K/618/8087 Unit 8 Mathematics for Construction Assignment Answer Guide

This K/618/8087 Unit 8 Mathematics for Construction assignment answer guide covers the Level 4 core unit of the Pearson BTEC Higher Nationals in Construction and the Built Environment. It explains all four learning outcomes and every Pass, Merit and Distinction criterion, and works through checked, step-by-step construction examples in trigonometry, matrices, statistics, calculus, vectors and arithmetic progressions.

What the Unit 8 Mathematics for Construction assignment asks you to do

Unit 8 is usually assessed through two or more assignments made up of construction-based problems. Typical tasks ask you to set out a plot or roof using trigonometry, solve equations for quantities or costs, analyse test data such as concrete cube strengths, use calculus to find areas, volumes or the best dimensions for a design, resolve forces with vectors and check formulae with dimensional analysis. You must show full working, state units and explain what each answer means for the construction problem. For the higher grades you also evaluate your methods, check results with software and justify the techniques you used.

Learning outcomes for Unit 8

Pass, Merit and Distinction criteria explained

Some older centre briefs show the unit code J/617/6366 for Mathematics for Construction. The learning outcomes and criteria are the same in substance; this guide follows the K/618/8087 version.

How to answer LO1: trigonometry, algebra and matrices

• Draw and label a diagram for every trigonometry problem.
• State the rule you are using (sine rule or cosine rule) and why.
• Keep full accuracy until the final answer, then round sensibly (to the nearest millimetre for setting out, for example).
• For M1, write the equations as AX = B, find A⁻¹ and check the answer by substitution.

How to answer LO2: statistics

1. Present the data in a table and a suitable chart produced in software (spreadsheet or statistics package), as LO2 expects.
2. Calculate the mean and standard deviation, stating whether you used the sample (n − 1) or population formula.
3. Apply the binomial distribution to pass/fail situations and the normal distribution to measured quantities.
4. For M2, state the null and alternative hypotheses, the significance level, the test result and a conclusion in context.

How to answer LO3: calculus

For P5 and P6, show each rule as you use it. For M3, apply integration to a realistic problem, such as the area of a curved section. For D2, find stationary points, use the second derivative to prove the nature of each, and explain what the result means on site.

How to answer LO4: vectors, arithmetic progressions and dimensional analysis

• Vectors (M4): resolve each force into horizontal and vertical components, add them, then find the magnitude and direction of the resultant.
• Arithmetic progressions (P8): identify the first term a and common difference d, then use u_n = a + (n − 1)d and S_n = n/2[2a + (n − 1)d].
• Dimensional analysis (P7): write each quantity in base dimensions (M, L, T) and show both sides of a formula match.

Worked examples

Matrices (M1): plant hire rates

Site A hired an excavator for 3 hours and a dumper for 2 hours for £360. Site B hired the excavator for 1 hour and the dumper for 4 hours for £320. Find the hourly rates x (excavator) and y (dumper).

1. Matrix form: [3 2; 1 4][x; y] = [360; 320].
2. Determinant: (3 × 4) − (2 × 1) = 10.
3. Inverse: (1/10)[4 −2; −1 3].
4. x = (4 × 360 − 2 × 320) ÷ 10 = (1,440 − 640) ÷ 10 = £80 per hour.
5. y = (−1 × 360 + 3 × 320) ÷ 10 = (−360 + 960) ÷ 10 = £60 per hour.
6. Check: 3 × 80 + 2 × 60 = 360 and 80 + 4 × 60 = 320.

Probability (P4): concrete strength and brick defects

1. Cube strengths are normally distributed with mean 32 N/mm² and standard deviation 1.5 N/mm². For P(strength < 30): z = (30 − 32) ÷ 1.5 = −1.33. From tables, P(Z < −1.33) ≈ 0.0918, so about 9% of cubes are expected below 30 N/mm².
2. 5% of bricks are defective and a sample of 10 is taken. P(no defects) = 0.95¹⁰ = 0.599. P(at most one defect) = 0.95¹⁰ + 10 × 0.05 × 0.95⁹ = 0.599 + 0.315 = 0.914.

Maxima (D2): largest storage compound

1. A rectangular compound is built against an existing wall using 120 m of fencing on the other three sides. If each side perpendicular to the wall is x m, the side parallel to it is 120 − 2x m.
2. Area: A = x(120 − 2x) = 120x − 2x².
3. dA/dx = 120 − 4x. Setting this to zero gives x = 30 m.
4. d²A/dx² = −4, which is negative, so this is a maximum.
5. Dimensions: 30 m × 60 m. Maximum area: 30 × 60 = 1,800 m².

Vectors (M4): resultant cable force

1. Force 1: 12 kN at 30° to the horizontal. Components: 12 cos 30° = 10.39 kN, 12 sin 30° = 6.00 kN.
2. Force 2: 8 kN at 120°. Components: 8 cos 120° = −4.00 kN, 8 sin 120° = 6.93 kN.
3. Totals: horizontal 6.39 kN, vertical 12.93 kN.
4. Resultant: √(6.39² + 12.93²) = 14.42 kN at tan⁻¹(12.93 ÷ 6.39) = 63.7° to the horizontal.

Arithmetic progression (P8): staged scaffold costs

A scaffold costs £850 in week 1 and rises by £50 each week as lifts are added. Week 12 cost: 850 + 11 × 50 = £1,400. Total for 12 weeks: 12/2 × (2 × 850 + 11 × 50) = 6 × 2,250 = £13,500. In general, the cost in week n is 850 + 50(n − 1) = 800 + 50n.

Common mistakes that cost marks

• Leaving the calculator in radians when angles are in degrees (or the reverse when using calculus with trigonometric functions).
• Rounding too early, so final answers drift from the correct value.
• Missing or wrong units, such as giving an area in metres.
• Not saying whether the sample or population standard deviation was used.
• Finding a stationary point for D2 but not proving whether it is a maximum or minimum.
• Producing statistics by hand only, when LO2 asks for appropriate computer software.
• Giving answers with no explanation of what they mean for the construction task.

How to move from Merit to Distinction

All three Distinction criteria require judgement, not just correct calculations. For D1, evaluate your LO1 and LO2 results: how accurate were they, which assumptions did you make (for example, normality of test data) and why was your chosen method better than an alternative? For D2, analyse the meaning of the maximum or minimum and its practical limits, such as site boundaries. For D3, compare analytical vector methods with scale drawings or software, discussing accuracy, speed and when each is appropriate.

FAQs

Is Unit 8 Mathematics for Construction hard?

It covers a wide range of topics, but most problems follow set methods. Regular practice with construction examples and careful working make the biggest difference.

Can I use a calculator or software?

Yes. LO2 expects software for statistics, and calculators are normally allowed. You must still show your method so the assessor can follow it.

Which criteria go together?

D1 covers LO1 and LO2 together, D2 is linked to LO3 and D3 to LO4. Many centres assess LO1 and LO2 in one assignment and LO3 and LO4 in another.

What is the difference between K/618/8087 and J/617/6366?

Both are codes for Unit 8 Mathematics for Construction in the BTEC Higher Nationals in Construction. Check which code appears on your own brief; the learning outcomes and criteria assessed are essentially the same.

Need one-to-one support from a subject specialist? Our BTEC Level 4 (HNC) assignment help service covers planning, feedback on drafts and referencing.

For more maths support, see our BTEC Level 4 maths assignment guide and the HNC Construction and the Built Environment answer guide. If you want your working checked before submission, you can get expert help with your BTEC assignment.