2018 JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS

Using the formula for two sets: $n(A \cup B) = n(A) + n(B) – n(A \cap B) – n(neither)$ where 40 = 32 + 24 – x – 4, solving for x gives us 20 students taking both subjects.

Cross multiply and solve: $3(x+2) – 4(2x-3) < 48$ Simplify: $3x + 6 - 8x + 12 < 48$ Therefore $-5x + 18 < 48$ $-5x < 30$ $x > -6$

Given that housing is twice school fees and total income is ₦7200, if we look at the pie chart sectors and calculate proportions, housing takes ₦2000 of the total expenditure.

To find maximum profit, differentiate $10x – x^2$ and set to zero: $\frac{d}{dx}(10x – x^2) = 10 – 2x = 0$ Therefore $x = 5$ bags gives maximum profit.

Convert each number to base 10 first: $23_5 = 13_{10}$ and $101_3 = 10_{10}$. Sum them: $13 + 10 = 23_{10}$. Convert to base 2: $23_{10} = 10111_2$

From the diagram, using angle properties of circles (angle in a semicircle is 90°, angles in same segment are equal), we can deduce that x = 36°

Multiply all terms by 12 to eliminate fractions: $9t + 4(21 – t) = 132$ Simplify: $9t + 84 – 4t = 132$ Therefore $5t = 48$ So $t = \frac{48}{5}$

Total fraction spent = $\frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12}$ Remaining fraction = $1 – \frac{7}{12} = \frac{5}{12}$

Multiply throughout by b: $\frac{bx}{a+1} + y = b$ Therefore $y = b – \frac{bx}{a+1} = \frac{b(a+1-x)}{a+1}$

Surface area = 2(length × width + length × height + width × height) = 2(12 × 10 + 12 × 8 + 10 × 8) = 2(120 + 96 + 80) = 592 cm²

In 0.04945, looking at the first non-zero digits, 4 and 9, the 9 means we round up the 4 to 5, giving 0.050

Probability of both failing = (1 – $\frac{3}{4}$)(1 – $\frac{3}{5}$) = $\frac{1}{4} × \frac{2}{5} = \frac{2}{20} = \frac{1}{10}$

Perimeter = arc length + 2 × radius = $\frac{300}{360} × 2πr + 2r$ = $\frac{300}{360} × 2 × \frac{22}{7} × 14 + 28$ = 73.33 cm

Using laws of indices: $25^{\frac{2}{3} – \frac{1}{6}} × (\frac{1}{5})^{\frac{7}{6} – \frac{1}{6}}$ = $25^{\frac{1}{2}} × (\frac{1}{5})^1$ = 5 × $\frac{1}{5}$ = 1

In the given equation, isolate T by first multiplying throughout by P³Q, then subtract R from both sides, and finally divide by 15

In 3.0492, the 9 is in the thousandths position, making its place value $\frac{9}{1000}$

Using formula $I = \frac{PRT}{100}$, where 123 = $\frac{P × 3 × 2.5}{100}$, solving for P gives N1,640

After first year: 20000 × 0.9 = 18000. After second year: 18000 × 0.9 = 16200

With frequencies 1,2,7,5,4,3 (total 22), the median position is at 11.5th item. Counting up through frequencies, this falls in the score of 2

Total students = 22, Number scoring 2 or 3 = 7 + 5 = 12. Probability = $\frac{12}{22} = \frac{6}{11}$

Speed = $\frac{distance}{time}$ = $\frac{0.8km}{\frac{1}{3}hr}$ = 2.4 km/h

N900 buys $\frac{900}{63}$ = 14.29 litres. At 14km per litre, total distance = 14.29 × 14 = 200km

Using alternate angles and angle in a circle properties, ∠EHF = 126°

Circumference = $π × 100$ ≈ 314m. Number of rounds = $\frac{1000}{314}$ ≈ 3.18 ≈ 3 rounds

Convert to standard form and multiply: $\frac{2.56 × 10^{-3} × 6.4 × 10^{-3}}{2.5 × 10^{-2} × 8 × 10^{-2}}$ = $8.8 × 10^{-1}$

Initial ratio 11:9 = 20 parts. $\frac{2}{3}$ of 9 parts = 6 parts costs N720. Therefore total value = $\frac{20}{6} × 720$ = N2,400

Using 3D Pythagoras theorem, diagonal = $\sqrt{12^2 + 9^2 + 8^2}$ = 17m. Floor diagonal = $\sqrt{12^2 + 9^2}$ = 15m. Therefore $\cos θ = \frac{15}{17}$

LCM = 240, HCF = 8. $\frac{240}{8}$ = 30

Using slope-point form, parallel lines have same slope. Slope = $-\frac{7}{5}$. Therefore equation is 7x + 5y = 70

After 2 years + 2 months = 4 increments. Salary = 540 + (4 × 36) = N684

Using tan 74° = $\frac{150}{x}$, where x is the distance. x = $\frac{150}{\tan 74°}$ ≈ 43cm

Integrate term by term: $\int(6x^2 – 2x + 1)dx = 2x^3 – x^2 + x + c$

Total letters = 6, with E appearing twice. Formula = $\frac{6!}{2!}$ = 360

Using similar triangles, $\frac{YM}{MX} = \frac{NZ}{XN}$. Therefore YM = $\frac{8 × 4}{12}$ × 24 = 24cm

Convert to same unit: 495g = 0.495kg. Percentage = $\frac{0.495}{16.5} × 100$ = 3%

Using difference of squares formula $a^2 – b^2$: = $12 – 16 = -4$

Derivative = $2x – 2$. At x = 2, slope = 2. Using point-slope form: $y = 2(x – 2)$ = $2x – 4$

From the graph shown, the vertex represents the minimum point, which occurs at 0.5

$\log_2 8 = 3$ and $\log_3 \frac{1}{9} = -2$. Therefore $3 – (-2) = 5$

In the fourth quadrant (270° to 360°), sine is negative while tangent is positive

Sum the frequencies: 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 = 40

Count elements not in A or B from the Venn diagram = 4 elements

The set of all points 4cm from a given point forms a circle with radius 4cm

Using the relationship $\sin A = \cos(90° – A)$, solve $5x – 28 = 90° – (3x – 50)$ to get x = 21°

First four primes > 10 are 11, 13, 17, 19. Average = $\frac{11 + 13 + 17 + 19}{4}$ = 15

From the frequency distribution, the age that appears most frequently (highest frequency) is 6

First two significant digits are 4 and 9. Rounding up gives 0.050

Convert $243_6 = 2×6^2 + 4×6^1 + 3×6^0 = 87_{10}$. $243_5 = 2×5^2 + 4×5^1 + 3×5^0 = 63_{10}$. Difference = 26

P(tail) = $\frac{1}{2}$, P(even) = $\frac{3}{6}$. P(both) = $\frac{1}{2} × \frac{1}{2}$ = $\frac{1}{4}$