Number Worked Examples for IGCSE Maths

Question

After a 15% increase, the price of a laptop is RM 2300. Find the original price.

Solution

1. 1

   Find the multiplier

   15% increase means the multiplier is 1.15

   An increase of r% gives a multiplier of 1 + r/100.

2. 2

   Divide to find the original

   Original price = 2300 / 1.15 = RM 2000

   The final price = original x multiplier, so original = final / multiplier.

Question

RM 5000 is invested at 3.5% per year compound interest. Find the value after 4 years.

Solution

1. 1

   Write the compound interest formula

   A = P(1 + r/100)^n

   P = principal, r = rate, n = number of years.

2. 2

   Substitute values

   A = 5000(1 + 3.5/100)^4 = 5000(1.035)^4

   Substitute P = 5000, r = 3.5, n = 4.

3. 3

   Calculate

   A = 5000 x 1.1475 = RM 5737.62 (to nearest cent)

   Use your calculator: 1.035^4 = 1.14752...

Question

A rectangle has length 12.4 cm and width 8.7 cm, both measured to 1 decimal place. Find the upper and lower bounds of the area.

Solution

1. 1

   Find bounds for each measurement

   Length: LB = 12.35, UB = 12.45. Width: LB = 8.65, UB = 8.75.

   For measurements to 1 d.p., the bounds are plus or minus 0.05.

2. 2

   Calculate upper bound of area

   Upper bound = 12.45 x 8.75 = 108.9375 cm squared

   Maximum area uses the largest possible length and width.

3. 3

   Calculate lower bound of area

   Lower bound = 12.35 x 8.65 = 106.8275 cm squared

   Minimum area uses the smallest possible length and width.

Question

Calculate (3.2 x 10^5) x (4.5 x 10^3). Give your answer in standard form.

Solution

1. 1

   Multiply the numbers

   3.2 x 4.5 = 14.4

   Multiply the decimal parts first.

2. 2

   Add the powers

   10^5 x 10^3 = 10^8

   When multiplying powers of 10, add the indices.

3. 3

   Combine and adjust to standard form

   14.4 x 10^8 = 1.44 x 10^9

   14.4 is not between 1 and 10, so divide by 10 and increase the power by 1.