Simultaneous Equations - IGCSE 10 / Form 4

Dear Students,

1. Maths may appear abstract to many (please see Q1 below). But it need not be once we can relate what seems abstract to real life situation - Q2 below is my attempt to relate Q1 to real life situation to my students.

2. You will also note from Q1 that I made my students revisit Form 3 (PMR) or pre-IGCSE Yr-10 level "solving simultaneous equations involving a pair of linear equations in 2 unknowns" before introducing "solving simultaneous equations involving 1 linear equation and 1 quadratic equation or other non-linear equations" 

3. Maths is a fun subject which you can score nearly 100% if not 100%. In year 2013, I do have a Korean student (in the international school) who has twice scored 100% for A-Maths. After I quit the school in August, she enlisted me to be her tutor since 15 Oct 2013.

Enjoy & try my questions below.

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IGCSE Yr 10 / Form 4: Simultaneous Equations

Tutorial Questions No. 4

1. A relation between 2 quantitative unknowns, say x and y, may be represented mathematically as an equation (e.g. y – x = 20). The same 2 unknown (x and y) may, at the same time, be related to one another by another relation (say, 5x = y) or other equations (say, x^2 = y).
1. What do you call a pair of equations with the same 2 unknowns?
2. Can you find the values of the 2 unknowns if you have 2 different equations with the same 2 unknowns?
3. The non-graphical method of finding the values of the 2 unknowns from 2 equations with the same 2 unknown is known as what?
4. Using 2 of the above 3 equations where x and y > 0, solve the simultaneous equations:

                                                               i.      y – x = 20 and 5x = y (Both linear equations – Form 3 “Flashback”)

1.      By Substitution Method

2.      By Elimination Method

                                                             ii.      y – x = 20 and x^2 = y (1 linear and 1 quadratic – Form 4 now)

                                                            iii.      5x = y and x^2 = y (1 linear and 1 quadratic – Form 4)

2. Real-life representation of Q1: Mei Ling’s mother is y years old and Mei Ling is x years old. Write the equation to show that the mother is 20 yrs older than Mei Ling
1. When Mei Ling was x years old, her mother’s age was 5 times Mei Ling’s. How old was Mei Ling when this happened?
2. When Mei Ling was x years old, her mother’s age was the square of Mei Ling’s age. How old was Mei Ling then?
3. When Mei Ling was x years old: Her mother’s age was 5 times Mei Ling’s age and at the same time also equal to the square of Mei Ling’s age. Use the relevant simultaneous equations to find out Mei Ling’ age and her mother’s age then.
4. Draw the graphs y – x = 20 and 5x = y, for -6 < x < 6, to find out the coordinates of their point of intersection.
5. Draw the graphs of 5x = y and y = x^2, for -6 < x < 6, to find out:

                                                               i.      their points of intersection

                                                             ii.      the point of intersection when x > 0.

3. Solve the following simultaneous equations:

x + 2y = 4

x^2 + xy + y^2 = 7

4. Solve the following simultaneous equations:

x/3 + y/4 = 3/2

3/x + 4/y = 3

5. Solve the following simultaneous equations:

2(x – y) = x + y – 1 = 2x^2 – 11y^2

6. Given that (2h, 3k) are solutions to the simultaneous equations y + 2x = 4 and 2/y – 3/2x = 1, find the values of h and the corresponding values of k.

7. Solve the following simultaneous equations x – y = 1 and x^2 + 3y = 6. Give your answers correct to three decimal places.

8. Amin travels from Kajang Toll to Johor Bahru Toll at an average speed, v km/h. If he travels 10 km/hr faster, he would have arrived 25 minutes earlier. Given that the distance between the two tolls is 300 km, how long would he take to complete the journey with the average speed, v km/hr? (Extracted from opening paragraph of Form 4 Textbook Chapter 4)

9. Aminah spends RM24 and RM15 in buying chicken and duck respectively. The price of 1 kg of duck is RM2 more than chicken. If the total mass of the chicken and duck is 10 kg, determine the price per kg for chicken and duck respectively.

10. The numerator and denominator of a fraction are each increased by 3, the fraction is equivalent to 2/3. If the fraction is multiplied by itself, the result is equivalent to 25/81. Find the fraction.

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