Question 1
1 markSolve the linear equation: \( \frac{x + 3}{2} = 5 \).
GCE O-Level · Mathematics (4052)
Equations and inequalities: Practice Questions
5 multiple-choice questions marked as you go, and 2 written questions with worked solutions. All on Equations and inequalities.
7 questions16 marksFree, no account
Question 2
1 markFind the solution set for the inequality: \( 7 - 2x \le 15 \).
Question 3
1 markSolve the simultaneous equations:
\( 2x + y = 7 \)
\( x^2 - y^2 = 8 \)
One of the possible values for \( x \) is:
Question 4
1 markFind the range of values of \( x \) satisfying both \( 3x - 5 \le 10 \) and \( 2x + 1 > 5 \).
Question 5
1 markConsider the simultaneous equations below:
\( 3x - 2y = 13 \)
\( x^2 + y^2 = 26 \)
Find the values of \( y \) that satisfy these equations.
Question 6
6 marksSolve the equation \( \frac{3}{x-2} + \frac{1}{x} = 2 \). Give your answers correct to 2 decimal places.
Write your answer out first, then check it against the worked solution.
Question 7
5 marksA rectangular plot of land has a length of \( (2x + 3) \) meters and a width of \( (x + 2) \) meters.
(a) Given that the area of the plot is \( 55 \) m\(^2\), form an equation in \( x \) and show that it simplifies to \( 2x^2 + 7x - 49 = 0 \).
(b) Solve the equation to find the value of \( x \) and hence calculate the perimeter of the plot.
Write your answer out first, then check it against the worked solution.
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