מ ש ר ד ה ח י נ ו ך ה פ ד ג ו ג י ת א ש כ ו ל מ ד ע י ם על ה ו ר א ת ה מ ת מ ט י ק ה מחוון למבחן מפמ"ר לכיתה ט', רמה מצומצמת , תשע"ב טור א'

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1 ה פ ו י ת ש כ ו ל מ ע י ם על ה ו ר ת ה מ ת מ ט י ק ה כ" ייר, תשע".5.0 מחוון למחן מפמ"ר לכיתה ט', רמה מצומצמת 0, תשע" שלה סעיף תשוות טור ' ניקו מפורט והערות תשוה: סעיף III נקוות תשוה מלה נק' לכל שיעור משיעורי הזו הסור תשוה: ) (0, נקוות תשוה: > 0 x תשוה מלה נק' לכל נקוה תשוה: (,0) (,0) x = 0 x = x =, x = הערה: יש לקל כתשוה ם ת ערכי x ל. נקוות הערה: יש לקל ם תשוה מילים ול כתי לרי. תשוה מלה נק' השווה ין הפונקציות נק' רון המשווה נק' הצה נוסחת השורשים ו פירוק לפי טרינום נק' - שני פתרונות ) נק' לכל פתרון( x, תשוה: < x < תשוה: = x =, x רך חישו פשרית: x = x x x = 0 ( ) ( ) ( ) 6 x, 6 x x ה ו תשוה: נק' על טעות חישו חת והמשך עקי תשוה מלה נק' חישו ההסתרות נק' הסר נכון נק' על טעות חישו חת והמשך עקי ל טעות סעיף ' והמשך עקי סעיף ' תשוה: הסר: ההסתרות שהמחו ייעצר על צע פור רולטה ' הי ורולטה ' הי ולכן הסתרות הי המכפלה של ההסתרויות: מחוון רמה מצומצמת שנת

2 ה פ ו י ת ש כ ו ל מ ע י ם על ה ו ר ת ה מ ת מ ט י ק ה כ" ייר, תשע" נקוות תשוה מלה נק' פתיחת סוריים ) נק' כל ף( נק' כינוס ירים ומים נק' רך פתרון )הוצת ורם משותף ו פתרון מצעות נוסחת השורשים( נק' שני פתרונות ) נק' לכל פתרון( נק' על טעות חישו חת והמשך עקי תשוה: = 0 x =, x רך פתרון פשרית: x(x + ) + = (x + ) x + x + = x + x + x x = 0 x(x ) = 0 x =, x = 0 תשוה: סעיף II x(x ) (x ) הערה: לקל כל נימוק נכון תשוה: עי צוקת. נימוק פשרי: ל יתכן ש- x יהיה ורך שלילי. תשוה: שטח המשולש 5 סמ"ר. רך חישו פשרית: הצה יטויים המתימים לורכי ( ) הצלעות משולש: 5 תשוה מלה נק' תשוה נק' הצת רך חישו נק' על טעות חישו חת והמשך עקי נקוות תשוה: 50 מ" תשוה: 6 קות תשוה: 9 קות תשוה: 00MB 5 תשוה: ABG = 5 נימוק: ריוע הלכסונים חוצי זוויות. 6 נקוות תשוה מלה נק' ציון ול הזווית נק' - נימוק. הערה: נימוק חלקי מזכה נקוה חת 0 נקוות תשוה מלה 6 נק' ציון ול הזוויות ) נק' לכל זווית( נק' נימוקים ) נק' לכל נימוק(. נק' על טעות חישו חת והמשך עקי הערה: נימוק חלקי מזכה מחצית הנקוות נק' לכל נתון תשוה :.5 HDC = נימוק: DH חוצה זווית תשוה :.5 DHC = נימוק: סכום זוויות משולש הו.80 תשוה : סמ"ר תשוה 6.96 : ס"מ ו 6.97 ס"מ. 6 מחוון רמה מצומצמת שנת

3 ה פ ו י ת ש כ ו ל מ ע י ם על ה ו ר ת ה מ ת מ ט י ק ה כ" ייר, תשע" נקוות תשוה מלה 6 נק' על הטיעונים ) נק' לכל טיעון( נק' על הנימוקים ) נק' לכל נימוק, כולל משפט החפיפה( הערה: נימוק חלקי מזכה מחצית הנקוות תשוה מלה נק' סימונים נכונים נק' סימונים נכונים נק' סימון ח נכון 0 נקוות תשוה מלה 6 נק' ציון היקף המעוין נק' נימוק הערה: נימוק חלקי מזכה מחצית הנקוות נקוות תשוה מלה 6 נק' לציון הלים ) נק' לכל ול( 6 נק' נימוקים ) נק' לכל נימוק מל( הערה: נימוק חלקי מזכה מחצית הנקוות פתרון פשרי: P = P כי נתון KP = PM כי צלעות המעוין שוות זו לזו K = M כי זוויות ניות מעוין שוות זו לזו לכן: KEP MFP לפי משפט החפיפה זווית, צלע, זווית תשוה: סעיף II L = EPF תשוה: הטענות הנכונות - BH AC - - משולש ADH שווה שוקיים תשוה: ס"מ פתרון פשרי: היקף הטרפז ס"מ: AB + BC + CH + HD + DA = ס"מ = HD AB + BC + CH + DA = 0 BC = AD = HA כי טרפז שווה שוקיים השוקיים שוות ומעוין הצלעות שוות AB + BC + CH + HA = 0 היקף המעוין ס"מ מ.ש.ל תשוה : AED = כי קטע מצעים משולש מקיל לצלע השלישית תשוה 6 : ס"מ = BC כי קטע המצעים משולש שווה מחצית הצלע השלישית נקוות תשוה מלה נק' סימון התשוה הנכונה נק' - נימוק תשוה: סעיף II ס"מ > AC כי סכום שתי צלעות משולש ול מצלע שלישית מחוון רמה מצומצמת שנת

4 ה ח י נ ו ך מ ש ר מ ע י ם ש כ ו ל ה פ ו י ת ה מ ת מ ט י ק ה ה ו ר ת על טור ' כ" ייר, תשע".5.0 שלה סעיף תשוות ניקו מפורט והערות תשוה: סעיף II נקוות תשוה מלה נק' לכל שיעור משיעורי הזו הסור תשוה: ) (0, נקוות תשוה: < 0 x תשוה מלה נק' לכל נקוה תשוה: (,0) (,0) x = 0 x = x =, x = הערה: יש לקל כתשוה ם ת ערכי x ל. נקוות הערה: יש לקל ם תשוה מילים ול כתי לרי. תשוה מלה נק' השווה ין הפונקציות נק' רון המשווה נק' הצה נוסחת השורשים ו פירוק לפי טרינום נק' שני פתרונות ) נק' לכל פתרון( x, תשוה: < x < תשוה: = x =, x רך חישו פשרית: x = x + x x = 0 ( ) ( ) ( ) x, 5 8 x 5 x תשוה: תשוה: הסר: ההסתרות שהמחו ייעצר על צע פור רולטה ' הי ה ו נק' על טעות חישו חת והמשך עקי תשוה מלה נק' חישו ההסתרות נק' הסר נכון נק' על טעות חישו חת והמשך עקי ל טעות סעיף ' והמשך עקי סעיף ' ורולטה ' הי ולכן הסתרות הי המכפלה של ההסתרויות: מחוון רמה מצומצמת שנת

5 ה פ ו י ת ש כ ו ל מ ע י ם על ה ו ר ת ה מ ת מ ט י ק ה כ" ייר, תשע" נקוות תשוה מלה נק' פתיחת סוריים ) נק' כל ף( נק' כינוס ירים ומים נק' רך פתרון )הוצת ורם משותף ו פתרון מצעות נוסחת השורשים( נק' שני פתרונות ) נק' לכל פתרון( נק' על טעות חישו חת והמשך עקי תשוה: = 0 x =, x רך פתרון פשרית: x(x + ) + 9 = (x + ) x + x + 9 = x + 6x + 9 x x = 0 x(x ) = 0 x =, x = 0 הערה: לקל כל נימוק נכון תשוה: סעיף III x(x ) (x ) תשוה: שירה צוקת. נימוק פשרי: ל יתכן ש- x יהיה ורך שלילי. תשוה: שטח המשולש סמ"ר. רך חישו פשרית: הצה יטויים המתימים לורכי ( ) הצלעות משולש: תשוה מלה נק' תשוה נק' הצת רך חישו נק' על טעות חישו חת והמשך עקי נקוות תשוה: 50 מ" תשוה: 7 קות תשוה: 9 קות תשוה: 00MB 5 תשוה: KMP = 5 נימוק: ריוע הלכסונים חוצי זוויות. 6 נקוות תשוה מלה נק' ציון ול הזווית נק' - נימוק. הערה: נימוק חלקי מזכה נקוה חת 0 נקוות תשוה מלה 6 נק' ציון ול הזוויות ) נק' לכל זווית( נק' נימוקים ) נק' לכל נימוק(. נק' על טעות חישו חת והמשך עקי הערה: נימוק חלקי מזכה מחצית הנקוות נק' לכל נתון תשוה :.5 TKR = נימוק: DH חוצה זווית תשוה : 67.5 KTR = נימוק: סכום זוויות משולש הו.80 תשוה : סמ"ר תשוה.6 : ס"מ 6 5 מחוון רמה מצומצמת שנת

6 ה פ ו י ת ש כ ו ל מ ע י ם על ה ו ר ת ה מ ת מ ט י ק ה כ" ייר, תשע" נקוות תשוה מלה 6 נק' על הטיעונים ) נק' לכל טיעון( נק' על הנימוקים ) נק' לכל נימוק, כולל משפט החפיפה( הערה: נימוק חלקי מזכה מחצית הנקוות תשוה מלה נק' סימונים נכונים נק' סימונים נכונים נק' סימון ח נכון 0 נקוות תשוה מלה 6 נק' ציון היקף המעוין נק' נימוק הערה: נימוק חלקי מזכה מחצית הנקוות נקוות תשוה מלה 6 נק' לציון הלים ) נק' לכל ול( 6 נק' נימוקים ) נק' לכל נימוק מל( הערה: נימוק חלקי מזכה מחצית הנקוות פתרון פשרי: D = B כי נתון AD = BC כי צלעות ניות מקילית שוות זו לזו A = C כי זוויות ניות מקילית שוות זו לזו לכן: AED CGB לפי משפט החפיפה זווית, צלע, זווית תשוה: סעיף III EBG = ADE תשוה: הטענות הנכונות - -משולש LRM משולש שווה שוקיים KM LT - תשוה: 6 ס"מ פתרון פשרי: היקף הטרפז ס"מ: KL + LR + RM + MT + TK = 5 ס"מ = RM KL + LR + TM + TK = 6 TK = RL = LM כי טרפז שווה שוקיים השוקיים שוות ומעוין הצלעות שוות KL + LM + MT + TK = 6 היקף המעוין 6 ס"מ מ.ש.ל תשוה : 7 KAB = כי קטע מצעים משולש מקיל לצלע השלישית תשוה 8 : ס"מ = LM כי קטע המצעים משולש שווה מחצית הצלע השלישית נקוות תשוה מלה נק' סימון התשוה הנכונה נק' - נימוק תשוה: סעיף I ס"מ > KM כי סכום שתי צלעות משולש ול מצלע שלישית 6 מחוון רמה מצומצמת שנת

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