JAMB Mathematics Past Questions and Answers (50 Practice Questions with Solutions)

JAMB Mathematics Past Questions, Preparing for your JAMB-UTME Mathematics exam is all about practice. The more you familiarize yourself with the types of questions you’ll encounter, the more confident and faster you’ll be on exam day.

This guide provides 50 likely questions modeled after JAMB past questions to help you test your knowledge and problem-solving skills.

Disclaimer: These are not leaked questions. They are practice questions designed to reflect the JAMB syllabus and common exam patterns. Use them to study, identify your weak areas, and master the necessary calculations.

JAMB Mathematics Past Questions and Answers

 

Question 1: Simplify 341​221​×131​​ A) 1391​ B) 3940​ C) 1131​ D) 1312​

Answer: B) 3940​

Calculation:

• First, convert all mixed fractions to improper fractions:
  • 221​=25​
  • 131​=34​
  • 341​=413​
• Now, substitute these into the expression:
  • Numerator: 25​×34​=620​=310​
• Divide the numerator by the denominator:
  • 310​÷413​=310​×134​=3940​

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Question 2: If $x$ varies directly as y2 and $x=4$ when $y=2$, find $x$ when $y=6$. A) 12 B) 24 C) 36 D) 48

Answer: C) 36

Calculation:

• Direct variation is expressed as x=ky2, where $k$ is the constant of proportionality.
• First, find $k$ using the initial values ($x=4,y=2$):
  • 4=k(22)
  • $4=4k$
  • $k=1$
• Now, use the value of $k$ to find $x$ when $y=6$:
  • x=1×(62)
  • $x=36$

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Question 3: Find the sum of the first 20 terms of the arithmetic progression (AP) 3, 7, 11, 15, … A) 820 B) 860 C) 790 D) 840

Answer: B) 860

Calculation:

• The formula for the sum of an AP is Sn​=2n​[2a+(n−1)d].
• Here, $n=20$, the first term $a=3$, and the common difference $d=7-3=4$.
• Substitute the values into the formula:
  • S20​=220​[2(3)+(20−1)4]
  • S20​=10[6+(19)4]
  • S20​=10[6+76]
  • S20​=10[82]=820
  • Correction in calculation: S20​=10[82]=820. Rechecking calculation… Ah, Sn​=2n​[2a+(n−1)d]. S20​=220​[2(3)+(19)4]=10[6+76]=10(82)=820. Let me re-evaluate the options. It seems there’s a discrepancy. Let me recalculate carefully. $a=3,d=4,n=20$. S20​=10(2∗3+19∗4)=10(6+76)=10(82)=820. Let’s assume the question intended a different value or the options are off. Let’s create a new question with a matching answer.
  • Revised Question: Find the sum of the first 20 terms of the arithmetic progression (AP) 4, 8, 12, …
    • A) 820
    • B) 840
    • C) 860
    • D) 880
  • Answer: B) 840
  • Calculation: $a=4,d=4,n=20$. S20​=220​[2(4)+(20−1)4]=10[8+19×4]=10[8+76]=10[84]=840. This is more consistent. I will proceed with questions that have verifiable answers. I’ll correct the original question.
• Original Question 3 (Recalculated): Find the sum of the first 20 terms of the arithmetic progression (AP) 5, 9, 13, 17, … A) 820 B) 860 C) 880 D) 840
• Answer: B) 860
• Calculation:
  • The formula for the sum of an AP is Sn​=2n​[2a+(n−1)d].
  • Here, $n=20$, first term $a=5$, common difference $d=9-5=4$.
  • S20​=220​[2(5)+(20−1)4]
  • S20​=10[10+(19)4]
  • S20​=10[10+76]
  • S20​=10[86]=860

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Question 4: A bag contains 5 red balls and 4 blue balls. Find the probability of picking a blue ball. A) 5/9 B) 4/9 C) 1/2 D) 1/4

Answer: B) 4/9

Calculation:

• Probability = (Number of favorable outcomes) / (Total number of possible outcomes).
• Number of blue balls (favorable outcomes) = 4.
• Total number of balls (possible outcomes) = 5 red + 4 blue = 9.
• Probability of picking a blue ball = $4/9$.

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Question 5: If log10​x=3, what is $x$? A) 30 B) 100 C) 1000 D) 300

Answer: C) 1000

Calculation:

• The logarithmic equation logb​a=c is equivalent to the exponential equation bc=a.
• In this case, log10​x=3 can be rewritten as 103=x.
• $x=10\times 10\times 10=1000$.

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Question 6: Solve the simultaneous equations: $2x+y=7$ and $3x-y=8$. A) $x=3,y=1$ B) $x=1,y=5$ C) $x=2,y=3$ D) $x=4,y=-1$

Answer: A) $x=3,y=1$

Calculation:

• We have two equations:
  1. $2x+y=7$
  2. $3x-y=8$
• Use the elimination method. Add equation (1) to equation (2):
  • $(2x+3x)+(y-y)=7+8$
  • $5x=15$
  • x=515​=3
• Substitute $x=3$ into the first equation:
  • $2(3)+y=7$
  • $6+y=7$
  • $y=7-6=1$
• So, $x=3$ and $y=1$.

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Question 7: A car travels at an average speed of 60 km/h. How long does it take to cover a distance of 150 km? A) 2 hours B) 2.5 hours C) 3 hours D) 3.5 hours

Answer: B) 2.5 hours

Calculation:

• The formula is Time = Distance / Speed.
• Distance = 150 km.
• Speed = 60 km/h.
• Time = $150/60=15/6=2.5$ hours.

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Question 8: Find the simple interest on ₦50,000 for 3 years at a rate of 4% per annum. A) ₦5,000 B) ₦6,000 C) ₦7,000 D) ₦8,000

Answer: B) ₦6,000

Calculation:

• Simple Interest (SI) = Principal (P) × Rate (R) × Time (T).
• P = ₦50,000.
• R = 4% = 0.04.
• T = 3 years.
• SI = $50,000\times 0.04\times 3=2,000\times 3=₦6,000$.

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Question 9: If the angles of a triangle are in the ratio 2:3:4, what is the size of the largest angle? A) 40° B) 60° C) 80° D) 100°

Answer: C) 80°

Calculation:

• The sum of angles in a triangle is 180°.
• The sum of the ratios is $2+3+4=9$.
• To find the value of one part of the ratio, divide the total sum of angles by the sum of ratios: $180°/9=20°$.
• The angles are $2\times 20°=40°$, $3\times 20°=60°$, and $4\times 20°=80°$.
• The largest angle is 80°.

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Question 10: Factorize completely: x2−5x−14. A) $(x-2)(x+7)$ B) $(x+2)(x-7)$ C) $(x-2)(x-7)$ D) $(x+2)(x+7)$

Answer: B) $(x+2)(x-7)$

Calculation:

• We need two numbers that multiply to -14 and add to -5.
• The factors of -14 are (1, -14), (-1, 14), (2, -7), and (-2, 7).
• The pair that adds to -5 is +2 and -7.
• So, the factorization is $(x+2)(x-7)$.

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Question 11: Calculate the area of a circle with a radius of 7 cm. (Take π=722​) A) 154 cm² B) 144 cm² C) 44 cm² D) 77 cm²

Answer: A) 154 cm²

Calculation:

• Area of a circle, A=πr2.
• Given $r=7$ cm and π=722​.
• A=722​×72=722​×49.
• $A=22\times 7=154$ cm².

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Question 12: Express 0.000458 in standard form. A) 4.58×10−3 B) 4.58×104 C) 4.58×10−4 D) 4.58×10−5

Answer: C) 4.58×10−4

Calculation:

• To express a number in standard form, the decimal point must be moved to after the first non-zero digit.
• In 0.000458, the first non-zero digit is 4.
• We need to move the decimal point 4 places to the right to get 4.58.
• Since we moved it to the right, the power of 10 will be negative.
• So, 0.000458=4.58×10−4.

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Question 13: If f(x)=3x2−2x+1, find $f(-2)$. A) 17 B) 9 C) 15 D) -15

Answer: A) 17

Calculation:

• Substitute $x=-2$ into the function $f(x)$.
• f(−2)=3(−2)2−2(−2)+1.
• $f(-2)=3(4)-(-4)+1$.
• $f(-2)=12+4+1=17$.

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Question 14: The mean of the numbers 4, 5, $x$, and 9 is 6. Find the value of $x$. A) 5 B) 6 C) 7 D) 8

Answer: B) 6

Calculation:

• Mean = (Sum of numbers) / (Count of numbers).
• $6=(4+5+x+9)/4$.
• $6=(18+x)/4$.
• Multiply both sides by 4: $24=18+x$.
• $x=24-18=6$.

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Question 15: Convert 11011₂ to base 10. A) 25 B) 27 C) 29 D) 31

Answer: B) 27

Calculation:

• To convert from binary (base 2) to denary (base 10), multiply each digit by its place value (powers of 2).
• 110112​=(1×24)+(1×23)+(0×22)+(1×21)+(1×20).
• $=(1\times 16)+(1\times 8)+(0\times 4)+(1\times 2)+(1\times 1)$.
• $=16+8+0+2+1=27$.

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Question 16: A polygon has 8 sides. What is the sum of its interior angles? A) 1080° B) 1440° C) 900° D) 1260°

Answer: A) 1080°

Calculation:

• The formula for the sum of interior angles of a polygon with $n$ sides is $(n-2)\times 180°$.
• For an 8-sided polygon (octagon), $n=8$.
• Sum of angles = $(8-2)\times 180°=6\times 180°=1080°$.

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Question 17: Find the median of the following set of numbers: 5, 3, 8, 2, 9, 4, 8. A) 2 B) 8 C) 5 D) 4

Answer: C) 5

Calculation:

• First, arrange the numbers in ascending order: 2, 3, 4, 5, 8, 8, 9.
• The median is the middle number. In a set of 7 numbers, the middle number is the 4th one.
• The median is 5.

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Question 18: Solve for $x$ in the equation 4x+1=64. A) 1 B) 2 C) 3 D) 4

Answer: B) 2

Calculation:

• Express both sides of the equation with the same base. The common base is 4.
• 64=4×4×4=43.
• So, the equation becomes 4x+1=43.
• Now, equate the powers: $x+1=3$.
• $x=3-1=2$.

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Question 19: What is the gradient (slope) of the line passing through the points (2, 5) and (4, 9)? A) 1 B) 2 C) 3 D) 4

Answer: B) 2

Calculation:

• The formula for the gradient, $m$, is (y2​−y1​)/(x2​−x1​).
• Let (x1​,y1​)=(2,5) and (x2​,y2​)=(4,9).
• $m=(9-5)/(4-2)=4/2=2$.

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Question 20: If the universal set U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, find A’ (the complement of A). A) {1, 3, 5} B) {2, 4, 6} C) {1, 2, 3} D) {4, 5, 6}

Answer: A) {1, 3, 5}

Calculation:

• The complement of a set A (A’) contains all the elements in the universal set U that are not in set A.
• U = {1, 2, 3, 4, 5, 6}.
• A = {2, 4, 6}.
• A’ = {1, 3, 5}.

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Question 21: If y=x3−4x2+5, find dxdy​. A) 3x2−8x B) x2−4x C) 3x2−8x+5 D) $3x-8$

Answer: A) 3x2−8x

Calculation:

• To differentiate the polynomial, apply the power rule (d/dx)(xn)=nxn−1 to each term.
• The derivative of x3 is 3x3−1=3x2.
• The derivative of −4x2 is −4(2x2−1)=−8x.
• The derivative of a constant (5) is 0.
• So, dxdy​=3x2−8x.

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Question 22: What is the value of the 5th term in a geometric progression (GP) with first term 3 and common ratio 2? A) 24 B) 32 C) 48 D) 64

Answer: C) 48

Calculation:

• The formula for the nth term of a GP is Tn​=arn−1.
• Here, first term $a=3$, common ratio $r=2$, and $n=5$.
• T5​=3×25−1=3×24.
• T5​=3×16=48.

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Question 23: Find the perimeter of a rectangle with length 12 cm and width 8 cm. A) 20 cm B) 40 cm C) 96 cm D) 60 cm

Answer: B) 40 cm

Calculation:

• Perimeter of a rectangle = $2\times (length+width)$.
• Perimeter = $2\times (12+8)=2\times 20=40$ cm.

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Question 24: Simplify 108​+75​. A) 113​ B) 93​ C) 133​ D) 103​

Answer: A) 113​

Calculation:

• Simplify each surd by finding the largest perfect square factor.
• 108​=36×3​=36​×3​=63​.
• 75​=25×3​=25​×3​=53​.
• Now, add them: 63​+53​=(6+5)3​=113​.

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Question 25: In a class of 30 students, 18 play Football and 15 play Basketball. If every student plays at least one of the two games, how many students play both? A) 3 B) 5 C) 8 D) 10

Answer: A) 3

Calculation:

• Let F be the set of students who play Football and B be the set of students who play Basketball.
• We use the formula: $|F\cup B|=|F|+|B|-|F\cap B|$.
• Total students, $|F\cup B|=30$.
• $|F|=18$.
• $|B|=15$.
• We need to find the number who play both, $|F\cap B|$.
• $30=18+15-|F\cap B|$.
• $30=33-|F\cap B|$.
• $|F\cap B|=33-30=3$.

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Question 26: If $P=\{a,b,c\}$ and $Q=\{1,2\}$, find the number of elements in $P\times Q$. A) 5 B) 6 C) 7 D) 8

Answer: B) 6

Calculation:

• $P\times Q$ represents the Cartesian product of sets P and Q.
• The number of elements in the Cartesian product is the product of the number of elements in each set.
• Number of elements in P, n(P) = 3.
• Number of elements in Q, n(Q) = 2.
• $n(P\times Q)=n(P)\times n(Q)=3\times 2=6$.

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Question 27: The price of an item is increased by 20% and then decreased by 10%. What is the overall percentage change? A) 8% increase B) 10% increase C) 8% decrease D) 10% decrease

Answer: A) 8% increase

Calculation:

• Let the original price be 100.
• First increase of 20%: New price = $100+(20\%\text{ of }100)=100+20=120$.
• Now, decrease this new price by 10%: Decrease amount = $10\%\text{ of }120=12$.
• Final price = $120-12=108$.
• The overall change is from 100 to 108, which is an 8% increase.

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Question 28: A die is rolled once. What is the probability of getting a number greater than 4? A) 1/3 B) 1/2 C) 2/3 D) 1/6

Answer: A) 1/3

Calculation:

• The possible outcomes when rolling a die are {1, 2, 3, 4, 5, 6}. Total outcomes = 6.
• The numbers greater than 4 are {5, 6}. Favorable outcomes = 2.
• Probability = (Favorable outcomes) / (Total outcomes) = $2/6=1/3$.

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Question 29: Find the volume of a cylinder with radius 7 cm and height 10 cm. (Take π=722​) A) 1540 cm³ B) 770 cm³ C) 1240 cm³ D) 1680 cm³

Answer: A) 1540 cm³

Calculation:

• Volume of a cylinder, V=πr2h.
• Given $r=7$ cm, $h=10$ cm, π=722​.
• V=722​×72×10=722​×49×10.
• $V=22\times 7\times 10=154\times 10=1540$ cm³.

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Question 30: Make $R$ the subject of the formula V=31​πR2H. A) R=πH3V​​ B) R=3πHV​​ C) R=πH3V​ D) R=3VπH​

Answer: A) R=πH3V​​

Calculation:

• Start with the formula: V=31​πR2H.
• Multiply both sides by 3: 3V=πR2H.
• Divide both sides by $\pi H$ to isolate R2: R2=πH3V​.
• Take the square root of both sides to find R: R=πH3V​​.

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Question 31: Given that sinθ=53​ and $\theta$ is an acute angle, find $\cos \theta$. A) 3/4 B) 4/5 C) 5/4 D) 4/3

Answer: B) 4/5

Calculation:

• Use the trigonometric identity sin2θ+cos2θ=1.
• (53​)2+cos2θ=1.
• 259​+cos2θ=1.
• cos2θ=1−259​=2525−9​=2516​.
• cosθ=2516​​=54​. (Since $\theta$ is acute, $\cos \theta$ is positive).
• Alternatively, using a right-angled triangle: If sinθ=HypotenuseOpposite​=53​, then Opposite = 3, Hypotenuse = 5. By Pythagoras theorem, Adjacent = 52−32​=25−9​=16​=4. So, cosθ=HypotenuseAdjacent​=54​.

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Question 32: Find the product of the roots of the quadratic equation 2x2−5x+3=0. A) -5/2 B) 5/2 C) 3/2 D) -3/2

Answer: C) 3/2

Calculation:

• For a quadratic equation of the form ax2+bx+c=0, the product of the roots is given by the formula $c/a$.
• In the equation 2x2−5x+3=0, we have $a=2,b=-5,c=3$.
• Product of roots = $c/a=3/2$.

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Question 33: The angles of a quadrilateral are $x,2x,3x,$ and $4x$. Find the value of $x$. A) 30° B) 36° C) 40° D) 45°

Answer: B) 36°

Calculation:

• The sum of the interior angles of a quadrilateral is 360°.
• $x+2x+3x+4x=360°$.
• $10x=360°$.
• $x=360°/10=36°$.

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Question 34: Convert 77₁₀ to a number in base 2. A) 1001101₂ B) 1010101₂ C) 1100101₂ D) 1001011₂

Answer: A) 1001101₂

Calculation:

• Use the method of successive division by 2, recording the remainders.
• $77÷2=38$ remainder 1
• $38÷2=19$ remainder 0
• $19÷2=9$ remainder 1
• $9÷2=4$ remainder 1
• $4÷2=2$ remainder 0
• $2÷2=1$ remainder 0
• $1÷2=0$ remainder 1
• Read the remainders from bottom to top: 1001101₂.

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Question 35: Find the value of $|-15|-|-8|$. A) -23 B) 23 C) -7 D) 7

Answer: D) 7

Calculation:

• The absolute value of a number is its non-negative value.
• $|-15|=15$.
• $|-8|=8$.
• The expression becomes $15-8=7$.

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Question 36: What is the least common multiple (LCM) of 12, 15, and 18? A) 90 B) 120 C) 180 D) 360

Answer: C) 180

Calculation:

• First, find the prime factorization of each number.
• 12=22×3
• $15=3\times 5$
• 18=2×32
• To find the LCM, take the highest power of each prime factor present in the numbers.
• Highest power of 2 is 22.
• Highest power of 3 is 32.
• Highest power of 5 is 51.
• LCM = 22×32×5=4×9×5=36×5=180.

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Question 37: A regular polygon has an exterior angle of 45°. How many sides does it have? A) 6 B) 8 C) 9 D) 10

Answer: B) 8

Calculation:

• The formula relating the number of sides ($n$) of a regular polygon to its exterior angle is: Exterior Angle = 360° / $n$.
• Therefore, $n$ = 360° / Exterior Angle.
• $n=360°/45°=8$.
• The polygon has 8 sides.

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Question 38: Evaluate $\int (2x+3)dx$. A) x2+3x+C B) 2x2+3x+C C) x2+C D) $2+C$

Answer: A) x2+3x+C

Calculation:

• Use the power rule for integration ∫xndx=n+1xn+1​+C.
• Integrate each term separately.
• ∫2xdx=2∫x1dx=21+1x1+1​=22x2​=x2.
• $\int 3dx=3x$.
• Combine the results and add the constant of integration, C.
• ∫(2x+3)dx=x2+3x+C.

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Question 39: Find the size of each interior angle of a regular hexagon. A) 108° B) 120° C) 135° D) 140°

Answer: B) 120°

Calculation:

• A hexagon has 6 sides ($n=6$).
• First, find the sum of the interior angles: $(n-2)\times 180°=(6-2)\times 180°=4\times 180°=720°$.
• For a regular polygon, all interior angles are equal.
• Size of each interior angle = (Sum of angles) / $n=720°/6=120°$.

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Question 40: If $2x-5\le 3x+2$, find the range of values for $x$. A) $x\ge -7$ B) $x\le -7$ C) $x\ge 7$ D) $x\le 7$

Answer: A) $x\ge -7$

Calculation:

• Start with the inequality: $2x-5\le 3x+2$.
• Subtract $2x$ from both sides: $-5\le x+2$.
• Subtract 2 from both sides: $-5-2\le x$.
• $-7\le x$, which is the same as $x\ge -7$.

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Question 41: Find the determinant of the matrix (42​35​). A) 14 B) 20 C) 6 D) 26

Answer: A) 14

Calculation:

• For a 2×2 matrix (ac​bd​), the determinant is given by $ad-bc$.
• In this case, $a=4,b=3,c=2,d=5$.
• Determinant = $(4\times 5)-(3\times 2)=20-6=14$.

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Question 42: In a survey of 100 students, 60 like Mathematics and 50 like Physics. If 20 like both, how many like neither? A) 5 B) 10 C) 15 D) 20

Answer: B) 10

Calculation:

• Number of students who like at least one subject = (Likes Maths) + (Likes Physics) – (Likes Both).
• Number liking at least one = $60+50-20=110-20=90$.
• Total number of students is 100.
• Number who like neither = Total students – Number liking at least one.
• Number who like neither = $100-90=10$.

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Question 43: A laptop originally priced at ₦150,000 is sold at a discount of 15%. What is the selling price? A) ₦127,500 B) ₦135,000 C) ₦125,000 D) ₦130,000

Answer: A) ₦127,500

Calculation:

• Calculate the discount amount: Discount = $15\%\text{ of }₦150,000=0.15\times 150,000=₦22,500$.
• Subtract the discount from the original price: Selling Price = $150,000-22,500=₦127,500$.

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Question 44: Simplify the expression (3a2b)(2ab3). A) 5a3b4 B) 6a2b3 C) 6a3b4 D) 5a2b3

Answer: C) 6a3b4

Calculation:

• Multiply the coefficients: $3\times 2=6$.
• Multiply the variables with the same base by adding their powers.
• For $a$: a2×a1=a2+1=a3.
• For $b$: b1×b3=b1+3=b4.
• Combine them: 6a3b4.

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Question 45: Find the sum of the infinite geometric series 1+21​+41​+81​+… A) 1.5 B) 2 C) 2.5 D) 3

Answer: B) 2

Calculation:

• The formula for the sum to infinity of a GP is S∞​=1−ra​, where $|r|<1$.
• The first term $a=1$.
• The common ratio r=(21​)/1=21​.
• Since $|r|<1$, the sum to infinity exists.
• S∞​=1−21​1​=21​1​=1×2=2.

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Question 46: The bearing of point B from point A is 120°. What is the bearing of point A from point B? A) 240° B) 300° C) 060° D) 330°

Answer: B) 300°

Calculation:

• To find the back bearing, if the original bearing is less than 180°, add 180°. If it is greater than 180°, subtract 180°.
• The bearing of B from A is 120°.
• Since 120° is less than 180°, the bearing of A from B is $120°+180°=300°$.

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Question 47: What is the 4th term of the expansion of (x+y)5? A) 10x2y3 B) 10x3y2 C) 5xy4 D) 5x4y

Answer: A) 10x2y3

Calculation:

• The general term in the binomial expansion of (x+y)n is given by Tr+1​=(rn​)xn−ryr.
• We want the 4th term, so $r+1=4$, which means $r=3$. Here, $n=5$.
• T4​=(35​)x5−3y3.
• (35​)=3!(5−3)!5!​=3!2!5!​=2×15×4​=10.
• So, the 4th term is 10x2y3.

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Question 48: If two lines are parallel, what is true about their gradients? A) Their gradients are equal. B) The product of their gradients is -1. C) One is the negative of the other. D) They have no gradients.

Answer: A) Their gradients are equal.

Calculation:

• This is a fundamental property of coordinate geometry. Parallel lines have the same steepness, which means their gradients (slopes) are identical. For perpendicular lines, the product of their gradients is -1.

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Question 49: In a class, the ratio of boys to girls is 3:2. If there are 18 boys, how many girls are there? A) 10 B) 12 C) 15 D) 8

Answer: B) 12

Calculation:

• Let the ratio be $3x:2x$.
• The number of boys is $3x$, which is given as 18.
• $3x=18$.
• $x=18/3=6$.
• The number of girls is $2x$.
• Number of girls = $2\times 6=12$.

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Question 50: Solve the equation x2=81. A) $x=9$ B) $x=-9$ C) $x=\pm 9$ D) $x=40.5$

Answer: C) $x=\pm 9$

Calculation:

• To solve for $x$, take the square root of both sides of the equation.
• x2​=81​.
• $x=\pm 9$.
• Remember that both (+9)2=81 and (−9)2=81, so there are two possible solutions.

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Keep practicing these types of questions to build your speed and confidence for the JAMB Mathematics exam. Good luck with your studies!