AQA
AS Paper 1
2019
June
Q11
11 A ball moves in a straight line and passes through two fixed points, \(A\) and \(B\), which are 0.5 m apart.
The ball is moving with a constant acceleration of \(0.39 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) in the direction \(A B\).
The speed of the ball at \(A\) is \(1.9 \mathrm {~ms} ^ { - 1 }\)
Find the speed of the ball at \(B\).
Circle your answer.
\(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(3.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(3.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
A particle \(P\), of mass \(m\) kilograms, is attached to one end of a light inextensible string.
The other end of this string is held at a fixed position, \(O\).
\(P\) hangs freely, in equilibrium, vertically below \(O\).
Identify the statement below that correctly describes the tension, \(T\) newtons, in the string as \(m\) varies.
Tick \(( \checkmark )\) one box.
\(T\) varies along the string, with its greatest value at \(O\) □
\(T\) varies along the string, with its greatest value at \(P\) □
\(T = 0\) because the system is in equilibrium □
\(T\) is directly proportional to \(m\) □
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AQA
AS Paper 1
2020
June
Q1
1 At the point ( 1,0 ) on the curve \(y = \ln x\), which statement below is correct? Tick ( \(\checkmark\) ) one box.
The gradient is negative and decreasing □
The gradient is negative and increasing
\includegraphics[max width=\textwidth, alt={}, center]{091aecd0-d812-4a8f-8596-a1c91f3bae1c-02_109_109_995_1306}
The gradient is positive and decreasing □
The gradient is positive and increasing □
AQA
AS Paper 1
2020
June
Q9
9 The diagram below shows a circle and four triangles.
\includegraphics[max width=\textwidth, alt={}, center]{091aecd0-d812-4a8f-8596-a1c91f3bae1c-12_974_739_356_648}
\(A B\) is a diameter of the circle. \(C\) is a point on the circumference of the circle.
Triangles \(A B K , B C L\) and \(C A M\) are equilateral.
Prove that the area of triangle \(A B K\) is equal to the sum of the areas of triangle \(B C L\) and triangle CAM.
AQA
AS Paper 1
2020
June
Q13
13 An object is moving in a straight line, with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), over a time period of \(t\) seconds.
It has an initial velocity \(u\) and final velocity \(v\) as shown in the graph below.
\includegraphics[max width=\textwidth, alt={}, center]{091aecd0-d812-4a8f-8596-a1c91f3bae1c-19_606_784_493_628}
Use the graph to show that
$$v = u + a t$$
\includegraphics[max width=\textwidth, alt={}, center]{091aecd0-d812-4a8f-8596-a1c91f3bae1c-21_2488_1728_219_141}