Edexcel A Level Maths Specimen Papers 1-3: question paper (9MA0 SAMs)

3 A Level questions like these, with worked solutions

Written and checked by us, not taken from the Pearson Edexcel paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Trigonometry · 5 marks

   Solve the equation $\tan 2x=4\tan x$ for $0^{\circ }\le x\le {180}^{\circ }$. Give your answers to 1 decimal place where appropriate.

   Worked solution

   1. M1 for substituting the identity $\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$.
   2. M1 for rearranging to $2\tan x=4\tan x(1-{\tan }^{2}x)$.
   3. M1 for grouping terms on one side and factorising to get $2\tan x(2{\tan }^{2}x-1)=0$.
   4. A1 for finding solutions from $\tan x=0$, giving $x=0^{\circ }$ and ${180}^{\circ }$.
   5. A1 for finding solutions from ${\tan }^{2}x=0.5⟹\tan x=\pm \frac{1}{\sqrt{2}}$, giving $x={35.3}^{\circ }$ and $x={144.7}^{\circ }$.

2. Sampling and data · 5 marks

   The data in a histogram is grouped into classes. A bar representing the class $100\le x<150$ has a width of $2.5\text{ cm}$ and a height of $4\text{ cm}$. The total area of all bars in the histogram is $90{\text{ cm}}^2$. If the bar for $100\le x<150$ represents a frequency of $20$, calculate the total frequency of the entire data set.

   Worked solution

   1. M1 for calculating the area of the specified bar: $2.5\times 4=10{\text{ cm}}^2$.
   2. M1 for establishing the relationship between area and frequency: $10{\text{ cm}}^2$ represents a frequency of $20$.
   3. A1 for calculating the scale factor: $1{\text{ cm}}^2$ represents $2$ items (since $20/10=2$).
   4. M1 for using the total area to find total frequency: $90{\text{ cm}}^2\times 2$.
   5. A1 for the final answer: $180$ items.

3. Kinematics · 5 marks

   A particle moving with constant acceleration passes three points $A$, $B$ and $C$, in that order, on a straight line. The distance $AB$ is $20\text{ m}$ and the distance $AC$ is $84\text{ m}$. The speed of the particle at $B$ is $12{\text{ m s}}^{-1}$ and its speed at $C$ is $20{\text{ m s}}^{-1}$. Find the acceleration of the particle and its speed at $A$.

   Worked solution

   1. M1 for $BC=84-20=64\text{ m}$.
   2. M1 for $v^2=u^2+2as$ from $B$ to $C$: ${20}^2={12}^2+2a(64)$.
   3. A1 for $128a=256\Rightarrow a=2{\text{ m s}}^{-2}$.
   4. M1 for $v^2=u^2+2as$ from $A$ to $B$: ${12}^2=u_A^2+2(2)(20)$.
   5. A1 for $u_A^2=64\Rightarrow u_A=8{\text{ m s}}^{-1}$.

More on these topics: Trigonometry · Sampling and data · Kinematics

What this paper covers

The sample assessment materials: one specimen of each of the three papers.

Not mapped question by question yet. The topics Papers 1-3 can test:

Pure

• Proof
• Algebra and functions
• Coordinate geometry
• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors

Statistics

• Sampling and data
• Probability
• Statistical distributions
• Hypothesis testing

Mechanics

• Kinematics
• Forces and Newton's laws
• Moments

Practise these topics (opens the practice engine)

• Pure I
• Pure II
• Pure III (calculus)
• Statistics
• Mechanics

Some Paper 3 statistics questions use Edexcel's large data set (weather data). We don't write large data set questions, so use your class materials for those.