AL-HIDAAYAH ACADEMY 2024-AMC FINAL [SENIOR]

ALPHA

100

Find the obtuse angle that satisfy the equation 2sin(x) =1.

150

200

 A pyramid has a rectangular base with dimensions

 12 m by 8 m. If its height is 14 m. Calculate the volume of the pyramid.

448 cm³

300

 If 30% of x is 720. Find the value of x.

2400

400

After spending 2/5 of her money on food and 1/6 on cosmetics, a woman was left with $1300. How much did she have originally?

$3000

500

A saver invests $5000 at 5% simple interest for 4 years. How much was her investment worth by the end of this period?

$6000

BETA

100

Given that;

3x + y = 5

5x + y = 9

Find 2x +y 

3

200

Find the sum of the  roots of the quadratic equation: 

2x² - 7x + 3 = 0

3.5

300

A father is four times as old as his son, in 18 year's time, he will be twice as old. Find their present ages.

Son: 9 years

Father: 36 years

400

If (x - 5)² + k =  x² - pk - 21. Find the value of k.

46

500

In a class of 36 students 29 do Mathematics and 20 do Chemistry. If 5 students do neither, how many students do Chemistry but not Mathematics?

2 students

GAMMA

100

Find the length of a diagonal of a rectangle whose adjacent sides are 5cm and 12cm.

13cm

200

Evaluate sin30⁰cos60⁰ + cos30⁰sin60⁰

1

300

Solve the equation: 2^2x - 5(2^x) + 4 = 0

2 or 0

400

The distance covered by a train is directly proportional to the time taken for the journey. The train travels 105 kilometers in 3 hours. What distance will the train cover in 5 hours?

175

500

 If 50 is subtracted from two-third of a number, the result is equal to sum of 40 and one-fourth of that number. What is the number?

216

DELTA

100

If g(x) = 4^{x + 3} = find the value of x when g(x) = 1

- 3

200

 A girl is 6 years younger than her brother. The product of their ages is 135. Find their present ages.

Brother = 15 years

Sister = 9 years

300

 In an examination, a candidate must secure 40% marks to pass. A candidate who gets 200 marks, fails by 20 marks. what is the maximum mark for the examination ?

550

400

 The first and the third term of an exponential sequence are 8 and 18 respectively. Find the common ratio

1.5 or 3/2

500

A photograph is mounted on a rectangular piece of cardboard a cm long and b cm wide, so as to leave a border x cm wide all round the outside of the photograph. Write down and simplify an expression for the number of square centimeters in area of the border. 

2x(a+b-2x) cm²