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Simultaneous Equations
Question Paper
Level
A LEVEL
Exam Board
Edexcel GCE
Subject
Mathematics
Module
Core 1
Topic
Algebra
Sub-Topic
Simultaneous Equations
Booklet
Question Paper
Time Allowed:
125 minutes
Score:
/ 104
Percentage:
/100
Grade Boundaries:
C1 Algebra – Simultaneous Equations
1.
PhysicsA dMathsTutor.co
Solve the simultaneous equations
y – 3x + 2 = 0
y2 – x – 6x2 = 0
(Total 7 marks)
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2.
The first term of an arithmetic series is a and the common difference is d.
1
2
The 18th term of the series is 25 and the 21st term of the series is 32 .
(a)
Use this information to write down two equations for a and d.
(2)
(b)
Show that a = –7.5 and find the value of d.
(2)
The sum of the first n terms of the series is 2750.
(c)
Show that n is given by
n 2 − 15n = 55 × 40.
(4)
(d)
Hence find the value of n.
(3)
(Total 11 marks)
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C1 Algebra: Simultaneous Equations – Questions
2
PhysicsA dMathsTutor.co
C1 Algebra – Simultaneous Equations
3.
(a)
By eliminating y from the equations
y = x – 4,
2x2 – xy = 8,
show that
x2 + 4x – 8 = 0.
(2)
(b)
Hence, or otherwise, solve the simultaneous equations
y = x – 4,
2x2 – xy = 8,
giving your answers in the form a ± b√3, where a and b are integers.
(5)
(Total 7 marks)
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4.
Solve the simultaneous equations
y = x – 2,
y2 + x2 = 10.
(Total 7 marks)
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5.
Solve the simultaneous equations
x – 2y = 1,
x2 + y2 = 29.
(Total 6 marks)
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6.
Solve the simultaneous equations
x + y = 3,
x2 + y = 15.
(Total 6 marks)
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C1 Algebra: Simultaneous Equations – Questions
3
PhysicsA dMathsTutor.co
C1 Algebra – Simultaneous Equations
7.
Solve the simultaneous equations
x+y=2
x2 + 2y = 12.
(Total 6 marks)
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8.
The curve C has equation y = x2 – 4 and the straight line l has equation y + 3x = 0.
(a)
In the space below, sketch C and l on the same axes.
(3)
(b)
Write down the coordinates of the points at which C meets the coordinate axes.
(2)
(c)
Using algebra, find the coordinates of the points at which l intersects C.
(4)
(Total 9 marks)
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C1 Algebra: Simultaneous Equations – Questions
4
PhysicsA dMathsTutor.co
C1 Algebra – Simultaneous Equations
9.
y
Q
y 2 = 4(x – 2)
2x – 3y = 12
O
x
A
P
The diagram above shows the curve with equation y2 = 4(x – 2) and the line with
equation 2x – 3y = 12.
The curve crosses the x-axis at the point A, and the line intersects the curve at the points
P and Q.
(a)
Write down the coordinates of A.
(1)
(b)
Find, using algebra, the coordinates of P and Q.
(6)
(c)
Show that ∠PAQ is a right angle.
(4)
(Total 11 marks)
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10.
Solve the simultaneous equations
x – 3y + 1 = 0,
x2 – 3xy + y2 = 11.
(Total 7 marks)
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C1 Algebra: Simultaneous Equations – Questions
5
PhysicsA dMathsTutor.co
C1 Algebra – Simultaneous Equations
11.
y
A
R
B
O
x
The diagram above shows the line with equation y = 9 – x and the curve with equation
y = x2 – 2x + 3. The line and the curve intersect at the points A and B, and O is the
origin.
(a)
Calculate the coordinates of A and the coordinates of B.
(5)
The shaded region R is bounded by the line and the curve.
(b)
Calculate the area of R.
(7)
(Total 12 marks)
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12.
(a)
Given that 3x = 9y −1, show that x = 2y – 2.
(2)
(b)
Solve the simultaneous equations
x = 2y – 2,
x2 = y2 + 7.
(6)
(Total 8 marks)
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C1 Algebra: Simultaneous Equations – Questions
6
C1 Algebra – Simultaneous Equations
13.
(a)
PhysicsA dMathsTutor.co
Show that eliminating y from the equations
2x + y = 8,
3x2 + xy = 1
produces the equation
x2 + 8x − 1 = 0.
(2)
(b)
Hence solve the simultaneous equations
2x + y = 8,
3x2 + xy = 1
giving your answers in the form a + b√17, where a and b are integers.
(5)
(Total 7 marks)
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C1 Algebra: Simultaneous Equations – Questions
7