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Simultaneous Equations
Question Paper 1
Level
Subject
Exam Board
Topic
Sub Topic
Booklet
Time Allowed:
A Level
Maths
OCR
Polynomials
Simultaneous Equations
Question Paper 1
54 minutes
Score:
/45
Percentage:
/100
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1
Solve the simultaneous equations
2x + y - 5 = 0,
2
[5]
2x2 + y2 = 57.
[6]
2x − y = 4.
[6]
y = x − 1.
[4]
Solve the simultaneous equations
4x2 + y2 = 10,
5
3x + y = 26.
Solve the simultaneous equations
x + 2y − 6 = 0,
4
[5]
Solve the simultaneous equations
y = 2(x − 2)2 ,
3
x 2 - y 2 = 3.
(i) Solve the simultaneous equations
y = x2 − 5x + 4,
(ii) State the number of points of intersection of the curve y = x2 − 5x + 4 and the line y = x − 1. [1]
(iii) Find the value of c for which the line y = x + c is a tangent to the curve y = x2 − 5x + 4.
6
[4]
(i) Solve the simultaneous equations
y = 2x 2 - 3x - 5,
10x + 2y + 11 = 0.
(ii) What can you deduce from the answer to part (i) about the curve y = 2x 2 - 3x - 5 and the line
10x + 2y + 11 = 0?
[5]
[1]
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7
(i) Find the gradient of the line l which has equation x + 2y = 4.
[1]
(ii) Find the equation of the line parallel to l which passes through the point (6, 5), giving your
[3]
answer in the form ax + by + c = 0, where a, b and c are integers.
(iii) Solve the simultaneous equations
y = x2 + x + 1
and
x + 2y = 4.
[4]