JAMB Mathematics revision

Five source-linked tasks from Myschool’s 2023 collection. Write your reasoning, then open the worked solution.

The year is the publisher’s collection label. These adapted tasks are a selected revision set, not a complete authenticated exam sitting or an official marking scheme.

Work through a question

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Question sources and worked guides

Arrangements with repeated letters

Count the distinct arrangements of all eight letters in SYLLABUS. Arrangements need not form dictionary words.

Source item 67243: Myschool’s JAMB 2023 collection

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10,080.

  1. There are eight letter positions. S occurs twice and L occurs twice; the other letters occur once.
  2. Temporarily distinguish repeated letters: there are 8! arrangements. Each actual arrangement is counted 2! × 2! times.
  3. Divide: 40320/4 = 10080.
Combine fractional powers

Find the value of 16^0.16 × 16^0.04 × 2^0.2.

Source item 67244: Myschool’s JAMB 2023 collection

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2.

  1. Combine powers with base 16: 16^(0.16 + 0.04) = 16^0.2.
  2. Rewrite 16 as 2⁴, so 16^0.2 = 2^0.8.
  3. Multiply powers with base 2: 2^(0.8 + 0.2) = 2¹ = 2.
Apply two defined operations

For a ★ b = a²b and a ◇ b = 2a + b, compute (−4 ★ 2) ◇ (7 ★ −1).

Source item 67245: Myschool’s JAMB 2023 collection

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15.

  1. Apply ★ inside the left brackets: (−4)² × 2 = 32.
  2. Apply ★ inside the right brackets: 7² × (−1) = −49.
  3. Apply ◇ to the two results: 2 × 32 + (−49) = 15.
Integrate a fractional power

Calculate the definite integral from 0 to 1 of (4x − 6x^(2/3)) dx.

Source item 67248: Myschool’s JAMB 2023 collection

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−8/5.

  1. For a power xⁿ, increase the exponent by one and divide by that new exponent.
  2. An antiderivative is 2x² − (18/5)x^(5/3). Differentiating it returns 4x − 6x^(2/3).
  3. At 1 this is 2 − 18/5 = −8/5; at 0 it is zero. Subtract the endpoint values.
Percentage decrease

A population changes from 1,230 to 1,040. Find its percentage decrease, rounded to two decimal places.

Source item 67251: Myschool’s JAMB 2023 collection

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15.45%.

  1. The decrease is 1230 − 1040 = 190.
  2. Use the original population as the denominator: 100 × 190/1230 = 15.447154…%.
  3. Round only the final percentage to two decimal places: 15.45%.