JAMB Mathematics 2021 practice collection

17 reviewed questions with answers and explanations.

These adapted questions come from a publisher-labelled 2021 collection. The original UTME sitting and question numbers are unconfirmed. Practice selection: full-paper coverage has not been confirmed.

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Answer 10 distinct reviewed Mathematics questions from this 2021 collection in 30 minutes, then see your raw score and explanations. This is a practice selection, not a confirmed complete UTME paper.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

For real x, determine the maximum value of y=3x²+5x−3.

  1. 6
  2. 0
  3. 2
  4. No correct option
Answer and explanation

D: No correct option

The coefficient of x² is positive, so the parabola opens upwards and y grows without bound as |x| increases. It has a minimum, y=3(x+5/6)²−61/12, but no finite maximum; none of the numerical options is a maximum.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Find the derivative of y=2x²(2x−1) at x=−1.

  1. 18
  2. 16
  3. −4
  4. −6
Answer and explanation

B: 16

Expand y=2x²(2x−1)=4x³−2x². Then dy/dx=12x²−4x. At x=−1 this is 12+4=16.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Evaluate 241.34(3×10⁻³)², correct to four significant figures.

  1. 0.0014
  2. 0.001448
  3. 0.0022
  4. 0.002172
Answer and explanation

D: 0.002172

First square 3×10⁻³ to obtain 9×10⁻⁶. Multiplying by 241.34 gives 0.00217206. To four significant figures, keep 2,1,7,2; the next digit is 0, so the result is 0.002172.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Three children share a basket of mangoes. The first takes 1/4 of the mangoes, and the second takes 3/4 of the remainder. What fraction of all the mangoes does the third receive?

  1. 3/16
  2. 7/16
  3. 9/16
  4. 13/16
Answer and explanation

A: 3/16

After the first child takes 1/4, the remainder is 3/4. The second takes 3/4 of that remainder, leaving 1/4 of it: (1/4)(3/4)=3/16 for the third child.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Simplify (0.00275×0.00640)/(0.025×0.08) and express the result in standard form.

  1. 8.8×10⁻¹
  2. 8.8×10⁻²
  3. 8.8×10⁻³
  4. 8.8×10³
Answer and explanation

C: 8.8×10⁻³

The numerator is 0.00275×0.00640=0.0000176 and the denominator is 0.025×0.08=0.002. Dividing gives 0.0088=8.8×10⁻³.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Three brothers share a profit. The first receives 1/3 of the total, and the second receives 2/3 of the remainder. The third receives the remaining ₦12,000. Find the total profit.

  1. ₦60,000
  2. ₦54,000
  3. ₦48,000
  4. ₦42,000
Answer and explanation

B: ₦54,000

The first brother leaves 2/3 of the profit. The second takes 2/3 of that, leaving 1/3×2/3=2/9 for the third. Thus (2/9)P=12000 and P=₦54,000. The shares ₦18,000,₦24,000,₦12,000 add to ₦54,000.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Each interior angle of a regular polygon is 140°. How many sides does it have?

  1. 9
  2. 8
  3. 7
  4. 5
Answer and explanation

A: 9

Each exterior angle is 180°−140°=40°. Exterior angles total 360°, so the number of sides is 360/40=9.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

A metal pipe is 3 cm thick and has an internal radius of 10 cm. Find the volume of metal in a 3 m length of pipe.

  1. 153π cm³
  2. 207π cm³
  3. 15,300π cm³
  4. 20,700π cm³
Answer and explanation

D: 20,700π cm³

The outer radius is 10+3=13 cm, and 3 m=300 cm. Subtract inner cylinder volume from outer: π(13²−10²)×300=π×69×300=20,700π cm³.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

The values 4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the sector angles for values greater than or equal to 16.

  1. 48°
  2. 84°
  3. 92°
  4. 276°
Answer and explanation

D: 276°

The values total 120. Those at least 16 are 16, 30, 20 and 26, totalling 92. Their share of the full circle is (92/120)×360°=276°.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

The mean of ten positive numbers is 16. After another number is added, the mean becomes 18. Find the eleventh number.

  1. 3
  2. 16
  3. 38
  4. 30
Answer and explanation

C: 38

The first ten numbers total 10×16=160. Eleven numbers with mean 18 total 11×18=198. The added number is 198−160=38.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

A car travels P km from Calabar to Enugu at an average speed of U km/h, then Q km to Benin at an average speed of W km/h. Find its average speed for the complete journey.

  1. (P+Q)/(PW+QU)
  2. UW(P+Q)/(PW+QU)
  3. UW(P+Q)/(PW)
  4. UW/(PW+QU)
Answer and explanation

B: UW(P+Q)/(PW+QU)

Average speed is total distance divided by total time. The two journey times are P/U and Q/W hours, so the average is (P+Q)/(P/U+Q/W)=UW(P+Q)/(PW+QU).

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

If g(x)=x²+3x, find g(x+1)−g(x).

  1. x+2
  2. 2(x+2)
  3. 2x+1
  4. x²+4
Answer and explanation

B: 2(x+2)

Substitute x+1: g(x+1)=(x+1)²+3(x+1)=x²+5x+4. Subtract x²+3x to obtain 2x+4=2(x+2).

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Factorize m³ − m² + 2m − 2.

  1. (m² + 1)(m − 2)
  2. (m − 1)(m + 1)(m + 2)
  3. (m − 2)(m + 1)(m − 1)
  4. (m² + 2)(m − 1)
Answer and explanation

D: (m² + 2)(m − 1)

Group the first two terms and the last two: m²(m − 1) + 2(m − 1). Both groups contain m − 1, so the result is (m² + 2)(m − 1). Expanding this product gives m³ − m² + 2m − 2.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Find the set of all integers x satisfying −2 < 2x − 6 < 4.

  1. {2, 3, 4, 5}
  2. {2, 3}
  3. {2, 5}
  4. {3, 4}
Answer and explanation

D: {3, 4}

Add 6 to each part to obtain 4 < 2x < 10. Divide by positive 2 to get 2 < x < 5. The inequalities are strict, so neither endpoint is allowed. The only integers in this interval are 3 and 4.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

X is due east of Y. Z is 6 km due south of Y, and XZ is 12 km. What is the bearing of Z from X?

  1. 240°
  2. 150°
  3. 60°
  4. 270°
Answer and explanation

A: 240°

The east-west and north-south directions form a right angle at Y. Seen from X, Z lies southwest. If θ is the angle south of west, sin θ = 6/12 = 1/2, so θ = 30°. West has bearing 270°, hence the bearing toward Z is 270° − 30° = 240°.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

A group of market sellers each sells at least one of maize, yam and plantain. In the group, 12 sell maize, 10 sell yam and 14 sell plantain. 5 sell both plantain and maize, 4 sell both yam and maize, 2 sell yam and plantain only, and 3 sell all three. How many sellers are in the group?

  1. 25
  2. 19
  3. 18
  4. 17
Answer and explanation

A: 25

The total who sell both yam and plantain is 2 + 3 = 5, including those who sell all three. Apply inclusion-exclusion: 12 + 10 + 14 − 5 − 4 − 5 + 3 = 25. Subtracting the three pair totals removes the triple group too often, so add its 3 sellers back once.

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Practice question

Myschool 2021 collection · Original sitting and question number unconfirmed.

Let P(x) = Lx + 2kx² + 24. If x + 2 and x − 1 are factors of P(x), find L and k.

  1. L = −12, k = −6
  2. L = −2, k = 1
  3. L = −2, k = −1
  4. L = 0, k = 1
Answer and explanation

A: L = −12, k = −6

The factors give P(−2) = 0 and P(1) = 0. Thus −2L + 8k = −24 and L + 2k = −24. Double the second equation and add it to the first: 12k = −72, so k = −6 and L = −12. Then P(x) = −12(x + 2)(x − 1), confirming both factors.

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