {2,3,5,7,11,15} Complement of P = elements in U not in P = odd numbers less than 15 21 / 50 Category: Jamb Mathematics 2016 21. Simplify $\frac{0.026\times0.36}{0.69}$ in standard form a) $1.36\times10^{-4}$ b) $1.36\times10^{-3}$ c) $1.36\times10^{-1}$ d) $1.36\times10^{-2}$ Convert to standard form: $\frac{2.6\times10^{-2}\times3.6\times10^{-1}}{6.9\times10^{-1}}=1.36\times10^{-2}$ 22 / 50 Category: Jamb Mathematics 2016 22. If Bisi got 5 pencils in ratio 2:3:5, how many were shared? a) 15 b) 25 c) 30 d) 50 If 2 parts = 5 pencils, then 1 part = 2.5 pencils. Total parts = 10, so total = 25 pencils 23 / 50 Category: Jamb Mathematics 2016 23. Calculate perimeter of sector, radius 9cm, angle $36°$ a) 18 cm b) $(18+\frac{9\pi}{5})$ cm c) $(9+\frac{9\pi}{5})$ cm d) $\frac{9\pi}{5}$ cm Perimeter = 2r + rθ = $18+9\cdot\frac{\pi}{5}=(18+\frac{9\pi}{5})$ cm 24 / 50 Category: Jamb Mathematics 2016 24. Evaluate $\frac{27^{\frac{1}{3}}-8^{\frac{2}{3}}}{16^{\frac{2}{4}}}\times2$ a) $\frac{23}{5}$ b) $-\frac{23}{5}$ c) $-\frac{1}{8}$ d) $\frac{21}{7}$ Simplify: $\frac{3-4}{2}\times2=-\frac{1}{2}\times2=-1$ 25 / 50 Category: Jamb Mathematics 2016 25. Find the median of the frequency distribution a) 3 b) 5 c) 4 d) 6 Order values and find middle: 3,3,5,5,5,5,2,2,2,2,2,2,6,6,6. Median = 5 26 / 50 Category: Jamb Mathematics 2016 26. Find $\frac{dy}{dx}$, if $y=\frac{2}{3}x^3-\frac{4}{x}$ a) $3x^2-\frac{4}{x}$ b) $2x^2+\frac{4}{x^2}$ c) $3x^2+\frac{4}{x^2}$ d) $2x^2-\frac{4}{x}$ Using power rule and chain rule: $\frac{dy}{dx}=2x^2+\frac{4}{x^2}$ 27 / 50 Category: Jamb Mathematics 2016 27. Evaluate $\frac{0.8\times0.43\times0.031}{0.05\times0.72\times0.021}$ to 4 s.f. a) 14.09 b) 14.1 c) 14.12 d) 14.11 Multiply numerator and denominator separately, then divide: 14.11 28 / 50 Category: Jamb Mathematics 2016 28. Calculate arc length for radius 12cm and angle $30°$ a) $6\pi$ cm b) $2\pi$ cm c) $3\pi$ cm d) $9\pi$ cm Arc length = $r\theta$ = $12\times\frac{\pi}{6}=2\pi$ cm 29 / 50 Category: Jamb Mathematics 2016 29. Evaluate $\int_{0}^{\frac{\pi}{2}}\sin x dx$ a) 2 b) -1 c) 1 d) -2 $[-\cos x]_{0}^{\frac{\pi}{2}}=(-0)-(-1)=1$ 30 / 50 Category: Jamb Mathematics 2016 30. Find radius if arc length $16\pi$ cm subtends $80°$ a) 24 cm b) 28 cm c) 36 cm d) 32 cm Using $L=r\theta$: $16\pi=r\cdot\frac{80\pi}{180}$, solve for r: $r=36$ 31 / 50 Category: Jamb Mathematics 2016 31. Find mean of $2-t,4+t,3-2t,2+t,t-1$ a) 2 b) t c) -t d) -2 Sum terms and divide by 5: $\frac{(10-t)}{5}=2$ 32 / 50 Category: Jamb Mathematics 2016 32. Evaluate $\frac{12.02\times20.06}{26.04\times60.06}$ to 3 s.f. a) 0.157 b) 0.154 c) 0.155 d) 0.158 Multiply numerator and denominator separately, then divide: 0.154 33 / 50 Category: Jamb Mathematics 2016 33. Find $\frac{dy}{dx}$ if $y=2x^3+6x^2+6x+1$ a) $6x^2+12x+1$ b) $6x^2+6x+1$ c) $6x^2+6x+6$ d) $6x^2+12x+6$ Using power rule: $\frac{dy}{dx}=6x^2+12x+6$ 34 / 50 Category: Jamb Mathematics 2016 34. Find nth term of sequence 3,9,27,81,… a) $3\times3^{n-2}$ b) $3\times3^{n-1}$ c) $3\times3^{n+2}$ d) $3\times3^{n+1}$ Each term is multiplied by 3, so formula is $3\times3^{n-1}$ 35 / 50 Category: Jamb Mathematics 2016 35. Simplify $1-(\frac{1}{7}\times3\frac{1}{2})\div\frac{3}{4}$ a) 2 b) $\frac{1}{3}$ c) 1 d) $\frac{2}{3}$ Convert mixed number, multiply fractions: $1-\frac{1}{7}\times\frac{7}{2}\times\frac{4}{3}=\frac{2}{3}$ 36 / 50 Category: Jamb Mathematics 2016 36. If 120km needs 45L petrol, how much for 600km? a) 720 L b) 160 L c) 225 L d) 960 L Using direct proportion: $\frac{600}{120}=\frac{x}{45}$, solve for x: $x=225$ 37 / 50 Category: Jamb Mathematics 2016 37. Find $\frac{dy}{dx}$ if $y=3x^3+2x^2+3x+1$ a) $9x^2+4x+3$ b) $9x^2-4x-3$ c) $9x^2+4x-3$ d) $9x^2-4x+3$ Using power rule: $\frac{dy}{dx}=9x^2+4x+3$ 38 / 50 Category: Jamb Mathematics 2016 38. Evaluate $\int(\sin x-5x^2)dx$ a) $-\cos x-10x+k$ b) $\cos x-\frac{5x^3}{3}+k$ c) $-\cos x-\frac{5x^3}{3}+k$ d) $\cos x-10x+k$ Integrate term by term: $-\cos x-\frac{5x^3}{3}+k$ 39 / 50 Category: Jamb Mathematics 2016 39. Find P when $N=\frac{P}{2}(\frac{T_1-T_2}{T_1})$, N=12, $T_1$=27, $T_2$=24 a) 48 b) 108 c) 54 d) 216 Substitute values and solve: $12=\frac{P}{2}(\frac{27-24}{27})$, $P=216$ 40 / 50 Category: Jamb Mathematics 2016 40. Solve system: 3x-5y=9, 6x-4y=12 a) $(\frac{3}{4},1)$ b) $(\frac{4}{3},1)$ c) $(\frac{3}{4},-1)$ d) $(\frac{4}{3},-1)$ Using elimination method: $x=\frac{4}{3}, y=-1$ 41 / 50 Category: Jamb Mathematics 2016 41. Find Q∩T where Q=factors of 18, T=primes between 2 and 18 a) (2,3) b) (2,3,18) c) (2,3,9) d) (2,3,6) Q={1,2,3,6,9,18}, T={2,3,5,7,11,13,17}. Intersection={2,3} 42 / 50 Category: Jamb Mathematics 2016 42. Find ∠TSV in cyclic quadrilateral a) $60°$ b) $80°$ c) $70°$ d) $50°$ Using cyclic quadrilateral properties: ∠TSV = $70°$ 43 / 50 Category: Jamb Mathematics 2016 43. Find mean of 10,8,5,11,12,9,6,3,15,23 a) 11.2 b) 10 c) 10.2 d) 11.3 Sum all numbers and divide by 10: $\frac{102}{10}=10.2$ 44 / 50 Category: Jamb Mathematics 2016 44. Find ∠PRO in cyclic quadrilateral a) $70°$ b) $20°$ c) $50°$ d) $30°$ Using cyclic quadrilateral properties: ∠PRO = $50°$ 45 / 50 Category: Jamb Mathematics 2016 45. OGIVE is constructed using… a) Third quartile range b) Semi-quartile range c) Cumulative frequency table d) Inter-quartile table OGIVE is a cumulative frequency curve plotted using cumulative frequency table 46 / 50 Category: Jamb Mathematics 2016 46. Rationalize $\frac{6\sqrt{}-4\sqrt{}}{6\sqrt{}+4\sqrt{}}$ a) $5+2\sqrt{6}$ b) $5-4\sqrt{6}$ c) $5+4\sqrt{6}$ d) $5-2\sqrt{6}$ Multiply numerator and denominator by conjugate: $5+2\sqrt{6}$ 47 / 50 Category: Jamb Mathematics 2016 47. How many students took the mathematics test? a) 40 b) 30 c) 10 d) 20 Sum all frequencies in bar chart: 30 48 / 50 Category: Jamb Mathematics 2016 48. Determine mean score of students a) 4.5 b) 4.3 c) 4.2 d) 4.6 Calculate weighted mean using frequencies: 4.3 49 / 50 Category: Jamb Mathematics 2016 49. Find fraction of shaded portion a) $frac{1}{3}$ b) $frac{1}{5}$ c) $frac{1}{4}$ d) $frac{1}{6}$ Count shaded squares relative to total: $\frac{1}{4}$ 50 / 50 Category: Jamb Mathematics 2016 50. Find required region of x from graph a) x≤−1, x≥4 b) x≤4 c) −1≤x≤4 d) x≤−1, 0≤x≤4 From graph, x satisfies: $-1\leq x\leq4$ Your score is The average score is 0% LinkedIn Facebook Twitter VKontakte 0% Restart quiz Anonymous feedback Send feedback
