IGCSE Maths Equations & inequalities topical questions

Solve each equation.

1. (a)x + 7 = 12[1]
2. (b)3x = 21[1]
3. (c)2x − 5 = 9[2]

Equations and inequalities.

1. (a)Solve 4x + 3 = 2x + 11.[2]
2. (b)Solve x + 3 < 8 and show your answer on a number line.[2]

Fractions, brackets and words.

1. (a)Solve x⁄4 = 6.[1]
2. (b)Solve 3(y − 4) = 15.[2]
3. (c)I think of a number n, double it and add 5. The result is 17. Write an equation for n and solve it.[1]

Tom is three years older than twice Amy’s age. Amy is a years old.

1. (a)Write an expression for Tom’s age.[1]
2. (b)Their ages add to 30. Form an equation in a.[2]
3. (c)Solve the equation and write down both ages.[2]

Equations and inequalities.

1. (a)Solve 3x − 2 ⩾ 7.[2]
2. (b)Describe how to show your answer to part (a) on a number line.[1]
3. (c)List all the integer values that satisfy 1 < 2x < 9.[2]

Solve the simultaneous equations x + 2y = 11 and 3x − y = 12.

1. (a)Solve the pair by elimination or substitution.[3]
2. (b)Check your solution in both original equations.[2]

Solve (2x + 1)⁄3 − (x − 4)⁄2 = 3. (Extended)

1. (a)Multiply through by the common denominator and simplify to a linear equation.[2]
2. (b)Solve the equation.[2]

Solve 2x² − 7x + 2 = 0 using the quadratic formula. Give your answers correct to 2 decimal places. (Extended)

1. (a)Substitute a = 2, b = −7, c = 2 into the formula.[2]
2. (b)Find both roots correct to 2 decimal places.[2]

At a café, three juices and two muffins cost 6.90, while two juices and one muffin cost 4.10.

1. (a)Write this information as a pair of simultaneous equations.[2]
2. (b)Solve the equations to find the cost of a juice and of a muffin.[3]
3. (c)Find the total cost of five juices and four muffins.[1]

Solve these equations. (Extended)

1. (a)x² − 2x − 15 = 0.[2]
2. (b)x² = 6x.[2]
3. (c)A student divides the equation in part (b) by x and finds only x = 6. Explain the mistake.[2]

A line and a curve. (Extended)

1. (a)Show that the intersection of y = x² and y = 3x + 4 leads to x² − 3x − 4 = 0.[1]
2. (b)Solve x² − 3x − 4 = 0.[2]
3. (c)Write down the coordinates of the two intersection points.[2]

Subject of a formula and a compound inequality. (Extended)

1. (a)Make r the subject of A = πr², where r is a length.[2]
2. (b)Make t the subject of v = u + at.[2]
3. (c)Solve −3 < 2x + 1 ⩽ 7 and describe the answer on a number line.[2]

Answer this question without a calculator. (Extended)

1. (a)Make x the subject of y = (2x + 5)/3.[2]
2. (b)Make r the subject of V = (4/3)πr³.[3]
3. (c)Hence find r when V = 36π.[1]

A line and a curve meet. (Extended)

1. (a)The line y = 2x − 3 meets the curve y = x² − 4x + 5. Show that the x-coordinates of the intersection points satisfy x² − 6x + 8 = 0.[2]
2. (b)Solve x² − 6x + 8 = 0.[2]
3. (c)Find the coordinates of both intersection points.[2]