Question

câu 1: A rectangle has a length of 60cm and a width of 30cm. It is cut into 2 indentical squares, 2 identical rectangles and a shaded small square. Find the area of the shaded square.
Find the area of the shaded square.

câu 2.The number of ordered pairs (x; y) where x, y ∈ N* such that x²y² - 2(x + y) is perfect square is ..........

câu 3.Let ABCD be the square with the side length 56cm. If E and F lie on CD, C respectively such that CF = 14cm and EAF = 45^o then CE = ........cm.

câu 4.

Given P(x) = (x² - 1/2 x - 1/2)¹⁰⁰⁸
If P(x) = a₂₀₁₆x²⁰¹⁶ + a₂₀₁₅x²⁰¹⁵ + ..... + a₁x + a₀
then the value of the sum a₀ + a₂ + a₄ + .... + a₂₀₁₄ is ...........

Write your answer by decimal in simplest form câu 5.Let ABC be an isoceles triangle (AB = AC) and its area is 501cm². BD is the internal bisector of the angle ABC (D ∈ AC), E is a point on the opposite ray of CA such that CE = CB. I is a point on BC such that CI = 1/2 BI. The line EI meets AB at K, BD meets KC at H. Find the area of the triangle AHC. câu 6. all roots of the polynomial P(x) = x² + 5x - 1 are also roots of the polynomial Q(x) = x³ + ax² + bx + c then the value of a + b + 6c is ............ câu 7.Suppose that the polynomial f(x) = x⁵ - x⁴ - 4x³ + 2x² + 4x + 1 has 5 solutions x₁; x₂; x₃; x₄; x₅. The other polynomial k(x) = x² - 4.
Find the value of P = k(x₁) x k(x₂) x k(x₃) x k(x₄) x k(x₅) câu 8.The smallest value of is ............. câu 9.Let ABCD be a trapezoid with bases AB, CD and O be the intersection of AC and BD. If the areas of triangle OAB, triangle OCD are 16cm², 40cm²respectively and M is the midpoint of BD, then the area of the triangle AMD is .........cm². câu 10.Bottle A contains 15% syrup. Bottle B contains 40% syrup. When these 2 bottles of syrup are mixed, the syrup content is 30% and the total volume is 600ml. How much syrup is in the bottle A at first? câu 11.Let ABCD.A'B'C'D' be a cube with AC' = √3cm. Find the total surface area of this cube. câu 12.Let ABC be a triangle with AB = 3cm, AC = 7cm. The internal bisector of the angle BAC intersects BC at D. The line passing through D and parallel to AC cuts AB at E. Find the measure of DE. câu 12.Given two numbers x, y such that (4y² - 12y + 25)(4x² + 6x + 4) = 28
The ratio of y to x is ........ câu 13.Mr.Joseph drives car from A to B at a constant speed. If the speed of the car is increased by 20%, it takes him one hour less than the usual time. If he drives at the constant speed for the first 100km before increasing the speed by 30%, it also takes him one hour less than the usual. The distance of AB is ..........km. câu 14.A triangle ABC has  = 120^o and the bisector AD (D ∈ BC). If AB = 40cm, AD = 30cm, then AC = ..... cm. câu 15.As shown in the figure, the length of BE is .............
câu 16.

Let f(x) the polynomial given by f(x) = (1 + 2x + 3x² + 4x³ + 5x⁴ + 84x⁵)
Suppose that f(x) = a_o + a₁x + a₂x² + ..... + ..... + a₅₀x⁵⁰.
The value of T = a₁ + a₂ + .... + a₅₀ is .........

a. 99¹⁰ - 1 b. 99¹⁰ c. 100¹⁰ d. 100¹⁰ - 1 câu 17.Find the area of the trapezoid ABCD, BC // AD, AB = CD = 5cm, BC = 10cm, AD = 16cm.
The area of the trapezoid ABCD is .........cm². câu 18.Find the least possible value of A = 4x² - 3x + 1/4x + 2015, where x varies in the set of positive real numbers. The least possible value of A is câu 19.