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      • A-Level Maths, Edexcel, June 2018, Paper Walkthroughs >
        • A-Level Maths, June 2018, Pure Paper 1 Question Walkthroughs
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      • A-Level Maths, Edexcel, June 2019, Paper Walkthroughs >
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Edexcel A-Level Maths, Pure Paper 1, June 2018
Question Walkthroughs

Pure Paper 1, 2018,Q1

1. Given that theta is small and is measured in radians, use the small angle approximations to find an approximate value of (1 - cos 4theta)/(2theta sin 3theta)​.

Pure Paper 1, 2018, Q2

2. A curve C has equation   y = x^2 - 2x - 24rootx, x>0.
ai. Find dy/dx
ii. Find d2y/dx2
b. Verify that C has a stationary point when x = 4.
c. Determine the nature of this stationary point, giving a reason for your answer.

Pure Paper 1, 2018, Q3

3. Figure 1 shows a sector AOB of a circle with centre O and radisu r cm. The angle AOB is theta radians. The area of the sector AOB is 11cm^2.
Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.

Pure Paper 1, 2018, Q4

4. The curve with equation y =2 ln(8 - x) meets the line y = x at a single point, x = alpha. Show that alpha is between 3 and 4. ​

Pure Paper 1, 2018, Q5

Given that y = 3 sin theta / (2 sin theta + 2 cos theta) show that dy/dtheta = A / (1 + sin 2theta).

Pure Paper 1, 2018, Q6

The circle C has centre A with coordinates (7, 5). The line l, with equation y = 2x + 1, is the tangent to C at the point P, as shown in the diagram. Show that an equation of the line PA is 2y + x = 17.

Pure Paper 1, 2018, Q7

Show that the integral of 2/(3x-k) with respect to x between k and 3k is independent of x.
Show that the integral of 2/(2x-k)^2 with respect to x is inversely proportional to k.

Pure Paper 1, 2018, Q8

The depth of water, D metres, in a harbour on a particular day is modelled by the formula D = 5 + 2sin(30t).

Pure Paper 1, 2018, Q9

Figure 4 shows a sketch of the curve with equation x^2 - 2xy +3y^2 = 50.
a. Show that dy/dx = (y - x)/(3y-x)

Pure Paper 1, 2018, Q10

The height above ground, H metres, of a passenger on a roller coaster can be modelled by the differential equation dH/dt = Hcos(0.25t)/40 where t is the time, in seconds, from the start of the ride.
a. Show that H = 5e^0.1sin(0.25t)
​b. State the maximum height of the passenger above the ground. The passenger reaches the maximum height for the second time, T seconds after the start of the ride. c. Find the value of T.

Pure Paper 1, 2018, Q11

Use binomial expansions to show that root (1+4x)/(1-x) = 1+5/2 x - 5/8 x.

Pure Paper 1, 2018, Q12

The value, £V, of a vintage car t years after it was first valued on 1st January 2001 is modelled by the equation V = Ap^t where A and p are constants.
Given that the value of the car was £32000 on 1st January 2005 and £50000 on 1st January 2012,
ai. find p to 4 decimal places
​ii. show that A is approximately 24 800.
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  • Home
  • Algebra
    • Algebraic expressions
    • Algebraic equations
    • Expanding brackets
    • Index notation
    • Inequalities
    • Quadratic equations
    • Sequences
    • Simultaneous equations
    • Straight line graphs
    • Substitution
  • Shapes, space and measures
    • Angles
    • Circles
    • Circle theorems
    • Compound measures
    • Construction
    • Distance/speed-time graphs
    • Length, area and volume
    • Metric and Imperial conversions
    • Metric units of measurement
    • Proof
    • Pythagoras' Theorem
    • Scale factors, similarity and congruence
    • Symmetry and reflection
    • Time
    • Trigonometry
  • Number
    • Primary Addition and Subtraction
    • Addition and subtraction
    • Basic number work
    • BODMAS/PEMDAS/BIDMAS
    • Compound percentage change
    • Decimals
    • Factors and Multiples
    • Fractions
    • Fractions, decimals and percentages
    • Money
    • Multiplication and division
    • Percentages
    • Ratio and Proportion
    • Rounding
    • Standard form
  • Statistics and Probability
    • Averages and the Range
    • Box plots
    • Collecting data
    • Pie charts
    • Probability
  • More
    • Starters >
      • Puzzles and riddles
      • Maths Wordsearches
      • More Maths Lesson Starter Ideas
    • Christmas Maths Activities
    • Internet articles
    • A-Level Maths Paper Walkthroughs >
      • A-Level Maths, Edexcel, June 2018, Paper Walkthroughs >
        • A-Level Maths, June 2018, Pure Paper 1 Question Walkthroughs
        • A-Level Maths, June 2018, Pure Paper 2, Question Walkthroughs
        • A-Level Maths, June 2018, Statistics and Mechanics, Question Walkthroughs
      • A-Level Maths, Edexcel, June 2019, Paper Walkthroughs >
        • A-Level Maths, June 2019, Pure Paper 1, Question Walkthroughs
        • A-Level Maths, June 2019, Pure Paper 2, Question Walkthrough
        • A-Level Maths, June 2019, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, October 2020, Paper Walkthroughs >
        • A-Level Maths, October 2020, Pure Mathematics Paper 1, Question Walkthroughs
        • A-Level Maths, October 2020, Pure Mathematics Paper 2, Question Walkthroughs
        • A-Level Maths, October 2020, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, October 2021, Paper Walkthroughs >
        • A-Level Maths, October 2021, Pure Mathematics, Paper 1 Walkthroughs
        • A-Level Maths, October 2021, Pure Mathematics Paper 2 Walkthroughs
        • A-Level Maths, October 2021, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, June 2022, Paper 1 Walkthroughs
    • Mathematician of the Month
    • Tricky Geometry Problems
    • DoingMaths video channel
    • DoingMaths Shop
    • Contact us
    • Privacy policy