Answer the following
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IGCSE Mathematics Worksheet - Differentiation (Calculus) -1
Answer the following
1.
Find the maximum value of A.
2.
(c) State whether the turning point is a maximum or a minimum.
3.
4.
Find the coordinates of the point of y=f(x) where the gradient is 8
5.
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(c) State whether the turning point is a maximum or a minimum.
3.
4.
Find the coordinates of the point of y=f(x) where the gradient is 8
5.
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IGCSE Mathematics Worksheet - Vectors-2
Answer the following
1.
OPQ is a triangle. T is the point on PQ for which PT : TQ = 2 : 1.
= a and = b.
= a and = b.
(a) Write down, in terms of a and b, an expression for .
(b) Express in terms of a and b. Give your answer in its simplest form.
2.
ABCD is a parallelogram. AB is parallel to DC. AD is parallel to BC. = p = q
Express, in terms of p and q
(i)
(ii)
= 2b = 2a = 6a
M is the midpoint of PQ and N is the midpoint of OR.
(a) Find the vector 
in terms of a and b.
in terms of a and b.
X is the midpoint of MN and Y is the midpoint of QR.
(b) Prove that XY is parallel to OR.
4. (a)Express in terms of a and/orb
(i) 
(ii)
X is the midpoint of BC.
(b) Express in terms of a and/or b
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GCSE Mathematics Worksheet - Compound Measures-1-Notes
Distance-time graphs
Acceleration
This is when:
- In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
- If an object is accelerating or decelerating, its speed can be calculated at any particular time by:
- drawing a tangent to the curve at that time
- measuring the gradient of the tangent
- The gradient of the line is equal to the acceleration of the object.
- The displacement of an object can be calculated from the area under a velocity-time graph.
Acceleration
- Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time.
- The change in velocity can be calculated using the equation:
- change in velocity = final velocity - initial velocity
- The average acceleration of an object can be calculated using the equation:
This is when:
- acceleration (α) is measured in metres per second squared (m/s²)
- change in velocity (∆v) is measured in metres per second (m/s)
- time taken (t) is measured in seconds (s)
- If an object is slowing down, it is decelerating (and its acceleration has a negative value).
- This equation applies to objects in uniform acceleration:
- This is when:
- final velocity (v) is measured in metres per second (m/s)
- initial velocity (u) is measured in metres per second (m/s)
- acceleration (a) is measured in metres per second squared (m/s2)
- displacement (s) is measured in metres (m)
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