2014 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 2014 JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS 1 / 47 Category: JAMB Mathematics 2014 1. Find the value of $1101112 + 101002$ a) $1101011_2$ b) $1001001_2$ c) $1001011_2$ d) $1001111_2$ To solve this binary addition, align digits and add: $110111_2 + 10100_2$. Carrying over when sum ≥ 2: $110111_2$ (55 in decimal) + $10100_2$ (20 in decimal) = $1001011_2$ (75 in decimal) 2 / 47 Category: JAMB Mathematics 2014 2. A woman bought a grinder for N60,000. She sold it at a loss of 15%. How much did she sell it? a) N53,000 b) N52,000 c) N51,000 d) N50,000 Loss = 15% of N60,000 = $\frac{15}{100} \times 60,000 = 9,000$. Selling price = N60,000 – N9,000 = N51,000 3 / 47 Category: JAMB Mathematics 2014 3. Express the product of 0.00043 and 2000 in standard form. a) $8.6 \times 10^{-3}$ b) $8.3 \times 10^{-2}$ c) $8.6 \times 10^{-1}$ d) $8.6 \times 10$ $0.00043 \times 2000 = 0.86$. In standard form: $8.6 \times 10^{-1}$ 4 / 47 Category: JAMB Mathematics 2014 4. A man donates 10% of his monthly net earnings to his church. If it amounts to N4,500, what is his net monthly income? a) N40,500 b) N45,000 c) N52,500 d) N62,000 Let x be the net income. $\frac{10}{100} \times x = 4,500$. Therefore, $x = 4,500 \times \frac{100}{10} = 45,000$ 5 / 47 Category: JAMB Mathematics 2014 5. If $\log7.5 = 0.8751$, evaluate $2 \log75 + \log750$ a) 6.6252 b) 6.6253 c) 66.252 d) 66.253 Using log rules: $2\log75 + \log750 = 2(1 + \log7.5) + (2 + \log7.5) = 2 + 2(0.8751) + 2 + 0.8751 = 6.6252$ 6 / 47 Category: JAMB Mathematics 2014 6. Solve for x in $8^{x-2} = \frac{2}{25}$ a) 4 b) 6 c) 8 d) 10 Taking $\log_8$ of both sides: $(x-2)\log_8 8 = \log_8 \frac{2}{25}$. Therefore $x-2 = -2$, so $x = 4$ 7 / 47 Category: JAMB Mathematics 2014 7. Simplify $\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}$ a) $-7\sqrt{6}/3$ b) $7\sqrt{6}/3$ c) $-\sqrt{6}/3$ d) $\sqrt{6}/3$ Multiply numerator and denominator by $\sqrt{2}+\sqrt{3}$ to rationalize: $= \frac{2-3}{2+2\sqrt{6}+3} = \frac{-1}{5+2\sqrt{6}}$ 8 / 47 Category: JAMB Mathematics 2014 8. Evaluate $\log_2 8 + \log_2 16 – \log_2 4$ a) 3 b) 4 c) 5 d) 6 Using log properties: $\log_2 8 = 3$, $\log_2 16 = 4$, $\log_2 4 = 2$. Therefore, $3 + 4 – 2 = 5$ 9 / 47 Category: JAMB Mathematics 2014 9. If P = {1,2,3,4,5} and $P \cup Q$ = {1,2,3,4,5,6,7}, list the elements in Q a) {6} b) {7} c) {6,7} d) {5,6} Elements in $P \cup Q$ but not in P must be in Q. Therefore, Q must contain 6 and 7 10 / 47 Category: JAMB Mathematics 2014 10. If $gt^2 – k – w = 0$, make g the subject of the formula a) $\frac{k+w}{t^2}$ b) $\frac{k-w}{t^2}$ c) $\frac{k+w}{t}$ d) $\frac{k-w}{t}$ Add k + w to both sides: $gt^2 = k + w$. Divide both sides by $t^2$: $g = \frac{k+w}{t^2}$ 11 / 47 Category: JAMB Mathematics 2014 11. Factorize $2y^2 – 15xy + 18x^2$ a) $(2y – 3x)(y + 6x)$ b) $(2y – 3x)(y – 6x)$ c) $(2y + 3x)(y – 6x)$ d) $(3y + 2x)(y – 6x)$ Group terms: $2y^2 – 15xy + 18x^2 = (2y – 3x)(y – 6x)$ 12 / 47 Category: JAMB Mathematics 2014 12. Find the value of k if y – 1 is a factor of $y^3 + 4y^2+ ky – 6$ a) -6 b) -4 c) 0 d) 1 When y = 1, the expression should equal 0: $1 + 4 + k – 6 = 0$. Therefore $k = 1$ 13 / 47 Category: JAMB Mathematics 2014 13. y varies directly as $w^2$. When y = 8, w = 2. Find y when w = 3 a) 18 b) 12 c) 9 d) 6 If $y \propto w^2$, then $y = kw^2$. When w = 2, 8 = 4k$, so $k = 2$. When w = 3, $y = 2(3^2) = 18$ 14 / 47 Category: JAMB Mathematics 2014 14. P varies directly as Q and inversely as R. When Q = 36 and R = 16, P = 27. Find the relation between P, Q and R. a) $P=\frac{Q}{12R}$ b) $P=\frac{12Q}{R}$ c) $P=12QR$ d) $P=\frac{12}{QR}$ $P = k\frac{Q}{R}$. Substitute values: $27 = k\frac{36}{16}$. Therefore $k = 12$, so $P = \frac{12Q}{R}$ 15 / 47 Category: JAMB Mathematics 2014 15. What is the solution of $\frac{x-5}{x+3}<-1$? a) -3 < x < 1 b) x < -3 or x > 1 c) -3 < x < 5 d) x < -3 or x > 5 Multiply both sides by (x+3): $(x-5)<-(x+3)$ when x+3>0, and reverse when x+3<0. Solve to get x<-3 or x>5 16 / 47 Category: JAMB Mathematics 2014 16. Evaluate the inequality $\frac{x^2+3}{4} \leq \frac{5x}{6}-\frac{7}{12}$ a) $x \geq 4$ b) $x \leq 3$ c) $x \geq -3$ d) $x \leq -4$ Multiply all terms by 12: $3x^2+9 \leq 10x-7$. Rearrange: $3x^2-10x+16 \leq 0$. Solve quadratic: $x \leq 4$ 17 / 47 Category: JAMB Mathematics 2014 17. The 4th term of an A.P. is 13 while the 10th term is 31. Find the 24th term. a) 89 b) 75 c) 73 d) 69 Let first term be a and common difference be d. From given terms: $a+3d=13$ and $a+9d=31$. Solve to get $d=3$. Therefore 24th term = $13+20d=73$ 18 / 47 Category: JAMB Mathematics 2014 18. What is the common ratio of the G.P. $(\sqrt{10}+\sqrt{5})+(\sqrt{10}+2\sqrt{5})+…$ a) $\sqrt{2}$ b) $\sqrt{5}$ c) 3 d) 5 For a GP, ratio = second term/first term = $\frac{\sqrt{10}+2\sqrt{5}}{\sqrt{10}+\sqrt{5}}=\sqrt{5}$ 19 / 47 Category: JAMB Mathematics 2014 19. A binary operation * is defined by x * y = xy. If x * 2 = 12 – x, find the possible values of x a) -3,4 b) -3,-4 c) 3,4 d) 3,-4 Given x * 2 = 2x = 12 – x. Solve: $3x = 12$, so $x = 4$ or $x = -4$ 20 / 47 Category: JAMB Mathematics 2014 20. Find y, if $\begin{pmatrix} 5 & -6 \ -7 & 2 \end{pmatrix}\begin{pmatrix} x \ y \end{pmatrix}=\begin{pmatrix} 7 \ -11 \end{pmatrix}$ a) 8 b) 5 c) 3 d) 2 Solve system of equations: $5x-6y=7$ and $-7x+2y=-11$. Solution gives $y=2$ 21 / 47 Category: JAMB Mathematics 2014 21. If $\begin{vmatrix} -x & -1 \ 12 & 4 \end{vmatrix}=-12$, find x. a) -6 b) -2 c) 3 d) 6 $-4x-(-1)(12)=-12$. Solve: $-4x+12=-12$. Therefore $x=6$ 22 / 47 Category: JAMB Mathematics 2014 22. Find the value of \( \begin{vmatrix} 0 & 1 & 0 \\ 3 & 7 & 5 \\ 2 & 8 & 4 \end{vmatrix} \) a) 12 b) 10 c) -1 d) -2 Using cofactor expansion along first row: $0(28-10)+1(12-0)+0(24-14)=-12$ 23 / 47 Category: JAMB Mathematics 2014 23. How many sides has a regular polygon whose interior angle is 135°? a) 12 b) 10 c) 9 d) 8 For a regular polygon with n sides: $\frac{(n-2)180°}{n}=135°$. Solve for n: $n=8$ 24 / 47 Category: JAMB Mathematics 2014 24. A cylindrical tank has a capacity of 6160m³. What is the depth of the tank if the radius of its base is 28cm? a) 8.0m b) 7.5m c) 5.0m d) 2.5m Volume = $\pi r^2h$. Convert units and solve: $6160 = \pi(0.28)^2h$. Therefore $h=25$ meters 25 / 47 Category: JAMB Mathematics 2014 25. Find the mid point of S(-5, 4) and T(-3, -2) a) -4, 2 b) 4, -2 c) -4, 1 d) 4, -1 Midpoint formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{-5-3}{2},\frac{4-2}{2})=(-4,1)$ 26 / 47 Category: JAMB Mathematics 2014 26. The gradient of a line joining (x,4) and (1,2) is $\frac{1}{2}$. Find the value of x a) 5 b) 3 c) -3 d) -5 Using gradient formula: $\frac{4-2}{x-1}=\frac{1}{2}$. Cross multiply and solve: $x=5$ 27 / 47 Category: JAMB Mathematics 2014 27. Calculate the mid point of the line segment y – 4x + 3 = 0, which lies between the x-axis and y-axis. a) $(\frac{3}{8},-\frac{3}{2})$ b) $(\frac{3}{8},\frac{3}{2})$ c) $(-\frac{2}{2},\frac{2}{2})$ d) $(-\frac{2}{3},\frac{3}{2})$ Find intercepts: (0,3) and ($\frac{3}{4}$,0). Use midpoint formula: $(\frac{3}{8},\frac{3}{2})$ 28 / 47 Category: JAMB Mathematics 2014 28. If $\sin\theta=\frac{12}{13}$, find the value of $\frac{1+\cos\theta}{\sin\theta}$ a) $\frac{25}{13}$ b) $\frac{18}{13}$ c) $\frac{8}{13}$ d) $\frac{5}{13}$ Using Pythagorean identity: $\cos\theta=\frac{5}{13}$. Therefore $\frac{1+\frac{5}{13}}{\frac{12}{13}}=\frac{18}{13}$ 29 / 47 Category: JAMB Mathematics 2014 29. If y = 4x³ – 2x² + x, find $\frac{dy}{dx}$ a) $8x^2-2x+1$ b) $8x^2-4x+1$ c) $12x^2-2x+1$ d) $12x^2-4x+1$ Using power rule: $\frac{dy}{dx}=12x^2-4x+1$ 30 / 47 Category: JAMB Mathematics 2014 30. If y = cos 3x, find $\frac{dy}{dx}$ a) $\frac{1}{3}\sin 3x$ b) $-\frac{1}{3}\sin 3x$ c) $3\sin 3x$ d) $-3\sin 3x$ Chain rule: $\frac{d}{dx}(\cos 3x)=-3\sin 3x$ 31 / 47 Category: JAMB Mathematics 2014 31. Find the minimum value of y = x² – 2x – 3 a) 4 b) 1 c) -1 d) -4 Set $\frac{dy}{dx}=0$: $2x-2=0$, so $x=1$. Second derivative is positive, so minimum value is $y=(1)^2-2(1)-3=-4$ 32 / 47 Category: JAMB Mathematics 2014 32. Evaluate $\int \sin^2x dx$ a) $\cos 2x+k$ b) $\frac{1}{2}\cos 2x+k$ c) $-\frac{1}{2}\cos 2x+k$ d) $-\cos 2x+k$ Using double angle formula: $\sin^2x=\frac{1-\cos 2x}{2}$. Integrate: $\frac{x}{2}-\frac{\sin 2x}{4}+C=-\frac{1}{2}\cos 2x+k$ 33 / 47 Category: JAMB Mathematics 2014 33. Evaluate $\int(2x+3)^\frac{1}{2}dx$ a) $\frac{1}{12}(2x+3)^6+k$ b) $\frac{1}{3}(2x+3)^\frac{1}{2}+k$ c) $\frac{1}{3}(2x+3)^\frac{3}{2}+k$ d) $\frac{1}{12}(2x+3)^\frac{3}{4}+k$ Let $u=2x+3$, $du=2dx$. Then $\int u^\frac{1}{2}\frac{du}{2}=\frac{1}{3}u^\frac{3}{2}+C=\frac{1}{3}(2x+3)^\frac{3}{2}+C$ 34 / 47 Category: JAMB Mathematics 2014 34. The mean of 2 – t, 4 + t, 3 – 2t, 2 + t and t – 1 is a) t b) -t c) 2 d) -2 Sum all terms and divide by 5: $\frac{(2-t)+(4+t)+(3-2t)+(2+t)+(t-1)}{5}=2$ 35 / 47 Category: JAMB Mathematics 2014 35. Find the mode of the distribution: 0(1), 1(2), 2(2), 3(1), 4(9) a) 1 b) 2 c) 3 d) 4 The mode is the value with highest frequency. Here, 4 occurs 9 times, more than any other value 36 / 47 Category: JAMB Mathematics 2014 36. Find the median of 5,9,1,10,3,8,9,2,4,5,5,5,7,3 and 6 a) 6 b) 5 c) 4 d) 3 Arrange in order: 1,2,3,3,4,5,5,5,5,6,7,8,9,9,10. Middle (8th) value is 5 37 / 47 Category: JAMB Mathematics 2014 37. Find the standard deviation of 5, 4, 3, 2, 1 a) $\sqrt{2}$ b) $\sqrt{3}$ c) $\sqrt{6}$ d) $\sqrt{10}$ Mean = 3. Sum of squares of differences = 10. Standard deviation = $\sqrt{\frac{10}{5}}=\sqrt{2}$ 38 / 47 Category: JAMB Mathematics 2014 38. In how many ways can a team of 3 girls be selected from 7 girls? a) $\frac{7!}{3!}$ b) $\frac{7!}{4!}$ c) $\frac{7!}{3!4!}$ d) $\frac{7!}{2!5!}$ This is combination $C(7,3)=\frac{7!}{3!4!}=35$ 39 / 47 Category: JAMB Mathematics 2014 39. From frequency table of die throw (100 times), probability of obtaining at least 4 a) $\frac{1}{5}$ b) $\frac{1}{2}$ c) $\frac{2}{5}$ d) $\frac{3}{4}$ Sum frequencies for 4,5,6: $(16+10+14)=40$ out of 100 total throws = $\frac{2}{5}$ 40 / 47 Category: JAMB Mathematics 2014 40. Probability that a random number from 10 to 30 is divisible by 3 a) $\frac{2}{15}$ b) $\frac{1}{10}$ c) $\frac{1}{3}$ d) $\frac{2}{5}$ Numbers divisible by 3: 12,15,18,21,24,27,30 (7 numbers) out of 21 total numbers = $\frac{7}{21}=\frac{1}{3}$ 41 / 47 Category: JAMB Mathematics 2014 41. Venn diagram shaded parts represent a) $(P∩Q)∪(P∩R)$ b) $(P∪Q)∩(P∩R)$ c) $(P∪Q)∪(P∪R)$ d) $(P∩Q)∪(P∪R)$ The shaded region shows elements in P∩Q or P∩R, which is $(P∩Q)∪(P∩R)$ 42 / 47 Category: JAMB Mathematics 2014 42. In triangle with KL//NM, LN bisects ∠KNM, ∠KLN=54°, ∠MKN=35° a) 91° b) 89° c) 37° d) 19° Due to parallel lines and angle bisector properties, $∠KMN=89°$ 43 / 47 Category: JAMB Mathematics 2014 43. Find value of p in given triangle a) 135° b) 90° c) 60° d) 45° Using angle properties in circle: inscribed angle is half of central angle, so $p=90°$ 44 / 47 Category: JAMB Mathematics 2014 44. Find value of x in given right triangle a) $20sqrt{3}$ cm b) $10sqrt{3}$ cm c) $5sqrt{3}$ cm d) $4sqrt{3}$ cm Using 30-60-90 triangle properties: $x=10\sqrt{3}$ cm 45 / 47 Category: JAMB Mathematics 2014 45. Find equation of line passing through (0,5) and (5,0) a) $y=x+5$ b) $y=-x+5$ c) $y=x-5$ d) $y=-x-5$ Using point-slope form: slope = $\frac{0-5}{5-0}=-1$. Equation: $y=-x+5$ 46 / 47 Category: JAMB Mathematics 2014 46. If N8,000 spent on rice in pie chart, how much spent on yam? a) N42,000 b) N18,000 c) N16,000 d) N12,000 If 60° represents N8,000, then 90° (for yam) represents N12,000 47 / 47 Category: JAMB Mathematics 2014 47. Find perimeter of sector with radius 10.5 cm and angle 120° a) 48 cm b) 40 cm c) 43 cm d) 45 cm Perimeter = 2r + rθ = $2(10.5) + 10.5(\frac{2π}{3})$ = 43 cm [using $π=\frac{22}{7}$] Your score is The average score is 0% LinkedIn Facebook Twitter VKontakte 0% Restart quiz Anonymous feedback Send feedback