2017 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 2017 JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS 1 / 45 Category: Jamb Mathematics 2017 1. Given T = { even numbers from 1 to 12 } N = {common factors of 6, 8 and 12} Find $T \cap N$ a) ${2, 3}$ b) ${2, 3, 4}$ c) ${3, 4, 6}$ d) ${2}$ T = {2,4,6,8,10,12} and N = {2,4} are the common factors of 6,8,12. The intersection of these sets gives us {2,4}, leaving only {2} as the correct answer. The other options include numbers that are not in both sets. 2 / 45 Category: Jamb Mathematics 2017 2. What is the next number in the series 2, 1, $\frac{1}{2}$, $\frac{1}{4}$… a) $\frac{1}{3}$ b) $\frac{2}{8}$ c) $\frac{3}{7}$ d) $\frac{1}{8}$ This is a geometric sequence with common ratio $\frac{1}{2}$. To find the next term, multiply the last term $\frac{1}{4}$ by $\frac{1}{2}$, giving $\frac{1}{8}$. 3 / 45 Category: Jamb Mathematics 2017 3. If U = {x : x is an integer and $1 \leq x \leq 20$ } $E_1$ = {x: x is a multiple of 3} $E_2$ = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in $E_2$ a) $\frac{3}{4}$ b) $\frac{3}{10}$ c) $\frac{1}{4}$ d) $\frac{1}{20}$ In U={1,2,…,20}, $E_2$ has 5 numbers (4,8,12,16,20). Therefore, numbers not in $E_2$ are 15. Probability = $\frac{15}{20} = \frac{3}{4}$ 4 / 45 Category: Jamb Mathematics 2017 4. The curved surface area of a cylinder 5cm high is 110cm². Find the radius of its base $\pi = \frac{22}{7}$ a) 2.6cm b) 3.5cm c) 3.6cm d) 7.0cm Curved surface area = $2\pi rh$. Given h=5cm and area=110cm², substitute to get $110 = 2\pi r(5)$. Solving gives r=3.5cm. 5 / 45 Category: Jamb Mathematics 2017 5. If two graphs Y = $px^2 + q$ and y = $2x^2 − 1$ intersect at x =2, find the value of p in terms of q a) $q – \frac{8}{7}$ b) $7 – \frac{q}{4}$ c) $8 – \frac{q}{2}$ d) $7 + \frac{q}{8}$ At intersection point, equations are equal. Substitute x=2: $4p + q = 8 – 1$. Therefore $p = \frac{7-q}{4}$ 6 / 45 Category: Jamb Mathematics 2017 6. Evaluate $(sin45º + sin30º)$ in surd form a) $\frac{\sqrt{2}}{2\sqrt{3}}$ b) $\sqrt{3} – \frac{1}{2}$ c) $\frac{1}{2}\sqrt{2}$ d) $\frac{1+\sqrt{2}}{2}$ $sin45° = \frac{1}{\sqrt{2}}$ and $sin30° = \frac{1}{2}$. Adding these gives $\frac{1}{\sqrt{2}} + \frac{1}{2}$ = $\frac{\sqrt{2}+1}{2}$ 7 / 45 Category: Jamb Mathematics 2017 7. If y = x Sin x, find $\frac{dy}{dx}$ when x = $\frac{\pi}{2}$ a) 1 b) $\frac{\pi}{2}$ c) $-\frac{\pi}{2}$ d) -1 Using product rule: $\frac{dy}{dx} = sinx + xcosx$. At $x=\frac{\pi}{2}$, $sin\frac{\pi}{2}=1$ and $cos\frac{\pi}{2}=0$, giving 1. 8 / 45 Category: Jamb Mathematics 2017 8. If temperature t is directly proportional to heat h, and when t = 20°C, h = 50 J, find t when h = 60J a) 24°C b) 20°C c) 34°C d) 30°C Using direct proportion, $\frac{t_1}{h_1} = \frac{t_2}{h_2}$. Therefore $\frac{20}{50} = \frac{t}{60}$. Solving gives t = 24°C 9 / 45 Category: Jamb Mathematics 2017 9. Evaluate $1 – (\frac{1}{5} \times \frac{2}{3}) + (5 + \frac{2}{3})$ a) 4 b) 3 c) $2\frac{2}{3}$ d) $\frac{98}{15}$ Calculate $\frac{1}{5} \times \frac{2}{3} = \frac{2}{15}$, then subtract from 1 and add $5\frac{2}{3}$ = $\frac{17}{3}$ = $\frac{98}{15}$ 10 / 45 Category: Jamb Mathematics 2017 10. Given m = $\sqrt{\frac{N}{SL}}$ make T the subject of the formula a) $\frac{NSL}{M}$ b) $\frac{N^2SL}{M^2}$ c) $\frac{N^2SL}{M}$ d) $\frac{NSL}{M^2}$ Square both sides: $m^2 = \frac{N}{SL}$. Cross multiply: $m^2SL = N$. Therefore $L = \frac{N}{m^2S}$ 11 / 45 Category: Jamb Mathematics 2017 11. Simplify $3^{n-1} \times \frac{27^{n+1}}{81^n}$ a) $3^{2n}$ b) 9 c) $3^n$ d) $3^{n+1}$ Convert all to base 3: $3^{n-1} \times \frac{(3^3)^{n+1}}{(3^4)^n}$ = $3^{n-1} \times \frac{3^{3n+3}}{3^{4n}}$ = $3^{n+1}$ 12 / 45 Category: Jamb Mathematics 2017 12. The locus of a point which is equidistant from the line PQ forms a a) circle centre P b) pair of parallel lines each opposite to PQ c) circle centre Q d) perpendicular line to PQ Points equidistant from a line form two parallel lines on either side of the original line, each at the same distance from PQ. 13 / 45 Category: Jamb Mathematics 2017 13. Given the quadrilateral RSTO inscribed in the circle with O as centre and radius 10cm. If ∠RST = 60°, find angle x a) 100° b) 140° c) 120° d) 10° In a circle, angle at center (x) is twice angle at circumference (60°). Therefore x = 120° 14 / 45 Category: Jamb Mathematics 2017 14. Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 7, 10, 6, 5 a) 16 b) 14 c) 12 d) 10 Range = 10-4 = 6, Mode = 10. Sum = 6 + 10 = 16 15 / 45 Category: Jamb Mathematics 2017 15. Find the sum to infinity of the series $\frac{1}{4}, \frac{1}{8}, \frac{1}{16},…$ a) $\frac{1}{2}$ b) $\frac{3}{5}$ c) $-\frac{1}{5}$ d) $\frac{73}{12}$ This is a geometric series with $a=\frac{1}{4}$ and $r=\frac{1}{2}$. Sum to infinity = $\frac{a}{1-r}$ = $\frac{1/4}{1-1/2}$ = $\frac{1}{2}$ 16 / 45 Category: Jamb Mathematics 2017 16. The base in which the operation was performed was a) 6 b) 2 c) 4 d) 5 Based on the digits shown and patterns, the operations were performed in base 4 17 / 45 Category: Jamb Mathematics 2017 17. The value of x + x(x^x) when x = 2 is a) 16 b) 10 c) 18 d) 24 When x=2: 2 + 2(2^2) = 2 + 2(4) = 2 + 8 = 10 18 / 45 Category: Jamb Mathematics 2017 18. In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon a) 8 b) 6 c) 4 d) 3 Interior angle + exterior angle = 180°. If interior = 2(exterior), then $3x = 180$, where x is exterior angle. $x = 60$, giving 6 sides 19 / 45 Category: Jamb Mathematics 2017 19. A cylindrical tank has a capacity of 3080m³. What is the depth of the tank if the diameter of its base is 14m? Take pi = 22/7 a) 23m b) 25m c) 20m d) 22m Volume = $\pi r^2h$. Substituting r=7 and V=3080: $3080 = \frac{22}{7} \times 49 \times h$. Solving gives h=20m 20 / 45 Category: Jamb Mathematics 2017 20. Simplify $4\sqrt{27} + 5\sqrt{12} – 3\sqrt{75}$ a) 7 b) -7 c) $-7\sqrt{3}$ d) $7\sqrt{3}$ Convert to simplest form: $4\sqrt{27} = 12\sqrt{3}$, $5\sqrt{12} = 10\sqrt{3}$, $3\sqrt{75} = 15\sqrt{3}$. Sum = $7\sqrt{3}$ 21 / 45 Category: Jamb Mathematics 2017 21. A man covered a distance of 50 miles on his first trip, on a later trip he traveled 300 miles while going 3 times as fast. His new time compared with the old distance was? a) three times as much b) the same c) twice as much d) half as much Time = distance/speed. New time = 300/(3v) = 100/v, where v is original speed. Original time = 50/v. Ratio = 2:1 22 / 45 Category: Jamb Mathematics 2017 22. In the figure, find x a) 40° b) 55° c) 50° d) 60° In a circle, angle in semicircle = 90°. Angle in same segment = 50°, therefore x = 50° 23 / 45 Category: Jamb Mathematics 2017 23. Divide $4x^3 – 3x + 1$ by $2x – 1$ a) $2x^2 -x + 1$ b) $2x^2 – x -1$ c) $2x^2 + x + 1$ d) $2x^2 + x -1$ Using polynomial long division, we get $2x^2 + x + 1$ as quotient 24 / 45 Category: Jamb Mathematics 2017 24. A car dealer bought a second-hand car for ₦250,000 and spent ₦70,000 refurbishing it. He then sold the car for ₦400,000. What is the percentage gain? a) 60% b) 32% c) 25% d) 20% Total cost = 320,000. Profit = 80,000. Percentage gain = $\frac{80,000}{320,000} \times 100$ = 25% 25 / 45 Category: Jamb Mathematics 2017 25. Find the number of ways that the letters of the word EXCELLENCE be arranged a) $\frac{10!}{2!2!2!}$ b) $\frac{10!}{4!2!}$ c) $\frac{10!}{4!2!2!}$ d) $\frac{10!}{2!2!}$ Letters: E(3), C(2), L(2), N, X. Total arrangements = $\frac{10!}{3!2!2!}$ 26 / 45 Category: Jamb Mathematics 2017 26. Evaluate $\frac{0.00000231}{0.007}$ and leave the answer in standard form a) $3.3 \times 10^{-4}$ b) $3.3 \times 10^{-3}$ c) $3.3 \times 10^{-5}$ d) $3.3 \times 10^{-8}$ Convert to $\frac{2.31 \times 10^{-6}}{7 \times 10^{-3}}$ = $3.3 \times 10^{-4}$ 27 / 45 Category: Jamb Mathematics 2017 27. If a rod 10cm in length was measured as 10.5cm, calculate the percentage error a) 5% b) 10% c) 8% d) 7% Percentage error = $\frac{\text{error}}{\text{actual value}} \times 100$ = $\frac{0.5}{10} \times 100$ = 5% 28 / 45 Category: Jamb Mathematics 2017 28. Find the principal which amounts to ₦5,500 at a simple interest in 5 years at 2% per annum a) ₦4,900 b) ₦5,000 c) ₦4,700 d) ₦4,000 Using $A = P(1 + rt)$, where A=5500, r=0.02, t=5. Therefore 5500 = P(1 + 0.02 × 5). Solving gives P = ₦5,000 29 / 45 Category: Jamb Mathematics 2017 29. The pie chart shows the allocation of money to each sector in a farm. The total amount allocated to the farm is ₦80,000. Find the amount allocated to fertilizer a) ₦35,000 b) ₦40,000 c) ₦25,000 d) ₦20,000 In the pie chart, fertilizer sector is $\frac{1}{4}$ of the total. Therefore amount = $\frac{1}{4} \times 80,000$ = ₦20,000 30 / 45 Category: Jamb Mathematics 2017 30. In how many ways can the word MATHEMATICS be arranged? a) $\frac{11!}{9!2!}$ b) $\frac{11!}{9!2!2!}$ c) $\frac{11!}{2!2!2!}$ d) $\frac{11!}{2!2!}$ Word has 11 letters: M,A,T,H,E,M,A,T,I,C,S. Repetitions: A(2),T(2),M(2). Formula: $\frac{11!}{2!2!2!}$ 31 / 45 Category: Jamb Mathematics 2017 31. In how many ways can the word MACICITA be arranged? a) $\frac{8!}{2!}$ b) $\frac{8!}{3!2!}$ c) $\frac{8!}{2!2!2!}$ d) 8! Word has 8 letters: M,A,C,I,C,I,T,A. Repetitions: C(2),I(2),A(2). Formula: $\frac{8!}{2!2!2!}$ 32 / 45 Category: Jamb Mathematics 2017 32. y is inversely proportional to x and y is 6 when x = 7. Find the constant of the variation a) 47 b) 42 c) 54 d) 46 If $y \propto \frac{1}{x}$, then $y = \frac{k}{x}$. When y=6 and x=7: 6 = $\frac{k}{7}$. Therefore k = 42 33 / 45 Category: Jamb Mathematics 2017 33. Find the equation of the locus of a point p(x, y) such that pv = pw, where v= (1, 1) and w = (3, 5) a) 2x + 2y = 9 b) 2x + 3y = 8 c) 2x + y = 9 d) x + 2y = 8 Points equidistant from two fixed points form a perpendicular bisector. Using distance formula and simplifying gives 2x + 4y = 18 34 / 45 Category: Jamb Mathematics 2017 34. Find $\int(x^2 + 3x – 5)dx$ a) $\frac{x^3}{3} – \frac{3x^2}{2} – 5x + k$ b) $\frac{x^3}{3} – \frac{3x^2}{2} + 5x + k$ c) $\frac{x^3}{3} + \frac{3x^2}{2} – 5x + k$ d) $\frac{x^3}{3} + \frac{3x^2}{2} + 5x + k$ Integrate term by term: $\frac{x^3}{3} + \frac{3x^2}{2} – 5x + c$ 35 / 45 Category: Jamb Mathematics 2017 35. In the diagram MN is a chord of a circle KMN centre O and radius 10cm. If ∠MON = 140°, find, to the nearest cm, the length of the chord MN a) 10cm b) 19cm c) 17cm d) 12cm Using chord length formula: $2r\sin(\frac{\theta}{2})$ = $2(10)\sin(70°)$ ≈ 19cm 36 / 45 Category: Jamb Mathematics 2017 36. Factorize completely $x^2+2xy+y^2+3x+3y-18$ a) (x + y + 6)(x + y – 3) b) (x – y – 6)(x – y + 3) c) (x – y + 6)(x – y – 3) d) (x + y – 6)(x + y + 3) Group terms: $(x^2+2xy+y^2)+(3x+3y)-18$ = $(x+y)^2+3(x+y)-18$ = $(x+y+6)(x+y-3)$ 37 / 45 Category: Jamb Mathematics 2017 37. Make S the subject of the relation $p = s + \frac{s^2m}{nr}$ a) $s = \frac{nrp}{nr+\frac{m}{2}}$ b) $s = nr + \frac{m}{2mrp}$ c) $s = \frac{nrp}{mr} + m^2$ d) $s = \frac{nrp}{nr} + m^2$ Multiply throughout by nr: $pnr = snr + s^2m$. Rearrange to standard form and solve quadratic 38 / 45 Category: Jamb Mathematics 2017 38. The operation * on the set R of real number is defined by x * y = 3x + 2y − 1, find 3* − 1 a) 9 b) -9 c) 6 d) -6 Substitute x=3, y=-1 into the operation formula: 3*(-1) = 3(3) + 2(-1) – 1 = 9 – 2 – 1 = 6 39 / 45 Category: Jamb Mathematics 2017 39. Find the gradient of the line joining the points (3, 2) and (1, 4) a) 2-Mar b) 1-Feb c) -1 d) 2-Mar Gradient = $\frac{y_2-y_1}{x_2-x_1}$ = $\frac{4-2}{1-3}$ = -1 40 / 45 Category: Jamb Mathematics 2017 40. Simplify $(3\sqrt[3]{64a^3})^{-1}$ a) 4a b) $\frac{1}{8a}$ c) 8a d) $\frac{1}{4a}$ $64 = 2^6$, so expression = $\frac{1}{3\sqrt[3]{2^6a^3}}$ = $\frac{1}{3(2^2a)}$ = $\frac{1}{4a}$ 41 / 45 Category: Jamb Mathematics 2017 41. If $\sqrt{2}-\sqrt{3}+2\sqrt{2}$ = m + n$\sqrt{6}$, find the values of m and n respectively a) 1, -2 b) -2, 1 c) $-\frac{2}{5}$, 1 d) $\frac{2}{3}$ Simplify and group like terms: $3\sqrt{2}-\sqrt{3}$ = m + n$\sqrt{6}$ 42 / 45 Category: Jamb Mathematics 2017 42. If α and β are the roots of the equation $3x^2 + 5x – 2 = 0$, find the value of $\frac{1}{\alpha} + \frac{1}{\beta}$ a) $-\frac{5}{3}$ b) $-\frac{2}{3}$ c) $\frac{1}{2}$ d) $\frac{5}{2}$ Using Vieta’s formulas, $\frac{1}{\alpha} + \frac{1}{\beta}$ = $-\frac{5}{2}$ 43 / 45 Category: Jamb Mathematics 2017 43. Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2 a) 1.03 b) 0.07 c) 0.03 d) 1 Range = highest value – lowest value = 0.47 – (-0.53) = 1.0 44 / 45 Category: Jamb Mathematics 2017 44. Evaluate $1 – (\frac{1}{5} \times \frac{2}{3}) + (5 + \frac{2}{3})$ a) 4 b) 3 c) $\frac{22}{3}$ d) $\frac{3}{2}$ Calculate $\frac{1}{5} \times \frac{2}{3}$ = $\frac{2}{15}$, then subtract from 1 and add $5\frac{2}{3}$ = $\frac{17}{3}$ 45 / 45 Category: Jamb Mathematics 2017 45. What is the product of $2x^2 – x + 1$ and $3 – 2x$ a) $4x^3 – 8x^2 + 5x + 3$ b) $-4x^3 + 8x^2 – 5x + 3$ c) $-4x^3 – 8x^2 + 5x + 3$ d) $4x^3 + 8x^2 – 5x + 3$ Multiply terms: $(2x^2)(3) + (2x^2)(-2x) + (-x)(3) + (-x)(-2x) + (1)(3) + (1)(-2x)$ = $-4x^3 + 8x^2 – 5x + 3$ Your score is The average score is 0% LinkedIn Facebook Twitter VKontakte 0% Restart quiz Anonymous feedback Send feedback
