MATHEMATICS 2023 UTME PAST QUESTION

1. EVALUATE 4610₈ – 2675₈

A. 1713₈
B. 1731₈
C. 1935₈
D. 2025₈

2.

A. 2 ⁸/₁₅
B. 5 ⁸/₁₅
C. 6 ⁷/₈
D. 8 ¹/₃

3.

A. 6
B. 2
C. 3
D. 4

4.

A. 2
B. -1
C. 1
D. -2

5.

A. ⁵/₆ √5
B. ⁶/₂₅ √5
C. ⁵/₁₁ √5
D. ⁶/₅ √5

6. SOLVE FOR X IN 27^x2 = 3^8x+3

A. 1 AND 3
B. –1 AND 1/3
C. –1/3 AND 1
D. 0 AND 1

7. SOLVE THE EQUATION log₂^x⁡ + log _x⁴ = 3

A. 1 AND 2
B. 2 AND 4
C. 1 TWICE
D. 2 TWICE

8. FIND THE REMINDER WHEN THE POLYNOMINAL 4x³ -6x+1 is divided by 2x-1.

A. 2¹/2
B. 2
C. 1/2
D. 3

9. FIND THE RANGE OF VALUE OF Y OF WHICH (2+5y)/2 - (4+3y)/5 < y + 2.

A. y > 2
B. y > –2
C. y < 2
D. y < 1

10. The simple interest on sum of money invested at 30% per annum for 4 year is N50,000, FIND THE PRINCIPAL.

A. 41666.67
B. 4166.67
C. 416.67
D. 416,666.67

11. The first and the last term of an arithmetic progression (AP) are 5 and 89 respectively. If the sum of the AP. IS 611, FIND THE COMMON DIFFERENCE.

A. 5
B. 13
C. 10
D. 7

12. THE THIRD AND THE SEVENTH TERM OF A GEOMENTRIC PROGRESSION (GP) ARE 72 AND 8/9 RESPCTIVELY. FIND THE FIFTH TERM.

A. 81
B. 648
C. 8
D. 24

13. IN A GROUP OF 72 STUDENTS, 47 STUDENTS STUDY PHYSICS, 59 STUDY CHEMISTRY AND 42 SUDY BOTH SUBJECT. HOW MANY STUDENT DO NOT STUDY ANY OF THE SUBJECTS?

A. 8
B. 25
C. 13
D. 34

14. AN OPERATION ⨂ IS DEFINED ON THE SET OF REAL NUMBER R SUCH THAT IF x, y∈R, then x ⨂ y = (x+y)/2, find (1/2⨂1/3)⨂1

A. 29/2
B. 17/2
C. 5/12
D. ½

15.

A. x= 2
B. x= -2
C. x= -8/5
D. 8/5

Find the range of the value of y for which (2+5y)/2-(4+3y)/5 < y+2.

A. Y>2
B. Y>-2
C. Y<2
D. Y>1

17. ONE OF THE PARALLEL SIDE OF A TRAPEZIUM IS LONGER THAN THE OTHER 6CM. IF THE AREA AND THE HEIGHT OF THE TRAPEZIUM ARE 180CM² AND 9CM RSPECTIVELY, FIND THE LENGTH OF THE SHORTER PARALLEL SIDE.

A. 23CM
B. 17CM
C. 18CM
D. 24CM

18. WHAT IS THE NUMBER OF SIDE OF A POLYGON WHOSE SUM OF INTERIOR ANGLE DIFFER BY 540°?

A. 8
B. 15
C. 7
D. 5

19. FINE THE VOLUME OF A CONE WHOSE SLANT HEIGHT IS 17CM AND RADIUS OF BASE IS 8CM [TAKE π = 22/7].

A. 893.5CM³
B. 1003.5CM³
C. 2003.5CM³
D. 4691.5CM³

20. IF THE VOLUME OF TWO SPHERE ARE IN THE RATIO 64:27. WHAT IS THE RATIO OF THEIR SURFACE areas

A. 4:3
B. 9:16
C. 16:9
D. 3:4

21. IF A SOLID METAL CYLINDER OF RADIUS 7.5CM AND HEIGHT 10CM IS MELTED AND RECASTED INTO A SPHERE, WHAT THEN IS THE RADIUS OF THE SPHERE?

A. 1/3CM
B. 13/2
C. 7/8CM
D. 15/2CM

22. WHICH OF THE FOLLOWING REPRESENTS (A∪B)∩(A∩B) ON A VEN DIAGRAM?

23. EVALUATE 10!/2!7!

A. 360
B. 36
C. 40
D. 100

24. FIND THE EQUATION OF ALINE THAT PASSES THROUGH THE POINT (1,2) AND WHOSE GRADIENT IS 1/3.

A. 3Y+ x =5
B. 3y+x=7
C. 3y-x=7
D. Y-3x=7

25. What is the value of n if n/(9! )+1/8!=100/10!?

A. 4
B. 3
C. 2
D. 1

26. Find the variance of the text observations 4.1,4, 4.2, 4.3

A. 0.3
B. 0.28
C. 0.31
D. 0.27

27. WHAT IS THE VALUE OF LIM (X^2-9)/(X-3)

A. INFINITY
B. 0
C. 3
D. 6

28. IF |7X-4| < 3, THEN

A. -3 ≤ X ≤3
B. X≤ 1/7
C. 1/7≤ X ≤1
D. 1/7≤X<1

29. A COMMITTEE OF FIVE TO BE SELECTED FROM A GROUP OF 8 MEN AND 10 WOMEN. HOW MANY WAYS CAN THIS BE DONE IF THE COMMITTEE MUST CONSIST 2 MEN AND 3 WOMEN?

A. 308
B. 3360
C. 252
D. 120

SIMPLIFY (COS 60°+SIN 30°)/(1+COS 45)(1-SIN 45°)

A. -1
B. 1
C. 2
D. -2

31. INTEGRATE ∫X/(X^2+1) dx

A. 1/2 in(x^2+1)+c
B. in(x^2+1)+c
C. 2in(x^2+1)
D. x/(x^3+1)+c

32. Obtain the minimum value of the function y =2x³-3x²-36x+6

A. -2
B. 3
C. -7
D. 80

33. By selling an article for 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:

A. #2,500
B. #2,700
C. #2,800
D. #3,000

34.

A. 2
B. ½
C. 4
D. 1

35.

A. 30°
B. 120°
C. 60°
D. 300°

36. 36. THE LETTER OF THE WORD UNIVERSITY ARE CUT AND PUT INTO A BOX. ONE LETTER IS DRAWN AT RANDOM FROM THE BOX. FIND THE PROBABILITY OF DRAWING A VOWEL.

A. 5/9
B. 2/5
C. ½
D. 2/9

37.in a class of 60 pupils, the statistical distribution of the numbers of pupils offering Biology, History, French, Geography, and additional mathematics is as shown in the pie chart. how many pupils offer additional.

A. 15
B. 10
C. 18
D. 12

38. In the figure, the area of the shaded segment is

A. 3π
B. 9^√3/₄
C. 3π-3^√3/₄
D. 3{^√3/₄ - π}

39. Simplify 0.0324x0.00064 / 0.48 x 0.012

A. 3.6x10²
B. 3.6x10^-2
C. 3.6x10^-3
D. 3.6x10^-4

40. Convert 241 in base 5 to base 8,

A. 71₈
B. 107₈
C. 176₈
D. 241₈