Quadratic Simultaneous Equations worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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4 marks
Solve these simultaneous equations.
\(y = x - 3\)
\(xy = 28\)
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5 marks
Solve the simultaneous equations
\(x^2 + y^2 = 65\)
\(y = -2x - 10\)
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5 marks
Solve these simultaneous equations.
\(y = x^2 + 5x - 8\)
\(y = 2x - 4\)
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5 marks
The sum of two numbers is \(8\).
The sum of the squares of the two numbers is \(40\).
Work out the two numbers.
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4 marks
A rectangle has a perimeter of \(48\) cm and an area of \(119\) cm².
Find the length and the width of the rectangle.
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4 marks
Here are the equations of a curve and a straight line.
\(y = x^2 + 6x - 20\)
\(y = 4x - 5\)
They meet at two points. One of them is \((-5, -25)\).
Calculate the coordinates of the other point.
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5 marks
The line \(y = 7x - 17\) and the curve \(y = x^2 +x - 8\) meet at exactly one point.
Find the coordinates of that point.
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6 marks
The line \(y = 3x + 7\) crosses the curve \(y = x^2 - 3\) at two points, \(A\) and \(B\).
Find the length of \(AB\).
Give your answer in the form \(a\sqrt{ b }\), where \(a\) and \(b\) are integers and \(b\) is as small as possible.
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4 marks
A circle has equation \(x^2 + y^2 = {rr}\).
A straight line has equation \(y = {mm:coef}x {cc:+}\).
Show that the line and the circle do not meet.
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4 marks
The line \(y = -2x + c\) is a tangent to the curve \(y = x^2 - 12x + 8\).
Work out the value of \(c\).
Answers
- \(x = -4,\ y = -7\) or \(x = 7,\ y = 4\)
- \(x = -7,\ y = 4\) or \(x = -1,\ y = -8\)
- \(x = -4,\ y = -12\) or \(x = 1,\ y = -2\)
- \(2\) and \(6\)
- The length is \(17\) cm and the width is \(7\) cm.
- \((3, 7)\)
- \((3, 4)\)
- \(7\sqrt{ 10 }\)
- Substituting the line into the circle gives \({lead}x^2 {twomc:coefsigned}x {ccoef:+} = 0\), whose discriminant is \({disc}\). It is negative, so there is no value of \(x\) that satisfies both equations, and the line and the circle never meet.
- \(c = -17\)