Homework

Fractional Equations and Problem Sums involving Quadratic Equations

1. Solve the equation , giving your answers correct to 4 significant figures

where necessary.

2. Two positive numbers differ by 4 and the reciprocals of their values differ by 4/21. Find the two numbers.

3. A rectangular grass field 60 m long and 50 m wide is surrounded by a path of uniform width x m. If the area of the path is 2/5 of the area of the grass field, find the value of x.

4. Solve the equation , x ≠ –3, x ≠ –5.

5. The diagonals of a rhombus ABCD intersect at E.

(a) Given that AC = (4x + 4) cm, BD = (8x + 6) cm and AB = (5x + 2) cm, form an equation in x and show that it reduces to 5x2 – 12x – 9 = 0.

(b) Solve the equation in (a) to find the values of x.

(c) Find the perimeter and the area of the rhombus ABCD.

6. Solve the equation , x ≠ 2, x ≠ –5, giving your answers in exact form.

7. A rectangle has sides of length (2x + 3) cm and width (x + 2) cm.

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x m

x m

50 m60 m

E

D C

BA

(a) Write down expressions, in terms of x, for the perimeter and the area of the rectangle.

(b) Given that the area of the rectangle is 54 cm2, form an equation in x and use it to find the perimeter of the rectangle, giving your answer correct to 2 decimal places.

8. Solve the equation , x ≠ –8.

9. On 24 January, Halima spent $1 to buy x cucumbers.

(a) Write down an expression, in terms of x, for the cost of 1 cucumber.

On 25 January, there was a Chinese New Year clearance sale and for $1 she could buy 3 more cucumbers.

(b) Write down an expression, in terms of x, for the cost of 1 cucumber during the sale.

(c) If the cost per cucumber on 25 January is 30 cents less than the cost per cucumber on 24 January, form an equation in x, and show that it reduces to x2 + 3x – 10 = 0.

(d) Solve the equation in (c) to find the value of x. Hence, find the cost of 1 cucumber on 25 January.

10. In a robotic car race, cars have to cover a distance of 100 m.

(a) Car A, in first position, covered the distance in x seconds. Write down an expression, in terms of x, for the speed of car A.

(b) Car B, which came in second position, took 2 seconds longer. Write down an expression, in terms of x, for the speed of car B.

(c) If the difference in their speeds is 2.5 m/s, obtain a quadratic equation in x and use it to find the time taken by car A.

(d) Car C, in third position, took 2 seconds more than car B. Calculate the exact speed of car C.

End of Homework

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