# Mathematics Past Questions | JAMB, WAEC, NECO and Post UTME Past Questions

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### Question 21

Find the derivative of $$y = sin^2(5x)$$ with respect to $$x.$$

### Options

A) $$10 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x$$

B) $$5 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x$$

C) $$2 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x$$

D) $$15 \; \mathrm{sin} \; 5x \; \mathrm{cos} \; 5x$$

### Question 22

The slope of the tangent to the curve $$y = 3x^2 - 2x + 5$$ at the point $$(1, 6)$$ is

### Options

A) $$4$$

B) $$1$$

C) $$6$$

D) $$5$$

### Question 23

Evaluate $$\int \mathrm{sin} \; 3x dx$$

### Options

A) $$\frac{2}{3} \mathrm{cos} 3x + c$$

B) $$\frac{1}{3} \mathrm{cos} 3x + c$$

C) $$\frac{-1}{3} \mathrm{cos} 3x + c$$

D) $$\frac{-2}{3} \mathrm{cos} 3x + c$$

### Question 24

A circle with radius $$5$$ cm has its radius increasing at the rate of $$0.2$$ m/s. What will be the corresponding increase in the area?

### Options

A) $$2\pi$$

B) $$5\pi$$

C) $$\pi$$

D) $$4\pi$$

### Question 25

The sum of the interior angles of regular polygon is $$1800^{\circ}$$. How many sides has the polygon?

A) 16

B) 12

C) 10

D) 8

### Question 26

Find the coefficient of m in the expression of $$(\frac{m}{2} - 1\frac{1}{2})(m + \frac{2}{3})$$

### Options

A) $$-\frac{1}{6}$$

B) $$-\frac{1}{2}$$

C) $$-1$$

D) $$-1\frac{1}{6}$$

### Question 27

The volume of a cuboid is 54 cm3. If the length, width and height of the cuboid are in the ratio 2:1:2 respectively, find its total surface area

A) 108 cm2

B) 90 cm2

C) 80 cm2

D) 72 cm2

### Question 28

A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area

A) 20 cm2

B) 24 cm2

C) 48 cm2

D) 96 cm2

### Question 29

Factorise completely: 32x2y - 3y3

### Options

A) 16x2y(2 - 3xy2)

B) 8xy(4x - 6x2y2)

C) 8x2y(4 - 6xy2)

D) 16xy(2x - 3x2y2)

### Question 30

If $$x$$ and $$y$$ are variables and $$k$$ is a constant, which of the following describes an inverse relationship between $$x$$ and $$y$$?

### Options

A) $$y = kx$$

B) $$y = \frac{k}{x}$$

C) $$y = k\sqrt{x}$$

D) $$y = x + k$$