10 - Algebraic Equations - Mathematical Sentences and Mathematical Expressions.pptx

10th Lesson - 9th Grade Mathematics (Algebraic Equations)

1. Algebraic Equations Mathematical Sentences and Mathematical Expressions

2. A _________________ in one variable is a mathematical sentence of degree ____ that can be written in the following standard form: ax 2 + bx + c = 0, where, a, b and c are real numbers a ≠ 0. When b = 0, in the equation ax 2 + bx + c = 0, the result is a quadratic equation of the form ____________. For example: x 2 – 16 = 0, 25x 2 – 81 = 0 and 5x 2 = 500. Furthermore, when c = 0, the quadratic equation is reduced to _______________. That is, in x 2 + 3x = 0 and 5x 2 – x = 0, there is no constant term, c = 0.

3.   If: b 2 – 4ac = 0, then the roots are real and equal . b 2 – 4ac > 0, then the roots are real and unequal. b 2 – 4ac < 0, then the roots are not real. The expression b 2 – 4ac, is the quadratic equation’s discriminant. The discriminant determines the nature of the roots in a quadratic equation.

4. 1 . Find the nature of the roots of the equation .   a = 1 b = -4 c = 9         Since b 2 – 4ac < 0, the roots of the equation , are not real.  

5. 2 . Find the sum and the product of the roots of the equation .   a = 1, b = -2, c = 0       Therefore, the sum of the roots of the equation, , is 2 .         Therefore, the product of the roots of the equation, , is 0.  

6. 2 . Find the nature of the roots of the equation .   a = 9 b = -8 c = -1         Since b 2 – 4ac > 0, the roots of the equation , are real and unequal.  

7. Structuring Mathematical Sentences into Mathematical Expressions

8. 1 . A number divided by thirty-six.   2 . Sixty-six subtracted from a number p .   3 . A square with an area of 16 square centimeters.   4 . The width of a rectangular plot is 5cm less than its length and its area is 75 square cm.  

9. Structuring Mathematical Sentences into Mathematical Expressions

10. Perimeter (Square)   Area (Square)   Perimeter (Rectangle)   Area (Rectangle)  

11. The length of the rectangle is 3 times its width and its area is 48 square cm.   The square lot has a perimeter of 400 centimeters.   The length of a rectangular lot is 2 cm more than its width and its perimeter is 36 cm.   The square lot has an area of 400 square centimeters.  

12. Algebraic Equations Mathematical Sentences and Mathematical Expressions

13. Learning Task #11: Translate the following verbal sentences to mathematical sentence. Then express into quadratic equations in terms of “x”. Mathematical Sentence Equation 1. The length of a wooden frame is 1 foot longer than its width and its area is equal to 12 ft 2 . 2. The length of the floor is 8 m longer than its width and its area is 20 square meters. 3. The length of a plywood is 0.9 m more than its width and its area is 0.36 m 2 . 4. The area of rectangle whose length is six less than twice its width is thirty-six. 5. The width of a rectangular plot is 5 m less than its length and its area is 84 m 2 .