Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
Express lga + 3lgb – 3 as a single logarithm.
Shade the region corresponding to the set given below each Venn diagram.
Solve the equation 16^(3x-2) = 8^(2x).
On the diagram above, sketch the curve y = 1 + 3sin2x for 0° ≤ x ≤ 180°. [Figure 5.1]
The curves y = x² and 3y = −2x² + 20x – 20 meet at the point A. [Figure 6.1]
The points A and B have coordinates (–2, 15) and (3, 5) respectively. The perpendicular to the line AB at the point A (–2, 15) crosses the y-axis a...
The matrices A, B and C are given by A = (2 1 / 1 3 / 2 5), B = (2 1 3 4 / 1 5 6 7) and C = (9 10). Write down, but do not evaluate, matrix product...
A body moves in a straight line such that, t s after passing through a fixed point O, its displacement from O is s m. The velocity v ms⁻¹ of the bo...
(a) A curve is such that dy/dx = ae^(1-x) - 3x², where a is a constant. At the point (1, 4), the gradient of the curve is 2.
(a) The function f is such that f(x) = 2x² – 8x + 5.
Find the value of k for which the x-axis is a tangent to the curve y = x² + (2k + 10)x + k² + 5.
The coefficient of x³ in the expansion of (2 + ax)⁵ is 10 times the coefficient of x in the expansion of (1 + (ax/3))⁴. Find the value of a.
The figure shows the graph of y= k+ m sin px for 0 ≤ x ≤ π, where k, m and p are positive constants. [Figure 3.1]
You must not use a calculator in Question 4. In the triangle ABC, angle B = 90°, AB = 4+ 2√2 and BC = 1 + √2 .
Show that 2x – 1 is a factor of 2x³ – 5x² + 10x – 4.
The figure shows the graph of a straight line with lg y plotted against x. The straight line passes through the points A (5,3) and B (15,5). [Figur...
A team of 6 members is to be selected from 6 women and 8 men.
Sketch the curve y = (2x - 5)(2x + 1) for −1 ≤ x ≤ 3, stating the coordinates of the where the curve meets the coordinate axes.
The figure shows a circle, centre O, radius r cm. The length of the arc AB of the circle is 9π cm. Angle AOB is θ radians and is 3 times angle OBA....
Relative to an origin O, points A and B have position vectors (5 -6) and (29 -13) respectively.
Solve 2cot² x – 5cosec x−1=0 for 0° < x < 180°,
Without using a calculator, express (5 + 2√3)² / (2 + √3) in the form p + q√3, where p and q are integers.
Find the coefficient of x³ in the expansion of (1 - x/2)¹².
Relative to an origin O, the position vectors of the points A and B are i – 4j and 7i + 20j respectively. The point C lies on AB and is such that A...
Find the set of values of k for which the line y = 2x – 5 cuts the curve y = x² + kx + 11 at two distinct points.
The expression x³ + 8x² + px – 25 leaves a remainder of R when divided by x – 1 and a remainder of –R when divided by x + 2.
A shelf contains 8 different travel books, of which 5 are about Europe and 3 are about other regions.
The variables x and y are related so that when lgy is plotted against lgx a straight line passing through the points (4, 12) and (6, 17) is obtaine...
The temperature, T° Celsius, of an object, t minutes after it is removed from a heat source, is given by T = 55e⁻⁰·¹ᵗ + 15.
A coastguard station receives a distress call from a ship which is travelling at 15 kmh⁻¹ on a bearing of 150°. A lifeboat leaves the coastguard st...
Solve the equation 3 sinx + 4 cosx = 0 for 0° < x < 360°.
Answer only one of the following two alternatives. EITHER The diagram shows an isosceles triangle AOB and a sector OCDEO of a circle with centre O...
Given that y = sin 3x, find dy/dx
(a) An outdoor club has three sections, walking, biking and rock-climbing. Using & to denote the set of all members of the club and W, B and R to d...
Given that A = (2 1 / -2 5)
Prove that 1/(1 - sinx) - 1/(1 + sinx) = 2 tanx secx.
Given that y = x√2x + 15, show that dy/dx = k(x + 5)/√2x + 15, where k is a constant to be found.
The line y = 3x – 9 intersects the curve 49x² – y² + 42x + 8y = 247 at the points A and B. Find the length of the line AB.
A particle moves in a straight line so that, t s after passing through a fixed point O, its velocity, v ms⁻¹, is given by v = 60/(3t + 4)².
Solve 3ˣ = 200, giving your answer to 2 decimal places.
Solutions to this question by accurate drawing will not be accepted. The diagram shows the quadrilateral ABCD in which A is the point (4, 2) and B ...
A function f is defined by f : x → 18 + 16x – 2x² for x ∈ R.
Sketch the graph of y = |2x – 5|, showing the coordinates of the points where the graph meets the coordinate axes.
The expression 2x³ + ax² + bx – 30 is divisible by x + 2 and leaves a remainder of –35 when divided by 2x – 1. Find the values of the constants a a...
Find the set of values of k for which the line y = 2x + k cuts the curve y = x² + kx + 5 at two distinct points.
the number of 5-letter arrangements if there are no restrictions,
Find the equation of the tangent to the curve y = x³ + 2x² – 3x + 4 at the point where the curve crosses the y-axis.
Given that 15cos²θ + 2sin²θ = 7, show that tan²θ = 8/5.
The table shows values of variables x and y. ``` x | 1 | 3 | 6 | 10 | 14 y | 2.5 | 4.5 | 0 | -20 | -56 ```
Find the value of x for which 2lg x – lg(5x + 60) = 1.