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PUTME Mathematics (Arts) past questions.

40 real Post-UTME Screening questions from 2008 to 2012, every one with a worked solution. Practise them timed, on the web, on Android, or offline on desktop.

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Questions held
40
Years covered
5
Questions per paper
40
Time allowed
30 min
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Sample Mathematics (Arts) questions, answered.

Taken straight from the papers below — one from each of the most recent years, with the answer marked and the reasoning written out.

PUTME Mathematics (Arts) 2012 · Question 36
If the mean of the numbers a,b,c,d,ea, b, c, d, e is xx, find the mean of the numbers a+k, b+2k, c−k, d−2k, ea+k,\ b+2k,\ c-k,\ d-2k,\ e.
  1. xx — correct answer
  2. x+kx+k
  3. x−kx-k
  4. 2x2x
Worked solution
The added terms are k+2k−k−2k+0=0k+2k-k-2k+0=0, so the sum is unchanged at 5x5x. The mean is still xx.
PUTME Mathematics (Arts) 2011 · Question 36
A binary operation is defined by a∗b=aba*b=a^b. If a∗2=2−aa*2=2-a, find the possible values of aa.
  1. −1,2-1, 2
  2. −2,1-2, 1 — correct answer
  3. 1,21, 2
  4. −1,−2-1, -2
Worked solution
a∗2=a2=2−aa*2=a^2=2-a, so a2+a−2=0a^2+a-2=0, i.e. (a+2)(a−1)=0(a+2)(a-1)=0. Hence a=−2a=-2 or a=1a=1.
PUTME Mathematics (Arts) 2010 · Question 36
If x+1x+1 is a factor of 2x3+3x2+kx+42x^3+3x^2+kx+4, find the value of kk.
  1. −5-5
  2. 55 — correct answer
  3. −4-4
  4. 44
  5. 33
Worked solution
By the factor theorem f(−1)=0f(-1)=0: 2(−1)3+3(−1)2−k+4=−2+3−k+4=5−k=02(-1)^3+3(-1)^2-k+4=-2+3-k+4=5-k=0, so k=5k=5.
PUTME Mathematics (Arts) 2009 · Question 36
The scores of 16 students in a mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65, 70. What is the sum of the median and modal scores?
  1. 125
  2. 130 — correct answer
  3. 140
  4. 150
Worked solution
Frequencies: 55 (1), 60 (4), 65 (6), 70 (4), 75 (1). The 8th and 9th ordered scores are both 65, so median =65=65; mode =65=65 (6 times). Sum =65+65=130=65+65=130.
PUTME Mathematics (Arts) 2008 · Question 11
Convert 72872_8 to a number in base three.
  1. 22112211
  2. 21212121
  3. 12121212
  4. 20112011 — correct answer
Worked solution
728=7×8+2=5872_8 = 7\times8+2 = 58. 58÷3=1958 \div 3 = 19 r 11; 19÷3=619\div3=6 r 11; 6÷3=26\div3=2 r 00; 2÷3=02\div3=0 r 22. Reading upwards: 201132011_3.
Every paper we hold

PUTME Mathematics (Arts), year by year.

2012
5 questions
2011
10 questions
2010
10 questions
2009
5 questions
2008
10 questions
Before you sit it

How PUTME Mathematics (Arts) is set.

Post-UTME Screening sets 40 questions in Mathematics (Arts), answered in 30 minutes — about 45 seconds a question. Practising against that clock is the part most candidates skip, and it is the part that costs marks.

We hold 40 published Mathematics (Arts) questions spanning 2008 to 2012. You can practise any single year’s paper, or sit a full timed mock that mirrors the real interface — the navigator, the flags and the auto-submit included.

Every question you get wrong comes back the next day, then at longer gaps until it sticks, and your home page leads with your weakest subjects.

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