Sec 3 E-Math Equations & Inequalities topical questions

Solve 5x − 3 = 2x + 12.

Solve (x + 4)/3 = 4.

Solve 3(2x − 1) = 4x + 7.

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

Solve x² − 4x − 12 = 0.

Solve 2(3x − 4) = 5x + 3.

Solve the inequality 4x + 9 < 25.

Solve (2x + 1)/3 − (x − 2)/4 = 1.

A school hall sells 250 tickets for a concert. Adult tickets cost $8 and child tickets cost $5, and the total takings are $1730. (a) Form two equations in a and c, where a is the number of adult tickets and c the number of child tickets. (b) Solve them to find how many of each ticket were sold.

1. (a)Form the two equations.[2]
2. (b)Solve the equations.[4]

A rectangle has a width of w cm. Its length is 3 cm more than its width and its area is 40 cm². (a) Show that w² + 3w − 40 = 0. (b) Solve the equation and state the dimensions of the rectangle.

1. (a)Show that w² + 3w − 40 = 0.[2]
2. (b)Solve and state the dimensions.[4]

Solve 3x² − 5x − 1 = 0, giving each root correct to 3 significant figures.

(a) Express x² − 8x + 3 in the form (x − p)² + q. (b) State the minimum value of x² − 8x + 3 and the value of x at which it occurs. (c) Hence solve x² − 8x + 3 = 0, giving your answers correct to 3 significant figures.

1. (a)Complete the square.[2]
2. (b)State the minimum.[1]
3. (c)Hence solve to 3 s.f.[2]

(a) Solve the inequality 4 − 3x ≥ −5. (b) Represent your answer on a number line.

1. (a)Solve the inequality.[3]
2. (b)Number-line representation.[1]

A rectangular garden is 3 m longer than it is wide. Its perimeter is 46 m. (a) Write an equation in w for the width and solve it. (b) State the dimensions of the garden.

1. (a)Form and solve the equation.[3]
2. (b)State the dimensions.[2]

Solve the simultaneous equations 5x + 2y = 23 and 3x − 2y = 9.

Solve 2/(x − 1) + 3/x = 3, giving each root correct to 3 significant figures.

The product of two consecutive even numbers is 168. Let the smaller number be n. (a) Form an equation in n and show that it simplifies to n² + 2n − 168 = 0. (b) Solve the equation and write down the two numbers.

1. (a)Show that n² + 2n − 168 = 0.[2]
2. (b)Solve and state the numbers.[3]

A courier service charges $4 for pickup plus $1.20 per kilometre. Ravi’s budget allows a fare of more than $10 but at most $16. (a) Write two inequalities in d, the distance in kilometres. (b) Solve them to find the range of distances Ravi can travel.

1. (a)Write the two inequalities.[2]
2. (b)Solve for d.[3]

A father is four times as old as his son now. In 14 years’ time he will be twice as old as his son. (a) Form an equation in the son’s present age s and solve it. (b) State both present ages and verify them.

A ball thrown upwards has height h = 20t − 5t² metres after t seconds. (a) Show that the times when the ball is 15 m high satisfy 5t² − 20t + 15 = 0. (b) Find both times. (c) By completing the square, find the greatest height reached and the time it occurs.

1. (a)Show the equation.[2]
2. (b)Find both times.[2]
3. (c)Greatest height and time.[2]