لالنضمام لمجموعات محمد ندا ( أبو يوسف )
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1 لالنضمام لمجموعات محمد ندا ( أبو يوسف ) ثالث محاضرات اسبوعيا مذكرات شرح و اختبارات سابقة مع ترجمة المصطلحات الرياضية خبرة عالية بالمنهج و شرحه و خبرة بأسئلة االختبارات شرح أكبر قدر من األسئلة لزيادة مهارة الطالب استخدام أحدث األجهزة التعليمية بالمركز االنضمام للمجموعات لراغبي المعدالت العالية فقط محمد ندا ( أبو يوسف ) محمد ندا
2 Chapter (المعادالت الخطية ( Equations Sec(-) : Linear المعادالت الخطية بمتغير واحد Linear equations in one variable Standard form is ax b المعادلة الخطية تكون بهذه الصورة القياسية 0 Example : Determine whether the following equations is linear or not If yes, find a and b حدد ماذا كانت المعادالت التالية خطية. 7x 0 is linear equation a 7, b. 6 x 5 x x 0 linear equation a, b نضع جميع الحدود بالطرف األيسر. x x 5 0 solution nonlinear : because x power is not 4. x 7 solution nonliner because x : root is not alowed l محمد ندا
3 (حل المعادالت الخطية) Example:- solve linear equations. y 0 - S. s 6 y 0 y 8 y 6 divide by نضع المتغيرات بطرف واألعداد بطرف آخر. 4x 7x 0 and check - S.s 4x 7x 0 divide by ( ) x L. H. S 4x R. H. S 7x L. H. S R. H. S. x 5 7 and check x 5 ()(7) x 5 x 5 x 6 divide by () x * L. H. S x 5 () 5 7 R. H. S محمد ندا
4 4. 5x x ( x ) 5x x 5x 5x 5x 5x االشارة على القوس أوال نوزع 0 has no solution 5. 7( x 6) 6( x ) 5( x 6) ( x ) 7x 4 6x 8 5x 0 6 4x x 60 x 6 x x 6 60 نوزع األعداد على األقواس أوال 0 4 has no solution 6. 6 y ( y ) 7y (y y ) 7y 0 6( y ) 7y 0 6y 7y 0 y 0 0 y y S.s بسط ما داخل القوس أوال x x multiply by LCM of (,5) is 5 x x (5) (5) 7(5) 5 ( x ) 5 x x 05 8x x 96 divide by (8) x S.s محمد ندا
5 8. m m LCM of (,5,4) is 60 m m (5 4) (5 4) ( 54) m 4 5m 0 m 5 m 4 5 m m, S.s ( n 0) multiply by LCM of (5,9) is (59) ( n 0) (59) 5 9 6( n 0) 40 6 n n n n S.s محمد ندا
6 Formulas :- الصيغ الرياضية : عالقة رياضية بين متغيرين أو أكثر Q : Solve each of the following formulas for the specified variables. حل الصيغ بالنسبة للمتغير المحدد. P T CM for C - P T CM P T M C C divide by P T M M z zrt. H for r multiply by H z z rt H z zrt H z r zt r divide by ( zt ) H z zt. S B PS for P - S B PS multiply by ( S B ) PS divide by S ( S B) P S ( S B) P S 6 محمد ندا
7 Gmm 4. F for d m multipy by ( d ) Fd F d Gm Gm m m m divide by ( Gm F d Gm ) 5. Solve d ( cr cz rz) for z d cr cz rz d cr cz rz d cr z (c r ) d cr z c r z d cr c r توزيع على القوس نجعل الحدود التي تحوي z باليمين نأخذ z عامل مشترك نقسم على القوس (c-r) 7 محمد ندا
8 Applications : تطبيقات رياضية على المعادالت الخطية. Find two consecutive odd integers such that three times the smaller one exceeds two times the larger one by 7 Let the first integer x Consecutive Integer متتالي عدد صحيح the second integer x فردي Odd ( three times the smaller one = two times larger + exceeds ) ثالثة أضعاف Three times ( x ) 7 x 4 7 يزيد Exceeds x x the first integer, the second integer. The sum of three consecutive even integers is 4. what are the integers. solution Let the integers x, x, x 4 Sum Even مجموع عدد زوجي * Sum of integers 4 ( x ) ( x ) ( x 4) x 6 x The even integers are, 4, 6. Find three consecutive odd integers such that the largest one is three more than twice the smallest one let the integers x, x, x 4 * the largest one is three more than twice the smallest one The largest (smallest) x 4 ( x) x x 4 x, x The integrs are,, 5 Largest one More than Smallest Twice العدد االكبر أكثر من األصغر ضعف ( مرتين ) 8 محمد ندا
9 4. The smaller of two numbers is 9 less than the larger, and their sum is 7 Find the numbers. Let the smaller number the larger number x x 9 أصغر من Less than * their sum 7 ( x) ( x 9) 7 x 9 7 x 8 divide by () x 4 numbers are 4, 5. If the width of a rectangle is 5cm more than one-half its length and perimeter is 46cm, what are the dimensions(length and width )? Let the length x the width x 5 * Perimeter of rectangle length + width ( x) ( x 5) 46 x x x the length the width () 5 Width Rectangle One-half Length Perimeter Dimensions العرض مستطيل نصف الطول المحيط األبعاد 9 محمد ندا
10 6 : A rectangle has a perimeter 84 meters. If the length is meters less than twice the width. find the dimensions of rectangle let the length x, the width x * perimeter ( length) ( width) ( x) (x ) 84 x 4x x 90 x 5 length 5, width (5) 7 7. The second angle of a triangle is 0 more than the first, and the third is 40 less than twice the first. Find the measure of each angle. let the first angle x second angle x 0 third angle x 40 * Sum of angles of triangle 80 ( x ) ( x 0) (x 40) 80 4x x 00 x 50 The angles first angle 50 second angle third angle (50) محمد ندا
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