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SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
OLD	
  -­‐	
  3	
  Tests	
   NEW	
  -­‐	
  2	
  Tests	
  
TIME:	
   TIME:	
  
25	
  Minutes	
  –	
  20	
  Ques.ons	
   25	
  Minutes	
  –	
  20	
  Ques.ons	
  (No	
  C)	
  	
  
25	
  Minutes	
  –	
  18	
  Ques.ons	
   55	
  Minutes	
  –	
  38	
  Ques.ons	
  (Calc)	
  
20	
  Minutes	
  –	
  16	
  Ques.ons	
  
CONTENT:	
   CONTENT:	
  
Algebra	
  I	
  
Geometry	
  
Some	
  Algebra	
  II	
  
Algebra	
  I	
  
Geometry	
  
Algebra	
  II	
  
Trigonometry	
  
Data	
  Analysis	
  (Prob	
  &	
  Stats)	
  
What’s Different!
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
OLD	
  
	
  
Free	
  Response	
  and	
  Mul2ple	
  
Choice	
  on	
  1	
  test	
  only.	
  
	
  
¼	
  point	
  deducted	
  for	
  wrong	
  
answers	
  on	
  mul2ple	
  choice	
  
ques2ons.	
  
NEW	
  
	
  
Free	
  Response	
  and	
  Mul2ple	
  
Choice	
  on	
  both	
  (all)	
  tests.	
  
	
  
No	
  points	
  deducted	
  for	
  wrong	
  
answers.	
  
	
  
What’s Different!
 
	
  3	
  Things	
  You	
  WANT	
  to	
  	
  
	
   	
  	
  
	
   	
   	
   	
  Memorize	
  for	
  the	
  Math	
  SAT	
  
	
  
	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
1.	
  The	
  Pythagorean	
  Theorem	
   	
  a2	
  +	
  b2	
  =	
  c2	
  	
  
•  The	
  Pythagorean	
  Theorem	
  is	
  used	
  for	
  
finding	
  the	
  length	
  of	
  the	
  hypotenuse	
  of	
  a	
  
right	
  triangle.	
  While	
  that	
  is	
  great	
  and	
  
useful,	
  it	
  can	
  be	
  used	
  for	
  much	
  more.	
  	
  
	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
The	
  Pythagorean	
  Theorem	
   	
  a2	
  +	
  b2	
  =	
  c2	
  	
  
•  Instead	
  of	
  memorizing	
  the	
  distance	
  formula,	
  
you	
  can	
  simply	
  use	
  the	
  Pythagorean	
  Theorem.	
  	
  
•  The	
  30-­‐60-­‐90	
  and	
  45-­‐45-­‐90	
  special	
  right	
  
triangle	
  formulas	
  are	
  given	
  on	
  the	
  SAT,	
  the	
  
Pythagorean	
  Theorem	
  can	
  be	
  used	
  in	
  place	
  of	
  
those	
  too.	
  	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
2.	
  Pythagorean	
  Triples	
  
•  Here	
  are	
  the	
  two	
  Pythagorean	
  Triples	
  
that	
  will	
  show	
  up	
  most	
  oWen	
  on	
  the	
  SAT:	
  	
  
	
  	
  	
  
	
  	
  	
  	
  	
  	
  	
   	
  3-­‐4-­‐5	
   	
  	
  	
  as	
  32	
  +	
  42	
  =	
  52	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
	
   	
   	
  5-­‐12-­‐13	
  as	
  52	
  +	
  122	
  =	
  132	
  	
  
	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
You	
  can	
  use	
  those	
  same	
  Pythagorean	
  Triples	
  to	
  
make	
  more	
  of	
  them.	
  What	
  do	
  I	
  mean	
  by	
  “make	
  
more	
  of	
  them?”	
  Just	
  count	
  by	
  each	
  number	
  to	
  
make	
  more.	
  For	
  example,	
  count	
  by	
  3’s,	
  4’s	
  and	
  
5’s!	
  
	
  	
  	
  	
  	
  	
  	
  	
  3-­‐4-­‐5	
  will	
  also	
  create	
  as	
  6-­‐8-­‐10,	
  and	
   	
   	
  	
  
	
  	
  	
  	
  9-­‐12-­‐15,	
  and	
  so	
  on.	
  
	
  	
  	
  	
  	
  	
  	
  	
  5-­‐12-­‐13	
  will	
  do	
  the	
  same	
  as	
  10-­‐24-­‐26.	
  
	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
3.	
  Know	
  what	
  f(x)	
  means	
  
•  f(x)	
  is	
  called	
  func.on	
  nota.on	
  and	
  is	
  read	
  
f	
  of	
  x.	
  
•  f(x)	
  is	
  just	
  a	
  fancy	
  way	
  to	
  say	
  “y”	
  in	
  an	
  
equa.on	
  that	
  also	
  has	
  an	
  “x.”	
  	
  	
  
	
   	
  f(x)	
  =	
  2x	
  +	
  5	
  really	
  means	
  y	
  =	
  2x	
  +	
  5	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
3.	
  Know	
  what	
  f(x)	
  means	
  
•  f(3)	
  is	
  read	
  f	
  at	
  3.	
  	
  
	
   	
  If	
  f(x)	
  =	
  2x	
  +	
  5	
  find	
  f(3).	
  
	
   	
  Replace	
  x	
  with	
  3!	
   	
  	
  
	
   	
  f(3)	
  =	
  2(3)	
  +	
  5	
  
	
   	
  f(3)	
  =	
  6	
  +	
  5	
  
	
   	
  f(3)	
  =	
  11	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
3.	
  Know	
  what	
  f(x)	
  means	
  
•  Find	
  x	
  if	
  f(x)	
  =	
  3	
  when	
  f(x)	
  =	
  2x	
  +	
  5.	
  
	
   	
  	
  	
  	
  	
  Replace	
  f(x)	
  with	
  3!	
  	
  
	
   	
   	
  3	
  =	
  2x	
  +	
  5	
  
	
   	
   	
  -­‐2	
  =	
  2x	
  
	
   	
   	
  -­‐1	
  =	
  x	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
a
Mr.	
  D’s	
  2	
  Step	
  Method	
  for	
  Taking	
  Tests	
  
	
  	
   	
   	
   	
  (any	
  test/any	
  subject)	
  
	
  	
  
Step	
  1	
  -­‐	
  Find	
  the	
  Ques.on	
  
Step	
  2	
  -­‐	
  Answer	
  the	
  Ques.on	
  
	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
On Saturday afternoon, Armand sent m text
messages each hour for 5 hours, and Tyrone sent p
text messages each hour for 4 hours. Which of the
following represents the total number of messages
sent by Armand and Tyrone on Saturday afternoon?
A) 9mp
B) 20mp
C) 5m + 4p
D) 4m + 5p
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
On Saturday afternoon, Armand sent m text
messages each hour for 5 hours, and Tyrone sent p
text messages each hour for 4 hours. Which of the
following represents the total number of messages
sent by Armand and Tyrone on Saturday afternoon?
A) 9mp
B) 20mp
C) 5m + 4p
D) 4m + 5p
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
Kathy is a repair technician for a phone company.
Each week, she receives a batch of phones that need
repairs. The number of phones that she has left to fix
at the end of each day can be estimated with the
equation P = 108 − 23d, where P is the number of
phones left and d is the number of days she has
worked that week. What is the meaning of the value
108 in this equation?
A) Kathy will complete the repairs within 108 days.
B) Kathy starts each week with 108 phones to fix.
C) Kathy repairs phones at a rate of 108 per hour.
D) Kathy repairs phones at a rate of 108 per day.
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
Kathy is a repair technician for a phone company.
Each week, she receives a batch of phones that need
repairs. The number of phones that she has left to fix
at the end of each day can be estimated with the
equation P = 108 − 23d, where P is the number of
phones left and d is the number of days she has
worked that week. What is the meaning of the value
108 in this equation?
A y-intercept is when x = 0 or when time begins!
A) Kathy will complete the repairs within 108 days.
B) Kathy starts each week with 108 phones to fix.
C) Kathy repairs phones at a rate of 108 per hour.
D) Kathy repairs phones at a rate of 108 per day.
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
A function f satisfies f(2) = 3 and f(3) = 5. A
function g satisfies g(3) = 2 and g(5) = 6.
What is the value of f(g(3))?
A) 2
B) 3
C) 5
D) 6
Since g(3) = 2, f(g(3)) = f(2)
f(2) = 3
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
A function f satisfies f(2) = 3 and f(3) = 5. A
function g satisfies g(3) = 2 and g(5) = 6.
What is the value of f(g(3))?
A) 2
B) 3
C) 5
D) 6
Since g(3) = 2, f(g(3)) = f(2)
f(2) = 3
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
If 16 + 4x is 10 more than 14, what is the value of 8x?
A) 2
B) 6
C) 16
D) 80
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
If 16 + 4x is 10 more than 14, what is the value of 8x?
A) 2
B) 6
C) 16
D) 80
16 + 4x = 24
Multiply by 2 to get 8x
32 + 8x = 48
8x = 16
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
The complete graph of the function f is shown in the
xy-plane above. For what value of x is the value of f(x)
at its minimum?
A) −5 C) −2
B) −3 D) 3
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
The complete graph of the function f is shown in the
xy-plane above. For what value of x is the value of f(x)
at its minimum?
A) −5 C) −2
B) −3 D) 3
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
The data in the table above were produced by a sleep researcher studying the
number of dreams people recall when asked to record their dreams for one week.
Group X consisted of 100 people who observed early bedtimes, and Group Y
consisted of 100 people who observed later bedtimes. If a person is chosen at
random from those who recalled at least 1 dream, what is the probability that the
person belonged to Group Y ?
A) 68 C) 79
100 164
B) 79 D) 164
100 200
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
The data in the table above were produced by a sleep researcher studying the
number of dreams people recall when asked to record their dreams for one week.
Group X consisted of 100 people who observed early bedtimes, and Group Y
consisted of 100 people who observed later bedtimes. If a person is chosen at
random from those who recalled at least 1 dream, what is the probability that the
person belonged to Group Y ?
A) 68 C) 79
100 164
B) 79 D) 164
100 200
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
A researcher conducted a survey to determine whether
people in a certain large town prefer watching sports
on television to attending the sporting event. The
researcher asked 117 people who visited a local
restaurant on a Saturday, and 7 people refused to
respond. Which of the following factors makes it least
likely that a reliable conclusion can be drawn about the
sports-watching preferences of all people in the town?
A) Sample size
B) Population size
C) The number of people who refused to respond
D) Where the survey was given
SAT	
  Math	
  –	
  Its	
  All	
  About	
  the	
  Ques2on!	
  
A researcher conducted a survey to determine whether
people in a certain large town prefer watching sports
on television to attending the sporting event. The
researcher asked 117 people who visited a local
restaurant on a Saturday, and 7 people refused to
respond. Which of the following factors makes it least
likely that a reliable conclusion can be drawn about the
sports-watching preferences of all people in the town?
A) Sample size
B) Population size
C) The number of people who refused to respond
D) Where the survey was given
Statistics is all about surveys
being done randomly!

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SAT Math: It's All About The Question

  • 1. SAT  Math  –  Its  All  About  the  Ques2on!   OLD  -­‐  3  Tests   NEW  -­‐  2  Tests   TIME:   TIME:   25  Minutes  –  20  Ques.ons   25  Minutes  –  20  Ques.ons  (No  C)     25  Minutes  –  18  Ques.ons   55  Minutes  –  38  Ques.ons  (Calc)   20  Minutes  –  16  Ques.ons   CONTENT:   CONTENT:   Algebra  I   Geometry   Some  Algebra  II   Algebra  I   Geometry   Algebra  II   Trigonometry   Data  Analysis  (Prob  &  Stats)   What’s Different!
  • 2. SAT  Math  –  Its  All  About  the  Ques2on!   OLD     Free  Response  and  Mul2ple   Choice  on  1  test  only.     ¼  point  deducted  for  wrong   answers  on  mul2ple  choice   ques2ons.   NEW     Free  Response  and  Mul2ple   Choice  on  both  (all)  tests.     No  points  deducted  for  wrong   answers.     What’s Different!
  • 3.    3  Things  You  WANT  to                  Memorize  for  the  Math  SAT       SAT  Math  –  Its  All  About  the  Ques2on!  
  • 4. 1.  The  Pythagorean  Theorem    a2  +  b2  =  c2     •  The  Pythagorean  Theorem  is  used  for   finding  the  length  of  the  hypotenuse  of  a   right  triangle.  While  that  is  great  and   useful,  it  can  be  used  for  much  more.       SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 5. The  Pythagorean  Theorem    a2  +  b2  =  c2     •  Instead  of  memorizing  the  distance  formula,   you  can  simply  use  the  Pythagorean  Theorem.     •  The  30-­‐60-­‐90  and  45-­‐45-­‐90  special  right   triangle  formulas  are  given  on  the  SAT,  the   Pythagorean  Theorem  can  be  used  in  place  of   those  too.     SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 6. 2.  Pythagorean  Triples   •  Here  are  the  two  Pythagorean  Triples   that  will  show  up  most  oWen  on  the  SAT:                          3-­‐4-­‐5        as  32  +  42  =  52                          5-­‐12-­‐13  as  52  +  122  =  132       SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 7. You  can  use  those  same  Pythagorean  Triples  to   make  more  of  them.  What  do  I  mean  by  “make   more  of  them?”  Just  count  by  each  number  to   make  more.  For  example,  count  by  3’s,  4’s  and   5’s!                  3-­‐4-­‐5  will  also  create  as  6-­‐8-­‐10,  and                9-­‐12-­‐15,  and  so  on.                  5-­‐12-­‐13  will  do  the  same  as  10-­‐24-­‐26.     SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 8. 3.  Know  what  f(x)  means   •  f(x)  is  called  func.on  nota.on  and  is  read   f  of  x.   •  f(x)  is  just  a  fancy  way  to  say  “y”  in  an   equa.on  that  also  has  an  “x.”          f(x)  =  2x  +  5  really  means  y  =  2x  +  5   SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 9. 3.  Know  what  f(x)  means   •  f(3)  is  read  f  at  3.        If  f(x)  =  2x  +  5  find  f(3).      Replace  x  with  3!          f(3)  =  2(3)  +  5      f(3)  =  6  +  5      f(3)  =  11   SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 10. 3.  Know  what  f(x)  means   •  Find  x  if  f(x)  =  3  when  f(x)  =  2x  +  5.              Replace  f(x)  with  3!          3  =  2x  +  5        -­‐2  =  2x        -­‐1  =  x   SAT  Math  –  Its  All  About  the  Ques2on!   a
  • 11. Mr.  D’s  2  Step  Method  for  Taking  Tests            (any  test/any  subject)       Step  1  -­‐  Find  the  Ques.on   Step  2  -­‐  Answer  the  Ques.on     SAT  Math  –  Its  All  About  the  Ques2on!  
  • 12. SAT  Math  –  Its  All  About  the  Ques2on!   On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon? A) 9mp B) 20mp C) 5m + 4p D) 4m + 5p
  • 13. SAT  Math  –  Its  All  About  the  Ques2on!   On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon? A) 9mp B) 20mp C) 5m + 4p D) 4m + 5p
  • 14. SAT  Math  –  Its  All  About  the  Ques2on!   Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 − 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation? A) Kathy will complete the repairs within 108 days. B) Kathy starts each week with 108 phones to fix. C) Kathy repairs phones at a rate of 108 per hour. D) Kathy repairs phones at a rate of 108 per day.
  • 15. SAT  Math  –  Its  All  About  the  Ques2on!   Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 − 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation? A y-intercept is when x = 0 or when time begins! A) Kathy will complete the repairs within 108 days. B) Kathy starts each week with 108 phones to fix. C) Kathy repairs phones at a rate of 108 per hour. D) Kathy repairs phones at a rate of 108 per day.
  • 16. SAT  Math  –  Its  All  About  the  Ques2on!  
  • 17. SAT  Math  –  Its  All  About  the  Ques2on!  
  • 18. SAT  Math  –  Its  All  About  the  Ques2on!  
  • 19. SAT  Math  –  Its  All  About  the  Ques2on!  
  • 20. SAT  Math  –  Its  All  About  the  Ques2on!   A function f satisfies f(2) = 3 and f(3) = 5. A function g satisfies g(3) = 2 and g(5) = 6. What is the value of f(g(3))? A) 2 B) 3 C) 5 D) 6 Since g(3) = 2, f(g(3)) = f(2) f(2) = 3
  • 21. SAT  Math  –  Its  All  About  the  Ques2on!   A function f satisfies f(2) = 3 and f(3) = 5. A function g satisfies g(3) = 2 and g(5) = 6. What is the value of f(g(3))? A) 2 B) 3 C) 5 D) 6 Since g(3) = 2, f(g(3)) = f(2) f(2) = 3
  • 22. SAT  Math  –  Its  All  About  the  Ques2on!   If 16 + 4x is 10 more than 14, what is the value of 8x? A) 2 B) 6 C) 16 D) 80
  • 23. SAT  Math  –  Its  All  About  the  Ques2on!   If 16 + 4x is 10 more than 14, what is the value of 8x? A) 2 B) 6 C) 16 D) 80 16 + 4x = 24 Multiply by 2 to get 8x 32 + 8x = 48 8x = 16
  • 24. SAT  Math  –  Its  All  About  the  Ques2on!   The complete graph of the function f is shown in the xy-plane above. For what value of x is the value of f(x) at its minimum? A) −5 C) −2 B) −3 D) 3
  • 25. SAT  Math  –  Its  All  About  the  Ques2on!   The complete graph of the function f is shown in the xy-plane above. For what value of x is the value of f(x) at its minimum? A) −5 C) −2 B) −3 D) 3
  • 26. SAT  Math  –  Its  All  About  the  Ques2on!   The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y ? A) 68 C) 79 100 164 B) 79 D) 164 100 200
  • 27. SAT  Math  –  Its  All  About  the  Ques2on!   The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y ? A) 68 C) 79 100 164 B) 79 D) 164 100 200
  • 28. SAT  Math  –  Its  All  About  the  Ques2on!   A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town? A) Sample size B) Population size C) The number of people who refused to respond D) Where the survey was given
  • 29. SAT  Math  –  Its  All  About  the  Ques2on!   A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town? A) Sample size B) Population size C) The number of people who refused to respond D) Where the survey was given Statistics is all about surveys being done randomly!