AS Maths Start of Year Test – 70% pass mark – MOCK – NON

AS Maths Start of Year Test – 70% pass mark – MOCK – NON CALCULATOR
54 marks
1 hour
Q1.
Simplify
..............................................................................................................................................
(Total for Question is 3 marks)
Q2.
Simplify completely
..............................................................................................................................................
(Total for Question is 3 marks)
Q3.
Simplify fully
...........................................................
(Total for question = 3 marks)
Q4.
(a) Solve
2x + 3 = x – 4
x=..................
(2)
(b) Solve
4(x – 5) = 14
x=..................
(2)
(Total for Question is 4 marks)
Q5.
–2 < n ≤ 3
(a) Represent this inequality on the number line.
(2)
(b) Solve the inequality 8x – 3 ≥ 6x + 4
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q6.
The point A has coordinates (2, 3).
The point B has coordinates (6, 8).
M is the midpoint of the line AB.
Find the coordinates of M.
Diagram NOT accurately drawn
...........................................................
(Total for Question is 2 marks)
Q7.
The diagram shows a straight line, L1, drawn on a grid.
A straight line, L2, is parallel to the straight line L1 and passes through the point (0, −5).
Find an equation of the straight line L2.
...........................................................
(Total for Question is 3 marks)
Q8.
* A is the point with coordinates (1, 3)
B is the point with coordinates (4, −1)
The straight line L goes through both A and B.
Is the line with equation 2y = 3x − 4 perpendicular to line L?
You must show how you got your answer.
(Total for Question is 4 marks)
Q9.
The straight line L has equation y = 2x − 5
Find an equation of the straight line perpendicular to L which passes through (−2, 3).
...........................................................
(Total for Question is 3 marks)
Q10.
(a) Find the value of
5°
..............................................................................................................................................
(1)
(b) Find the value of
27
1⁄3
..............................................................................................................................................
(1)
(c) Find the value of
-3
2
..............................................................................................................................................
(1)
(Total for Question is 3 marks)
Q11.
(a) Rationalise the denominator of
..............................................................................................................................................
(2)
(b) Expand and simplify
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q12.
(a) Simplify 54 × 56
...........................................................
(1)
(b) Simplify 75 ÷ 72
...........................................................
(1)
(Total for Question is 2 marks)
Q13.
(a) Write down the value of 271⁄3
..............................................................................................................................................
(1)
-½
(b) Find the value of 25
..............................................................................................................................................
(2)
(Total for Question is 3 marks)
Q14.
Solve the simultaneous equations
5x + 2y = 11
4x – 3y = 18
x=......................
y=......................
(Total for Question is 4 marks)
Q15.
The graph of y = f(x) is shown on each of the grids.
(a) On this grid, sketch the graph of y = f(x – 3)
(2)
(b) On this grid, sketch the graph of y = 2f(x)
(2)
(Total for Question is 4 marks)
Q16.
The diagram shows part of a sketch of the curve y = sin x°.
(a) Write down the coordinates of the point P.
(.............................. , ..............................)
(1)
(b) Write down the coordinates of the point Q.
(.............................. , ..............................)
(1)
Here is a sketch of the curve y = a cos bx° + c, 0 ≤ x ≤ 360
(c) Find the values of a, b and c.
a =...........................................................
b =...........................................................
c =...........................................................
(3)
(Total for Question is 5 marks)
Mark Scheme
Q1.
Q2.
Q3.
Q4.
Q5.
Q6.
Q7.
Q8.
Q9.
Q10.
Q11.
Q12.
Q13.
Q14.
Q15.
Q16.

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