2015 Grade 9 MTAP Math Challenge – Division Orals 15-second question (2 points each) 1.) Determine all positive number x that satisfy Answer: x = 2 2.) What is the fourth power of ? Answer: 3.) implify Answer: !.) "f a # b = Answer: 13
.
$ what is the value of %3 # !) # 12?
&.) uppose that x $ y an' an' z are are positive inte(ers suh that xy = = *$ xz = = 1+ an' yz = = 1&. What is the value of xyz ? Answer: 3+ *.) ,he yearly han(es in population of a ertain town for two onseutive years are 2+- inrease on the rst year an' 2+- 'erease on the seon' year. What is the net han(e in perent over the two year perio'? Answer: !- 'erease /.) What is the slope of the line parallel to 2 x 0 0 & y 0 0 2 = +. Answer: 2& .) ,he area of a trian(le is 1++ s4. m. What will be its area if its altitu'e is inrease' by 1+- an' its base is 'erease' by 1+-? Answer: 55 s4. m. 5.) ,he sum of two numbers is 2+1&. "f 5 is a''e' to eah of the numbers an' then eah of the resultin( numbers is 'ouble'$ what is the sum of the nal two numbers? Answer: !+** 1+.) A s4uare an' a trian(le t rian(le have the same perimeter. perimeter. "f the s4uare has area 1!! s4. m.$ what is the area of the trian(le? Answer: s4 m. 11.) 6et r an' s be the solutions of of ? Answer: &
30-second question (3 points each)
. What is the value
1.) If satises !ns"er# 1$2
, nd the sum of all numbers that .
2.) ! man "al%s 1 %m east then 1 %m north"est. &o" far is he from his startin' point !ns"er# 2-2 %m 3.) *our men "or%in' for four das can paint + cars. &o" man cars can men "or%in' for das paint !ns"er# cars
+.) he lon'er base of a trape/oid measures 10 cm and the line se'ment oinin' the midpoint of the dia'onals measures 3 cm. hat is the len'th of the shorter base !ns"er# + cm 5.) hat is the least possible alue of !ns"er# , -1$+
.) he point is the midpoint of the side 4 of equilateral trian'le !4 and 6 is the midpoint of !. &o" lon' is 46 if a side of 7!4 measures 8 cm !ns"er# 29 cm 1-minute question (5 points each) 1.) If the roots of alue of n !ns"er# 8
are t"ice those
, "hat is the
2.) he len'ths of the sides of a trian'le are 10, 19 and 21 cm. &o" lon' is the altitude of the trian'le to lon'est side !ns"er# 3.) rian'le !4 is isosceles. If : ! ; 50<, "hat are the possible measures of :4 !ns"er# 50<, 80< +.) he medians ! and 46 of 7!4 are perpendicular. *ind the len'th of !4 if 4 ; 3 cm and ! ; + cm. !ns"er# 5 cm 5.) he product of three consecutie positie inte'ers is 1 times their sum. hat is the sum of the three numbers !ns"er# 21 .) =oint 6 is on the side ! of 7!4 and points and * are chosen on the side !4 such that 6 >> 4 and 6* >> . *ind the len'th of 4 if !* ; * ; 3 cm. !ns"er# cm
lincher ?uestion 1.) In 7!4, : ; 30<. If is the foot of the altitude from ! to 4 and 6 is the midpoint of !, nd the measure of : 6. !ns"er# 30< 2.) @ne candle "ill burn completel at a uniform rate in + hours "hile another in 3 hours. !t "hat time should the t"o candles be simultaneousl li'hted so that one "ill be half the len'th of the other at #00 =A !ns"er# 3#3 =A 3.) =oints = and ? are dra"n on the sides 4 and ! of trian'le !4 such that :!?4 and : !=4 measures 110< and 80< respectiel. If point B is chosen inside 7!4 such that !B and 4B bisects :!= and :!? respectiel, "hat is the measure if :!B4 !ns"er# 5< o or ie ?uestion =oint 6 is the midpoint of the side 4 of 7!4 and * is the midpoint of !6. he line thru 4* intersects ! at . *ind the area of 7!* if the area of the trian'le is +8 cmC2. !ns"er# + cmC2
