Name:……………………………………………………….
AS Mathematics Test 1 2017
Total: 50 marks
Time allowed: 50 minutes
Answer all questions. Where unspecified or where the answer is not exact, give
to 3 sf.
Please set your work out neatly, working in one column only.
1
2
Expand and simplify the following:
(3√7 − √5)2
[2]
Rationalise the following:
19
[1]
√17
√3+1
√3 −1
in the form 𝑎𝑎 + √3.
3
Express
[3]
4
Simplify: (leaving your ans as a power of 2 and a power of 3)
63𝑛𝑛+1
5
6
[3]
4 𝑛𝑛−2 ×32𝑛𝑛−1
Solve for 𝑥𝑥 (showing all steps):
[3]
5(3)𝑥𝑥+1 + 3(3)𝑥𝑥 = 162
The diagram shows a triangle ABC in which A has coordinates (1,3) and B has
coordinates A(5,11) and angle ABC 90°. The point X (4,4) lies on AC. Find
(i)
(ii)
The equation of BC,
The coordinates of C.
[3]
[3]
[Please turn over]
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7
In the diagram, the points A and C lie on the x- and y- axes respectively and
the equation of AC is 2𝑦𝑦 + 𝑥𝑥 = 16. The point B has coordinates (2,2). The
perpendicular from B to AC meets AC at the point X.
(i)
Find the coordinates of X.
[4]
The point D is such that the quadrilateral ABCD has AC as a line of symmetry.
(ii) Find, by calculation, the coordinates of D.
[2]
(iii) Find, leaving your answer in surd form, the perimeter of ABCD.
[3]
8 (i) Complete the square of 𝑦𝑦 = −𝑥𝑥 2 − 2𝑥𝑥 + 5 leaving your answer in the form
𝑦𝑦 = −(𝑥𝑥 − 𝑎𝑎)2 + 𝑐𝑐.
[3]
(ii) Use part i) to write down the coordinates of the vertex.
[1]
(iii) Show clearly on a large sketch of the graph, the coordinates of the x and y
intercepts and the vertex.
[4]
9
Find the real roots of the equation:
10
2+ =
3
11
𝑥𝑥
7
[5]
√𝑥𝑥
Find the coordinates of the points of intersection of the line 𝑥𝑥 + 2𝑦𝑦 = 7and the
circle 𝑥𝑥 2 + 𝑦𝑦 2 = 10.
Solve the following inequation for values of x:
𝑥𝑥 2 − 4𝑥𝑥 + 3 > 0
12
[4]
[2]
Find the set of values of k for which the line 𝑦𝑦 = 4𝑥𝑥 + 𝑘𝑘 does not intersect the
curve y = 𝑥𝑥 2 .
End of Test
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