Edexcel 2020 Pure Maths Paper 1 (pdf)
- (a) Find the first four terms, in ascending powers of x, of the binomial expansion of
(1 + 8x)1/2
giving each term in simplest form.
(b) Explain how you could use x = 1/32 in the expansion to find an approximation for √5
There is no need to carry out the calculation.
- By taking logarithms of both sides, solve the equation
43p−1 = 5210
giving the value of p to one decimal place.
- Relative to a fixed origin O
- point A has position vector 2i + 5j − 6k
- point B has position vector 3i − 3j − 4k
- point C has position vector 2i − 16j + 4k
(a) Find AB
(b) Show that quadrilateral OABC is a trapezium, giving reasons for your answer.
- The function f is defined by
f(x) = (3x - 7)/(x - 2), x ≠ 2
(a) Find f−1(7)
(b) Show that ff(x) = (ax + b)/(x - 3) where a and b are integers to be found.
- A car has six forward gears.
The fastest speed of the car
- in 1st gear is 28 km h–1
- in 6th gear is 115 km h–1
Given that the fastest speed of the car in successive gears is modelled by an
(a) find the fastest speed of the car in 3rd gear.
Given that the fastest speed of the car in successive gears is modelled by a
(b) find the fastest speed of the car in 5th gear.
- (a) Express sin x + 2 cos x in the form Rsin (x + α) where R and α are constants, R > 0 and 0 < α < 2π
Give the exact value of R and give the value of α in radians to 3 decimal places.
The temperature, θ °C, inside a room on a given day is modelled by the equation
where t is the number of hours after midnight.
Using the equation of the model and your answer to part (a),
(b) deduce the maximum temperature of the room during this day,
(c) find the time of day when the maximum temperature occurs, giving your answer to
the nearest minute.
- Figure 1 shows a sketch of a curve C with equation y = f(x) and a straight line l.
The curve C meets l at the points (−2,13) and (0,25) as shown.
The shaded region R is bounded by C and l as shown in Figure 1.
- f(x) is a quadratic function in x
- (−2,13) is the minimum turning point of y = f(x)
use inequalities to define R.
- A new smartphone was released by a company.
The company monitored the total number of phones sold, n, at time t days after the
phone was released.
The company observed that, during this time, the rate of increase of n was proportional to n
Use this information to write down a suitable equation for n in terms of t.
(You do not need to evaluate any unknown constants in your equation.)
- Figure 2 shows a sketch of the curve C with equation y = f(x) where
- (a) Use the substitution x = u2 + 1 to show that
- Circle C1 has equation x2 + y2 = 100
Circle C2 has equation (x − 15)2 + y2 = 40
- (a) Show that
cosec θ − sin θ ≡ cos θ cot θ
- A sequence of numbers a1, a2, a3, … is defined by
- A large spherical balloon is deflating.
At time t seconds the balloon has radius r cm and volume Vcm3
The volume of the balloon is modelled as decreasing at a constant rate.
(a) Using this model, show that
- The curve C has equation
- Prove by contradiction that there are no positive integers p and q such that
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