Applied mathematics · UK A-level

Edexcel Statistics & Mechanics Year 1

Choose statistical models, interpret data and translate motion into equations. Find your chapter, open the matching worked solutions, and try a short practice check.

Chapters & worked solutions

Use your textbook for the questions. Every exercise button below opens the corresponding SolutionBank PDF.

1. Data Collection

Identify the population, sampling frame and sampling method. Explain a possible source of bias in the context of the question.

Exercise 1A Exercise 1B Exercise 1C Exercise 1D Exercise 1E Mixed Exercise 1

2. Measures of Location and Spread

Distinguish a change in the centre from a change in the spread. Predict the effect of coding before calculating.

Exercise 2A Exercise 2B Exercise 2C Exercise 2D Exercise 2E Exercise 2F Mixed Exercise 2

Further practice: Coding and spread practice check.

3. Representations of Data

Read axes and units before comparing diagrams. For a histogram, use frequency density and remember that area represents frequency.

Exercise 3A Exercise 3B Exercise 3C Exercise 3D Exercise 3E Mixed Exercise 3

4. Correlation

Define the population parameter and state hypotheses clearly. Give the conclusion in context, keeping correlation separate from causation.

Exercise 4A Exercise 4B Mixed Exercise 4

5. Probability

Write events carefully and check whether cases overlap.

Exercise 5A Exercise 5B Exercise 5C Exercise 5D Mixed Exercise 5

Further practice: Counting and overlap.

6. Statistical Distributions

State the random variable and check that the model fits: fixed trial count, independence and constant success probability.

Exercise 6A Exercise 6B Exercise 6C Mixed Exercise 6

Further practice: Binomial-probability practice check.

7. Hypothesis Testing

Define the population parameter and state hypotheses clearly. Give the conclusion in context, keeping correlation separate from causation.

Exercise 7A Exercise 7B Exercise 7C Exercise 7D Mixed Exercise 7

8. Modelling in Mechanics

Extend modelling skills with clearly labelled historical physics and engineering questions.

Exercise 8A Exercise 8B Exercise 8C Exercise 8D Mixed Exercise 8

Further practice: ESAT and physics practice.

9. Constant Acceleration

Extend modelling skills with clearly labelled historical physics and engineering questions.

Exercise 9A Exercise 9B Exercise 9C Exercise 9D Exercise 9E Mixed Exercise 9

Further practice: ESAT and physics practice.

10. Forces and Motion

Extend modelling skills with clearly labelled historical physics and engineering questions.

Exercise 10A Exercise 10B Exercise 10C Exercise 10D Exercise 10E Exercise 10F Mixed Exercise 10

Further practice: ESAT and physics practice.

11. Variable Acceleration

Extend modelling skills with clearly labelled historical physics and engineering questions.

Exercise 11A Exercise 11B Exercise 11C Exercise 11D Exercise 11E Mixed Exercise 11

Further practice: ESAT and physics practice.

Review & practice-paper solutions

Review Exercises: worked solutions

Review Exercise 2

Practice Exam Paper: worked solutions

Practice Exam Paper

Textbooks and linked SolutionBank materials: Pearson Education, accessed through Physics & Maths Tutor’s Edexcel SolutionBank. Original practice questions, hints and explanations on this page: Arij Asad. This is an independent companion to the UK Edexcel 2017 series; match the chapter and exercise labels to your book. International A-level and older modular books use different numbering.

Original practice by Arij Asad

A short practice check

Try these three questions before opening the hints. They sample a few useful skills; use them to choose what to revisit, rather than as a complete assessment of the book.

1. Binomial probability

A biased coin has probability $1/3$ of landing heads on each toss. Four tosses are independent. Find the probability of at least one head.

Show a hint

The complement of at least one head is no heads.

Show the full solution

The probability of a tail on one toss is $2/3$ . Independence means that the probability of four tails is $(2/3)^4=16/81$ .

Therefore $P(\text{at least one head})=1-16/81=65/81$ .

Answer: $\dfrac{65}{81}$ .

2. Coding and measures of spread

A data set has mean $12$ and standard deviation $3$ . Every value $x$ is replaced by $y=2x-5$ . Find the mean and standard deviation of the new data set.

Show a hint

A translation changes the centre but not the spread; multiplying every value scales the spread.

Show the full solution

The mean transforms in the same way as each value: $\bar y=2\bar x-5=2(12)-5=19$ .

Subtracting $5$ does not change deviations from the mean. Multiplication by $2$ doubles their sizes, so the standard deviation is $2(3)=6$ .

Answer: Mean $19$ ; standard deviation $6$ .

3. Newton's second law and constant acceleration

A particle of mass $3\,\mathrm{kg}$ starts from rest on a smooth horizontal surface. A constant horizontal force of $12\,\mathrm{N}$ acts on it. Find its displacement after $4\,\mathrm{s}$ .

Show a hint

Find the acceleration from the horizontal resultant force, then use a constant-acceleration equation.

Show the full solution

The surface is smooth, so there is no friction. Vertically, weight and the normal reaction balance. Horizontally, $F=ma$ gives $12=3a$ , so $a=4\,\mathrm{m\,s^{-2}}$ .

With $u=0$ and $t=4$ , $s=ut+\tfrac12at^2=0+\tfrac12(4)(4^2)=32\,\mathrm{m}$ .

Answer: $32\,\mathrm{m}$ in the direction of the force.

Find the mistake

A particle has velocity $v=(6-2t)\,\mathrm{m\,s^{-1}}$ for $0\leq t\leq5$ , with $t$ in seconds. A student finds a displacement of $5\,\mathrm{m}$ and calls this the distance travelled. Find the actual distance.

Show the correction

The particle changes direction when $6-2t=0$ , at $t=3$ . Its displacement over the whole interval is indeed $[6t-t^2]_0^5=5\,\mathrm{m}$ .

From $0$ to $3$ seconds it travels $[6t-t^2]_0^3=9\,\mathrm{m}$ . From $3$ to $5$ seconds its displacement is $[6t-t^2]_3^5=-4\,\mathrm{m}$ , so it travels a further $4\,\mathrm{m}$ .

Total distance is $9+4=13\,\mathrm{m}$ .

Take the practice into a lesson

The printable sheet contains the questions first, followed by hints and full worked solutions. The editable LaTeX source is ready for Overleaf.

Practice sheet & solutions (PDF)All six sheets for Overleaf (ZIP)