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**BTEC Level 4 Maths Assignment Sample UK**

This BTEC Level 4 Maths assignment sample in UK typically covers advanced mathematical concepts relevant to various fields such as engineering, business, and science. Students can expect to delve into topics such as calculus, statistics, algebra, and geometry, with an emphasis on practical application rather than pure theory.

Assignments may involve problem-solving scenarios, data analysis, and mathematical modelling exercises. The aim is to equip learners with the mathematical skills necessary for success in their chosen career paths or further academic pursuits. This level of study builds upon foundational mathematical knowledge and encourages critical thinking and problem-solving abilities.

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**Assignment Task 1: **

A company sells widgets for £10 each. The fixed costs of running the company are £1000 per month, and the variable costs of producing each widget are £5.

a) Write an equation to represent the total monthly cost (C) of the company.

b) Write an equation to represent the total monthly revenue (R) of the company, assuming they sell x widgets.

c) Calculate the breakeven point, i.e., the number of widgets the company needs to sell in order to cover its costs.

d) If the company sells 200 widgets in a month, calculate its profit.

**Solution:**

a) The total monthly cost (C) can be represented as:

C=Fixed costs+(Variable cost per widget×Number of widgets produced)

Given that fixed costs are £1000 and variable cost per widget is £5:

C=1000+5x

b) The total monthly revenue (R) can be represented as:

R=Price per widget×Number of widgets sold

Given that the price per widget is £10:

R=10x

c) To find the breakeven point, we set the total revenue equal to the total cost:

10x=1000+5x

10x−5x=1000

5x=1000

x=1000/5=200

So, the breakeven point is 200 widgets.

d) If the company sells 200 widgets, the total revenue is:

R=10×200=£2000

The total cost is:

C=1000+5×200=£2000

Profit = Revenue – Cost = £2000 – £2000 = £0

So, the company makes no profit when selling 200 widgets.

**Assignment Task 2:**

Solve the following simultaneous equations:

2x+3y=11

4x−2y=2

**Solution:**

To solve the simultaneous equations, we can use the method of substitution or elimination.

Let’s use the elimination method:

Multiply the first equation by 2 and the second equation by 3 to eliminate

4x+6y=22

12x−6y=6

Now, add the equations together:

(4x+6y)+(12x−6y)=22+6

16x=28

x=28/16=7/4

Now, substitute the value of x into one of the original equations. Let’s use the first one:

2(7/4)+3y=11

7/2+3y=11

3y=11−7/2

3y=22/2−7/2

3y=15/2

y=15/6=5/2

So, the solution to the simultaneous equations is

x=7/4 and y=5/2

### Assignment Task 3:

A rectangular garden has a length that is 4 meters longer than its width. If the perimeter of the garden is 36 meters, find the dimensions of the garden.

**Solution:**

Let the width of the garden be w meters.

According to the given information, the length of the garden is w+4 meters.

The perimeter of a rectangle is given by the formula:

Perimeter=2×(length+width)

Substituting the given values:

36=2×(w+(w+4))

36=2×(2w+4)

18=2w+4

2w=18−4

2w=14

w=14/2

w=7

So, the width of the garden is 7 meters.

The length of the garden is w+4=7+4=11 meters.

Therefore, the dimensions of the garden are 7 meters by 11 meters.

### Assignment Task 4 :

A triangle has one angle measuring 30∘ and another angle measuring 60∘. Find the measure of the third angle in the triangle.

**Solution:**

The sum of the angles in any triangle is always 180∘.

Given that two angles of the triangle measure 30∘ and 60∘, we can find the measure of the third angle by subtracting the sum of the known angles from 180∘:

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