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# Mathematics Post UTME Past Questions | Federal University of Technology Owerri (FUTO)

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### Question 1

Simplify $$(\cfrac{16}{81})^{-\frac{3}{4}}$$

### Options

A) $$\frac{8}{17}$$

B) $$\frac{27}{1}$$

C) $$\frac{27}{8}$$

D) $$\frac{2}{3}$$

E) $$\frac{9}{4}$$

### Question 2

If $$x = \cfrac{a^n + a^{-n}}{2}$$ and $$y = \cfrac{a^n - a^{-n}}{2}$$, find the value of $$x^2 - y^2$$

A) 5

B) 4

C) 1

D) 3

E) 2

### Question 3

What is the remainder when $$4x^3 - 5x + 2$$ is divided by $$(x-1)$$

A) 1

B) 2

C) 3

D) -1

E) -2

### Question 4

If $$a = 2 + \sqrt{3}$$, find the value of $$a - \frac{1}{a}$$.

### Options

A) $$\sqrt{3}$$

B) $$3\sqrt{5}$$

C) $$2\sqrt{5}$$

D) $$2\sqrt{3}$$

E) $$\sqrt{5}$$

### Question 5

The 2nd and 5th terms of a geometric progression are 24 and 81 respectively, find the common ratio.

### Options

A) $$\frac{2}{3}$$

B) $$\frac{3}{2}$$

C) $$\frac{5}{2}$$

D) $$\frac{7}{2}$$

E) $$\frac{9}{4}$$

### Question 6

A family of 5 is to sit round a dining table. In how many different ways possible can they sit?

A) 12

B) 16

C) 24

D) 8

E) 14

### Question 7

An article bought for ₦8.75 was sold for ₦6.65. What is the percentage loss?

A) 12%

B) 15%

C) 21%

D) 24%

E) 16%

### Question 8

The percentage score of 10 students in test are 12, 56, 42, 21, 25, 18, 10, 53, 42, 24, what is the median score?

A) 25.4

B) 27.6

C) 26.3

D) 27.5

E) 24.5

### Question 9

Simplify $$\cfrac{2^{n + 1} - 2^{n - 1}}{2^{n+1} - 2^n}$$

### Options

A) $$\frac{2}{3}$$

B) $$\frac{7}{2}$$

C) $$\frac{9}{2}$$

D) $$\frac{3}{2}$$

E) $$\frac{2}{5}$$

### Question 10

Find the value of x if 3(2$$^x$$) = 24.

A) 5

B) 2

C) 7

D) 8

E) 3