2015 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 2015 JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS 1 / 48 Category: Jamb Mathematics 2015 1. In a town of 6250 inhabitants, there were 62 births during 1984. Find the percentage birth rate a) 3% b) 1.00% c) 2.50% d) 5.40% To find the percentage birth rate, divide the number of births by total population and multiply by 100: $\frac{62}{6250} \times 100 = 0.992%$ (rounded to 1.0%) 2 / 48 Category: Jamb Mathematics 2015 2. Simplify $1\frac{1}{4} \div (2 \div \frac{1}{4} \text{ of } 28)$ a) $1\frac{3}{8}$ b) $2\frac{3}{4}$ c) $4\frac{3}{8}$ d) $3\frac{1}{5}$ Convert mixed numbers to improper fractions: $\frac{5}{4} \div (2 \div \frac{28}{4}) = \frac{5}{4} \div \frac{8}{28} = \frac{5}{4} \times \frac{28}{8} = \frac{35}{8} = 4\frac{3}{8}$ 3 / 48 Category: Jamb Mathematics 2015 3. Factorize $x^2 + 9x + 20$ a) $(x – 5)^2$ b) $(x + 5)(x + 4)$ c) $(x – 5)(x + 3)$ d) $(x + 3)^2$ Using factorization method: Find factors of 20 that sum to 9. 5 and 4 work: $(x + 5)(x + 4)$ 4 / 48 Category: Jamb Mathematics 2015 4. If three staff of Pdfmadeazy eBookstore agreed to share their salary arrears in the ratio of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is N120,000.00K, How much does the second staff received? a) N36,000 b) N44,000 c) N40,000 d) N15,000 Using ratio 18:20:22, total parts = 60. Second staff’s share = $\frac{20}{60} \times 120000 = 40000$ 5 / 48 Category: Jamb Mathematics 2015 5. X and Y are two sets such that $n(X) = 15$, $n(Y) = 12$ and $n{X \cap Y} = 7$. Find $n{X \cup Y}$ a) 21 b) 225 c) 15 d) 20 Using the formula: $n(X \cup Y) = n(X) + n(Y) – n(X \cap Y)$ = $15 + 12 – 7 = 20$ 6 / 48 Category: Jamb Mathematics 2015 6. Find the x and z intercepts of the graph of $3x – z \leq 9$ a) (3, -9) b) (-3, 9) c) (-3, -9) d) (-3, 0) For x-intercept, set z=0: $3x \leq 9$, $x \leq 3$. For z-intercept, set x=0: $-z \leq 9$, $z \geq -9$ 7 / 48 Category: Jamb Mathematics 2015 7. Simplify $\log_{10}1.5 + 3\log_{10}2 – \log_{10}0.3$ a) $\log_{10}4$ b) $\log_{10}40$ c) $\log_{10}-40$ d) $\log_{10}4-$ Using log properties: $\log_{10}(1.5) + \log_{10}(2^3) – \log_{10}(0.3) = \log_{10}(\frac{1.5 \times 8}{0.3}) = \log_{10}40$ 8 / 48 Category: Jamb Mathematics 2015 8. Find the total surface area of a cylinder of base radius 5cm and length 7cm ($\pi = 3.14$) a) $17.8\text{ cm}^2$ b) $15.8\text{ cm}^2$ c) $75.4\text{ cm}^2$ d) $54.7\text{ cm}^2$ Total surface area = $2\pi r^2 + 2\pi rh$ = $2(3.14)(5^2) + 2(3.14)(5)(7)$ = $377.0 \text{ cm}^2$ 9 / 48 Category: Jamb Mathematics 2015 9. If $x + y = 90$ simplify $(\sin x + \sin y)^2 – 2\sin x\sin y$ a) 1 b) 0 c) 2 d) -1 When $x + y = 90°$, $\sin y = \cos x$. Substituting: $(\sin x + \cos x)^2 – 2\sin x\cos x = 1$ 10 / 48 Category: Jamb Mathematics 2015 10. A man with an annual salary of N2000, has allowances of N600. If Income Tax is 5%. How much income tax expenses does he pay each year? a) 15 b) 50 c) 70 d) 25 Total taxable income = 2000 + 600 = 2600. Tax = $5% \text{ of } 2600 = \frac{5}{100} \times 2600 = 130$ 11 / 48 Category: Jamb Mathematics 2015 11. Solve the equation $3x^2 – 4x – 5 = 0$ a) x = 1.75 or -0.15 b) x = 2.12 or -0.79 c) x = 1.5 or -0.34 d) x = 2.35 or -1.23 Using quadratic formula: $x = \frac{4 \pm \sqrt{16 + 60}}{6} = \frac{4 \pm \sqrt{76}}{6}$ ≈ 1.75 or -0.15 12 / 48 Category: Jamb Mathematics 2015 12. The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms a) nth = 3 b) nth = 4 c) nth = 5 d) nth = 6 Using AP sum formula: $40 = \frac{n}{2}(6 + 10)$ = $\frac{n}{2}(16)$ = $8n$, Therefore n = 5 13 / 48 Category: Jamb Mathematics 2015 13. Find the equation of a line which is from origin and passes through the point (-3, -4) a) $y = \frac{3x}{4}$ b) $y = \frac{4x}{3}$ c) $y = \frac{2x}{3}$ d) $y = \frac{x}{2}$ Gradient = $\frac{y_2-y_1}{x_2-x_1}$ = $\frac{-4-0}{-3-0}$ = $\frac{4}{3}$. Therefore y = $\frac{4}{3}x$ 14 / 48 Category: Jamb Mathematics 2015 14. The amount A to which a principal P amounts at r% compound interest for n years is given by the formula $A = P(1 + (r \div 100))^n$. Find A, if P = 126, r = 4 and n = 2 a) N132.50K b) N136.30K c) N125.40K d) N257.42K $A = 126(1 + 0.04)^2$ = $126(1.04)^2$ = 126(1.0816) = 136.30 15 / 48 Category: Jamb Mathematics 2015 15. Make x the subject of the equation $s = 2 + \frac{t}{5}(x + \frac{3}{5}y)$ a) $x = 5[(s – 2) \div t] – \frac{3}{5}y$ b) $x = 25[(s – 2) \div t] – 3ty$ c) $x = [1 \div (s – 2)3ty]$ d) $x = [5(s – 2) 2 \div 3ty] \times t$ Multiply both sides by 5: $5s = 10 + t(x + \frac{3}{5}y)$. Solve for x: $x = 5[\frac{s-2}{t}] – \frac{3}{5}y$ 16 / 48 Category: Jamb Mathematics 2015 16. If $\log_520 = x$, find x a) 1.761 b) 1.354 c) 1.861 d) 2.549 Using change of base formula: $x = \frac{\ln 20}{\ln 5}$ ≈ 2.861 17 / 48 Category: Jamb Mathematics 2015 17. Find at which rate per annum simple interest N525 will amount to N588 in 3 years a) 3% b) 2% c) 5% d) 4% Using $I = \frac{PRT}{100}$, $63 = \frac{525 \times R \times 3}{100}$. Solving for R: $R = 4%$ 18 / 48 Category: Jamb Mathematics 2015 18. Given that A = {1, 5, 7}, B = {3, 9, 12, 15}, C = {2, 4, 6, 8}. Find $(A \cup B) \cup C$ a) {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15} b) {1, 2, 3, 5, 6, 8, 12, 15} c) {2, 4, 5, 9, 12, 15} d) {1, 5, 6, 7, 8, 9, 12, 15} Combine all unique elements from sets A, B, and C 19 / 48 Category: Jamb Mathematics 2015 19. The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newton’s is 2cm, find the extension produced by a tension of 12 newton’s a) 2 b) 1 c) 0 d) 3 Using direct proportion: $\frac{e_1}{t_1} = \frac{e_2}{t_2}$. Therefore, $\frac{2}{8} = \frac{x}{12}$. Solving: x = 3 20 / 48 Category: Jamb Mathematics 2015 20. Factorize $x^2 – 2x – 15$ a) $(x + 3)^2$ b) $(x + 5)(x – 3)$ c) $(x – 5)^2$ d) $(x – 5)(x + 3)$ Find factors of -15 that sum to -2: -5 and 3. Therefore: $(x – 5)(x + 3)$ 21 / 48 Category: Jamb Mathematics 2015 21. If A = (-3,5) and B = (4,-1) find the co-ordinate of the mid point a) 2, ½ b) ½, 2 c) 1, ½ d) 0, 2 Midpoint formula: $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ = $(\frac{-3 + 4}{2}, \frac{5 + (-1)}{2})$ = $(0.5, 2)$ 22 / 48 Category: Jamb Mathematics 2015 22. Find the simple interest on N325 in 5 years at 3% per annum a) N48.75K b) N50.10K c) N75.50K d) N15.75K Using SI = $\frac{P \times R \times T}{100}$ = $\frac{325 \times 3 \times 5}{100}$ = N48.75 23 / 48 Category: Jamb Mathematics 2015 23. Simplify $(0.09)^2$ and give your answer correct to 4 significant figures a) 0.81 b) 0.081 c) 0.0081 d) 8.0001 $(0.09)^2$ = 0.0081 24 / 48 Category: Jamb Mathematics 2015 24. Simplify $\frac{1}{x^2+3x+2} + \frac{1}{x^2+5x+6}$ a) $\frac{2x}{(x+1)(x-3)}$ b) $\frac{2}{(x+1)(x+2)}$ c) $\frac{2}{(x+1)(x+2)}$ d) $\frac{2}{(x+1)(x+3)}$ Using common denominator and factoring: $\frac{2}{(x+1)(x+2)}$ 25 / 48 Category: Jamb Mathematics 2015 25. One bag contains 3 blue and 5 red balls, another bag contains 2 blue and 4 red balls respectively. One ball is drawn for each bag. What is the probability both balls are blue a) $\frac{2}{15}$ b) $\frac{3}{24}$ c) $\frac{3}{21}$ d) $\frac{3}{28}$ P(both blue) = $\frac{3}{8} \times \frac{2}{6}$ = $\frac{3}{24}$ 26 / 48 Category: Jamb Mathematics 2015 26. Given that A = {3, 4, 1, 10, ⅓}, B = {4, 3, ⅓, ⅓, 7}. Find $A \cap B$ a) {} b) {⅓, 1, 2} c) {3, 4, ⅓} d) {1, 3, ⅓} Intersection contains elements present in both sets: {3, 4, ⅓} 27 / 48 Category: Jamb Mathematics 2015 27. Find x if $13^{2x} = 70_8$ a) 5 b) 3 c) 6 d) 1 Convert 70₈ to base 10 (56), then solve: $13^{2x} = 56$, therefore x = 3 28 / 48 Category: Jamb Mathematics 2015 28. A man sells his new brand car for N420,000 at a gain of 15%. What did it cost him? a) N410,000 b) N365,217 c) N157,250 d) N257,000 Cost = $\frac{Selling Price}{1 + \frac{Profit%}{100}}$ = $\frac{420000}{1.15}$ = N365,217 29 / 48 Category: Jamb Mathematics 2015 29. Find the value of x if $\frac{1}{64^{(x+2)}} = \frac{4^{(x-3)}}{16^x}$ a) $\frac{3}{2}$ b) $\frac{2}{3}$ c) $\frac{1}{3}$ d) $-\frac{3}{2}$ Convert to same base and equate powers: $-\frac{x+2}{3} = x-3-2x$ Solve to get $x = \frac{3}{2}$ 30 / 48 Category: Jamb Mathematics 2015 30. Solve $x^2 – 2x – 3 = 0$ a) x = 2 or 1 b) x = 3 or -1 c) x = 1 or 0 d) x = 1 or 2 Using quadratic formula: $x = \frac{2 \pm \sqrt{4+12}}{2}$ = $1 \pm 2$ = 3 or -1 31 / 48 Category: Jamb Mathematics 2015 31. The volume of a cylinder whose height is 4cm and whose radius 5cm is equal to ($\pi = 3.14$) a) 3.13cm² b) 145cm² c) 314cm² d) 214cm² Volume = $\pi r^2h$ = $3.14 \times 5^2 \times 4$ = 314cm³ 32 / 48 Category: Jamb Mathematics 2015 32. The probability of an event A is $\frac{1}{5}$. The probability of B is $\frac{1}{3}$. The probability both A and B is $\frac{1}{15}$. What is the probability of either event A or B or both a) $\frac{2}{15}$ b) $\frac{3}{4}$ c) $\frac{9}{15}$ d) $\frac{1}{15}$ P(A∪B) = P(A) + P(B) – P(A∩B) = $\frac{1}{5} + \frac{1}{3} – \frac{1}{15}$ = $\frac{9}{15}$ 33 / 48 Category: Jamb Mathematics 2015 33. If $(159.75)_{10} = (x)_6$. Find x a) x₆ = 123.346 b) x₆ = 424.56 c) x₆ = 122.436 d) x₆ = 124.456 Convert 159.75 to base 6: 424.56₆ 34 / 48 Category: Jamb Mathematics 2015 34. A man bought a car for N800 and sold it for N520. Find his loss percent a) 15% b) 25% c) 35% d) 10% Loss% = $\frac{Loss}{CP} \times 100$ = $\frac{280}{800} \times 100$ = 35% 35 / 48 Category: Jamb Mathematics 2015 35. Simplify $6\frac{1}{12} – 2\frac{3}{4} + 1\frac{1}{2}$ a) $3\frac{5}{6}$ b) $4\frac{5}{6}$ c) $2\frac{1}{6}$ d) $1\frac{3}{1}$ Convert to improper fractions and subtract: $\frac{73}{12} – \frac{11}{4} + \frac{3}{2}$ = $4\frac{5}{6}$ 36 / 48 Category: Jamb Mathematics 2015 36. Find the distance between the points (-2,-3) and (-2,4) a) 3m b) 2.4m c) 3.2m d) 7.0m Distance = $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ = $\sqrt{0 + 7^2}$ = 7.0m 37 / 48 Category: Jamb Mathematics 2015 37. Determine the third term of a geometrical progression whose first and second term are 2 and 54 respectively a) 1458 b) 1485 c) 1345 d) 1258 Common ratio = $\frac{54}{2}$ = 27. Third term = 54 × 27 = 1458 38 / 48 Category: Jamb Mathematics 2015 38. Given that S and T are sets of real numbers such that S = {x : 0 ≤ x ≤ 5} and T = {x : -2 < x < 3} Find S ∪ T a) -3 < x ≤ 3 b) -2 < x ≤ 5 c) 2 < x ≥ -5 d) -1 < x ≥ ≤ 2 Union includes all elements from -2 to 5: -2 < x ≤ 5 39 / 48 Category: Jamb Mathematics 2015 39. If an investor invest N450,000 in a certain organization in order to yield X as a return of N25,000. Find the return on an investment of N700,000 by Y in the same organization a) N14,950.50K b) N25,150.30K c) N15,000.00K d) N38,888.90K Using direct proportion: $\frac{25000}{450000} = \frac{x}{700000}$. x = N38,888.90 40 / 48 Category: Jamb Mathematics 2015 40. Evaluate $\log_717$ a) 1.35 b) 1.353 c) 1.455 d) 0.455 Using change of base formula: $\frac{\ln 17}{\ln 7}$ = 1.353 41 / 48 Category: Jamb Mathematics 2015 41. $10011_2 + *****_2 + 11100_2 + 101_2 = 1001111_2$ a) 1111₂ b) 11011₂ c) 10111₂ d) 11001₂ Convert to decimal, subtract known values, convert back to binary: Missing number is 11011₂ 42 / 48 Category: Jamb Mathematics 2015 42. Evaluate $\log_5(\frac{y^2x^5}{125b^{\frac{1}{2}}})$ a) 2log₅y + 5log₅y² – 3 b) log₅y² + 5log₅x + 3 c) 25logy 5 + 3 d) 2log₅y + 5log₅x – ½log₅b – 3 Using log properties: $2\log_5y + 5\log_5x – \frac{1}{2}\log_5b – 3$ 43 / 48 Category: Jamb Mathematics 2015 43. Integral $\int(5x^3 + 7x^2 – 2x + 5)dx$ a) $\frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C$ b) $\frac{5x^4}{4} + \frac{7x^3}{3} – x^2 + 5x + C$ c) $\frac{5x^3}{3} + \frac{7x^2}{x} – x + C$ d) $\frac{2x^2}{3} + \frac{x}{5} – C$ Integrate term by term: $\frac{5x^4}{4} + \frac{7x^3}{3} – x^2 + 5x + C$ 44 / 48 Category: Jamb Mathematics 2015 44. Find the area of the curved surface of a cone whose base radius is 3cm and whose height is 4cm (π = 3.14) a) 17.1cm² b) 27.2cm² c) 47.1cm² d) 37.3cm² Area = $\pi r\sqrt{r^2 + h^2}$ = $3.14 \times 3 \times \sqrt{9 + 16}$ = 37.3cm² 45 / 48 Category: Jamb Mathematics 2015 45. Simplify $\frac{1}{(x+1)} + \frac{1}{(x-1)}$ a) 2x/(x + 1)(x-3) b) 2x/(x + 1)(x-1) c) 2x/(x + 1)² d) 2x(x+1)² Using common denominator: $\frac{2x}{(x+1)(x-1)}$ 46 / 48 Category: Jamb Mathematics 2015 46. The area of a circle of radius 4cm is equal to (Take π = 3.142) a) 10.3cm² b) 15.7cm² c) 50.3cm² d) 17.4cm² Area = $\pi r^2$ = $3.142 \times 16$ = 50.3cm² 47 / 48 Category: Jamb Mathematics 2015 47. The area of an ellipse is 132cm². The length of its major axis is 14cm. Find the length of its minor axis a) 10.5cm b) 5cm c) 10cm d) 3cm Area = $\pi ab$, where a=7, Area=132. Solve for b: $b = \frac{132}{22}$ = 6. Minor axis = 12cm 48 / 48 Category: Jamb Mathematics 2015 48. The volume of a cone (s) of height 6cm and base radius 5cm is a) 157cm³ b) 155cm³ c) 175cm³ d) 145cm³ Volume = $\frac{1}{3}\pi r^2h$ = $\frac{1}{3} \times 3.14 \times 25 \times 6$ = 157cm³ Your score is The average score is 0% LinkedIn Facebook Twitter VKontakte 0% Restart quiz Anonymous feedback Send feedback
