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markscheme for as pure set a paper 1
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It is designed according to a level 2015 specification. it is an As exam paper and all pure mathematics topics are covered
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2 hours AS level Mathematics Edexcel100 marks Paper 1 (Set A)
Q Answer Mark Comments
1
1 Gradient = B1
2
1
y 7 x 4 M1 Substituting “their” value for the gradient
2
into the equation y y1 m( x x1 )
1
y x9 A1 Equation correct, in this or equivalent form
2
2 Stretch; B1
Parallel to y-axis; B1 Accept ‘vertical stretch’
Scale factor 2 B1
2 x 23
3 x 1
3 a B1
x 3(3x 1) M1 Attempt at an equation in x using index
laws or taking logs on both sides
3
x A1
8
x x2 1
b log 1 or log x 2log x log x M1 Apply either
2 2
x ab
log a log b log c log or
c
log a k log a for each term
k
5 5
log x 2 or log x M1 Use laws of indices or
2 collect up like terms (this scores both M1
& A1 marks)
5
Apply log a k log a and express as
k
log x A1
2
single logarithm in log x
© Oxford University Press 2017
Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements AS level Mathematics Paper 1 (Set A)
, 4 Gradient PR × Gradient QR 1 M1 Use of m1 m2 1 for perpendicular lines
4 3 k A1
1 k 7
8 2
PQ is the diameter of the circle, since
angle subtended at circumference is 90°
Centre of circle is at
midpoint of PQ: (2, 3)
B1 Correct deduction; leading to correct
r 5 2 7 3
2 2 2
method to find radius
r 5
Area of circle: r 2 25 M1 Correctly calculating the radius
A1 Accept 78.5
dy
5 2x 3 M1 Attempt at differentiating equation of C
dx
A1 Gradient of tangent at x 2
At x 2 , m = 2(2) – 3 =1
B1 Evaluate y at x 2
M1 Use of equation of straight line
y 0 at x 2
A1
y x2
6 1 cos x 3cos x 2 0
2 M1 Use of identity
cos2 x 3cos x 3 0
M1 Find solutions for cos 𝑥
3 32 4(1)(3) 3 21
cos x
2 2 A1
cos x 0.7913 or –3.7913 (reject)
M1 Subtract first solution from 360° or other
method to find second solution
x = 37.7° A1 Both correct
or 322.3°
7 a 18 + 8C1(1)7(2x)1 + 8C2(1)6(2x)2 +
8 M1 Uses binomial theorem to expand bracket
C3(1)5(2x)3
1 + 16x + 112x2 + 448x3 A1 1 + 16x
A1 Completely correct
b 1 + 16(0.01) + 112(0.01)2 + 448(0.01)3 B1 Selects x 0.01
M1 Substitute chosen value of x into a
1.171648
A1
© Oxford University Press 2017
Acknowledgements: www.oxfordsecondary.co.uk/acknowledgements AS level Mathematics Paper 1 (Set A)
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