Applied mathematics · UK A-level

Edexcel Statistics & Mechanics Year 2

Develop conditional probability, normal distributions, forces and kinematics. 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. Regression, Correlation and Hypothesis Testing

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

Exercise 1A Exercise 1B Exercise 1C Mixed Exercise 1

2. Conditional Probability

Write events carefully and check whether cases overlap.

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

Further practice: Counting and overlap.

3. The Normal Distribution

Sketch and shade the required region. Standardise with the standard deviation, then check which tail you need.

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

Further practice: Normal-distribution practice check.

4. Moments

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

Exercise 4A Exercise 4B Exercise 4C Exercise 4D Exercise 4E Mixed Exercise 4

Further practice: ESAT and physics practice.

5. Forces and Friction

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

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

Further practice: ESAT and physics practice.

6. Projectiles

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

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

Further practice: ESAT and physics practice.

7. Applications of Forces

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

Exercise 7A Exercise 7B Exercise 7C Exercise 7D Exercise 7E Exercise 7F Mixed Exercise 7

Further practice: ESAT and physics practice.

8. Further Kinematics

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

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

Further practice: ESAT and physics practice.

Review & practice-paper solutions

Review Exercises: worked solutions

Review Exercise 1 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. Normal distribution

$X$ is normally distributed with mean $50$ and standard deviation $4$ . Find $P(X>54)$ , giving your answer to three significant figures.

Show a hint

Standardise using the standard deviation, then choose the upper tail.

Show the full solution

With $Z=(X-50)/4$ , the threshold $X=54$ corresponds to $Z=1$ .

Hence $P(X>54)=P(Z>1)=1-\Phi(1)\approx0.158655$ , where $\Phi$ is the standard normal cumulative distribution function.

Answer: $1-\Phi(1)\approx0.159$ (three significant figures).

2. Projectiles

A particle is projected from level ground at $20\,\mathrm{m\,s^{-1}}$ , at $30^\circ$ above the horizontal. Neglect air resistance and take $g=9.8\,\mathrm{m\,s^{-2}}$ . Find its time of flight and horizontal range when it returns to the same level.

Show a hint

Resolve the initial velocity into components. Use zero vertical displacement to find the non-zero flight time.

Show the full solution

The initial horizontal and vertical velocity components are $20\cos30^\circ=10\sqrt3\,\mathrm{m\,s^{-1}}$ and $20\sin30^\circ=10\,\mathrm{m\,s^{-1}}$ .

Taking upward as positive, vertical displacement is $y=10t-4.9t^2$ . At landing, $y=0$ ; the non-zero solution is $t=10/4.9=100/49\,\mathrm{s}\approx2.04\,\mathrm{s}$ .

Horizontal velocity is constant, so the range is $(10\sqrt3)(100/49)=1000\sqrt3/49\,\mathrm{m}\approx35.3\,\mathrm{m}$ .

Answer: Time $\dfrac{100}{49}\,\mathrm{s}$ ; range $\dfrac{1000\sqrt3}{49}\,\mathrm{m}$ (approximately $2.04\,\mathrm{s}$ and $35.3\,\mathrm{m}$ ).

3. Moments and equilibrium

A uniform horizontal beam $AB$ is $4\,\mathrm{m}$ long and weighs $40\,\mathrm{N}$ . It is supported at $A$ and $B$ . A further downward load of $20\,\mathrm{N}$ acts $1\,\mathrm{m}$ from $A$ . Find the upward reactions at the two supports.

Show a hint

The beam's weight acts at its midpoint. Taking moments about one support eliminates its reaction.

Show the full solution

Let the upward reactions be $R_A$ and $R_B$ . Vertical equilibrium gives $R_A+R_B=40+20=60\,\mathrm{N}$ .

Taking moments about $A$ , $4R_B=40(2)+20(1)=100$ . Therefore $R_B=25\,\mathrm{N}$ .

It follows that $R_A=60-25=35\,\mathrm{N}$ .

Answer: $R_A=35\,\mathrm{N}$ , $R_B=25\,\mathrm{N}$ .

Find the mistake

Events $A$ and $B$ satisfy $P(A)=0.4$ , $P(B)=0.5$ and $P(A\cap B)=0.3$ . A student writes $P(A\mid B)=P(A)=0.4$ . Explain why this is wrong and find the correct conditional probability.

Show the correction

$P(A\mid B)=P(A\cap B)/P(B)=0.3/0.5=0.6$ .

The student's equality would hold for independent events. Here $P(A)P(B)=0.4(0.5)=0.2$ , which differs from $P(A\cap B)=0.3$ ; the events are not independent.

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)