SPM Questions for Quadratic Equations

Frequently Asked Questions in SPM for Quadratic Equations

We will discuss some pass year SPM exam questions based on:

  • Solve the quadratic equations – SPM 2003, SPM 2005
  • Form a quadratic equation – SPM 2009
  • Determine the conditions for the type of roots – SPM2010

Solve the quadratic equations – SPM 2003 Paper 1 Question 3

Solve the quadratic equation 2x(x-4) =(1-x)(x+2). Give your answer correct to four significant figures.
(3 marks)

Answer:


Note: If you have any doubt, please refer back my previous post on how to solve the equation using completing the square method.


SPM 2005 Paper1 Question 5

Solve the quadratic equation x(2x-5) =2x-1. Give your answer correct to three decimal places.
(3 marks)

Answer:


Form a quadratic equation –
SPM 2009 Paper 2 Question 2

The quadratic equation x2 – 5x + 6 = 0 has roots h and k, where h > k.

(a) Find

i) the value of h and of k.
ii) the range of x if x2 – 5x + 6 > 0
(5 marks)

(b) Using the values of h and k from 2(a)(i), form the quadratic equation which has roots h + 2 and 3k – 2.
(2 marks)

Answer:

a i) For x– 5x + 6 = 0, given roots are h and k,

ii)

(b)

h + 2
= 3 + 2
= 5

3k - 2
= 3(2) - 2
= 4

SOR = 5 + 4 = 9
\text{POR = 5 x 4 = 20}

Equations:
{{x}^{2}}-(\text{SOR)}x+(\text{POR)}=0
\underline{{{x}^{2}}-9x+20=0}


Determine the conditions for the type of roots
SPM 2010 Paper1 Question 5

The quadratic equation (1-p)x2 – 6x +10 = 0, where p is a constant, has two different roots. Find the range of values of p.

(3 marks)

Answer:

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