**I/GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Short Questions**

**Exam Questions: **

1) Find the area of triangle ABC (in sq. units).

2) If k, 2k−1 and 2k+1 are three consecutive terms of an A.P., what is the value of k?

**Answers:**

For I/GCSE Mathematics, you should know:

1) We're given that the coordinates of points A, B and C are **A(1,3), B(-1, 0) and C(4, 0)**.

Next, let's draw a downward line from** point A to the X-axis**, which lands on **(1, 0)** (which we will call point D).

In triangle ADC, **AD = 3 units and DC = 3 units**.

The area of triangle ADC is 1 / 2 x DC x AD

= 1 / 2 x 3 x 3 = **9 / 2 cm**^{2}.

In triangle ADB, **AD = 3 units and DB = 2 units**.

The area of triangle ADB = 1 / 2 x DB x AD

= 1 / 2 x 2 x 3 = **3 cm**^{2}

So, adding these two together:

Area of triangle ABC = **area of triangle ADC + area of triangle ABD**

= 9 / 2 + 3 = 15 / 2 = **7.5 cm**^{2}

2) The three consecutive terms k, 2k - 1 and 2k + 1 are an **arithmetic progression** (A.P.).

From this, we can understand that the **second term - first term** is **equivalent **to the **third term - second term**.

i.e.

2k - 1 - k = 2k + 1 - 2k + 1

k - 1 = 2

k = 3

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!