Edexcel IGCSE Math A 2.7 quadratic equations

Use this quadratic-equations page to solve by factorisation, connect answers to formula form and form a quadratic from a worded or geometric context.

Exam points

Solve quadratics by factorising first, then state both roots from brackets clearly.
Use the quadratic formula or completed-square form to connect constants and solutions.
Form a quadratic equation from a context before simplifying or solving it.

Covered syllabus points

2.7.A Factorising simple quadratic equations 2.7.HA Factorising quadratic equations 2.7.HB Quadratic formula and completing the square 2.7.HC Forming quadratic equations 2.7.HD Linear and quadratic simultaneous equations

[Maximum number: 1]

Hence, solve $y^{2}-2 y-48=0$

[Maximum number: 6]

The diagram shows a trapezium.

Figure for Question 2.7 Quadratic equations question 2 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

All measurements shown on the diagram are in centimetres.
The area of the trapezium is $133 \mathrm{~cm}^{2}$

(a)

Show that $8 x^{2}-6 x-275=0$

[ 3 ]

Area of the trapezium:
$\frac12\bigl(x+5+3x-2\bigr)(2x-3)=133$ $\frac12(4x+3)(2x-3)=133$ $8x^2-12x+6x-9=266$ $8x^2-6x-275=0$

Shown.

(b)

Find the value of x.

Show your working clearly.

[ 3 ]

Solve:
$8x^2-6x-275=0$ x=6.25

Final answer:
6.25

[Maximum number: 3]

Here is a quadratic equation.

ax^2+4x+c=0

The solutions of this equation are given by

x=\frac{-4\pm2\sqrt{39}}{10}

Find the value of a and the value of c.
Show your working clearly.

\begin{gathered} a= \\ c= \end{gathered}

The denominator in the quadratic formula is 2a:
$2a=10\quad\Rightarrow\quad a=5$
The surd part gives:
$b^2-4ac=4\times39$
with b=4 and a=5:
$16-20c=156 \quad\Rightarrow\quad c=-7$

Final answer:
$a=5,\qquad c=-7$

M1 for 2a=10. M1 for using the discriminant correctly. A1 for a=5 and c=-7.

All question bank results loaded

Covered syllabus points

2.7 Quadratic equations question 1

2.7 Quadratic equations question 2

Question (a)

Question (b)

2.7 Quadratic equations question 3