OCR GCSE Maths: Equations and Inequalities

A picture frame has the shape of a rectangle. Its length is $(x + 5)$(x+5) cm and its width is $(x + 2)$(x+2) cm. The area of the frame is $40 \text{ cm}^2$40 cm2.

(a) Show that $x^2 + 7x - 30 = 0$x2+7x−30=0. (2 marks)

(b) Solve the equation $x^2 + 7x - 30 = 0$x2+7x−30=0. (2 marks)

(c) Hence work out the length and the width of the frame. (1 mark)

(a) Rearrange the formula $V = \dfrac{1}{3}\pi r^2 h$V=31​πr2h to make $h$h the subject. (2 marks)

(b) Rearrange the formula $x = \dfrac{y + 3}{y - 2}$x=y−2y+3​ to make $y$y the subject. (2 marks)

Solve the simultaneous equations $y = x^2 - 2x - 1,$y=x2−2x−1, $y = 2x - 4.$y=2x−4. (4 marks)

Solve $2x^2 + 6x + 1 = 0$2x2+6x+1=0, giving your answers to $2$2 decimal places. (3 marks)

Solve the inequality $4x - 3 \le 2x + 9$4x−3≤2x+9 and describe how its solution would be shown on a number line. (2 marks)

Solve $7x - 4 = 3x + 16$7x−4=3x+16. (1 mark)