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7/29/2019 FA - H Definition of the Derivative
1/11
Jill$Gough$in$collaboration$with$Sam$Gough$for$AP$Calculus$ July,$2013$
A$Definition$of$the$Derivative$ $ Name$
f (x) = limh0
f(x + h) f(x)
h$
Formative$Assessment$$$ $ $ $ Date$ $ $ $ Period$
$
I$can$find$ f (x) $using$the$ limh0
f(x + h) f(x)
h$limit$definition$of$a$derivative.$
$
Level%1:$$I$can$evaluate$functions$using$function$notation$when$x $is$a$constant.$
$
1. If$ f(x) = 3x 4 ,$find$ f(3) .$$$
$
$
$$
2. If$ f(x) = x2 3x + 22x 1
x 2
x < 2,$
find$ f(4) .$
$$
3. If$ f(x) = 2x 4x2 4
,$find$ f(2) .$
$
$
$
$$
$4. If$ f(x) = 3cos(x) ,$find$ f() .$
$
$
$
$$
$
$$
$
Level%2:$$I$can$simplify$polynomial$and$rational$expressions.$
$
5. Expand$and$simplify$(x+ 3)2 (x 3)+ 2 .$$$
$
$
$$
$
6. Expand$and$simplify$(x+ 2)2 x2 .$$
$
$
$
7/29/2019 FA - H Definition of the Derivative
2/11
Jill$Gough$in$collaboration$with$Sam$Gough$for$AP$Calculus$ July,$2013$
7. $$Simplify:$ 3x2 + 6xx
.$
$
$
$
$$
$$
$
8. Simplify:$ x2 4x
2 3x10
.$
$
$$
$$
$
$$
$
$
$
$
Level%2:$$I$can$evaluate$functions$using$function$notation$when$x $is$a$variable$$
$$ $$$$expression.$
$9. If$ f(x) = 2x +1 ,$find$ f(1 h) .$
$
$
$
$$
$
$
$
10.If$ f(x) = 2x2 ,$find$ f(x + h) .$$
$
$
$
$
$
$
7/29/2019 FA - H Definition of the Derivative
3/11
Jill$Gough$in$collaboration$with$Sam$Gough$for$AP$Calculus$ July,$2013$
11.If$ f(x) = x2 x 2 ,$find$ f(x h) .$$
$
$
$
$$
$$
$
$
12.If$ f(x) = 2x2 x ,$find$ f(2 + h) .$$
$
$
$
$$
$
$
$
$$
$
$
Level%3:$$I$can$find$ f (x) $using$the$ limh
0
f(x + h) f(x)
h
$limit$definition$of$a$derivative.$$$
$
13.$$If$ f(x) = 2x + 5 ,$find$ f (2) $.$$
$
$
$
$
$
$
$
$$
$$
$$
$
$
7/29/2019 FA - H Definition of the Derivative
4/11
Jill$Gough$in$collaboration$with$Sam$Gough$for$AP$Calculus$ July,$2013$
$
14.$$If$ f(x) = x2 3x + 2 ,$find$ f (1) $.$$
$
$
$$
$$
$
$$
$$
$
$
$$
$
$
15.$$If$ f(x) = x2 2x ,$find$ f (x) $.$$$
$
$
$
$$
$
$
$
$
$$
$$
$
$$
$$
$
$
$
7/29/2019 FA - H Definition of the Derivative
5/11
Jill$Gough$in$collaboration$with$Sam$Gough$for$AP$Calculus$ July,$2013$
$
$
16.$$If$ f(x) = 2x2 x +1 ,$find$ f (x) .$$
$
$$
$$
$
$$
$$
$
$
$$
$
$
$
Level%4:$$I$can$find$a$function,$f(x) ,$when$given$ f (x) .$$$
$17.$$If$$ f (x) = 4x 5 ,$find$ f(x) .$
$
$
$$$
18.$$If$$ f (x) = x2 3x + 2 ,$find$ f(x) .$$
$
$
$$
19.$$If$$ f (x) = 4 ,$find$ f(x) .$$
$$
$
$
20.$$If$$ f (x) = x3 x2 + 2 ,$find$ f(x) .$.$$$
$
$
7/29/2019 FA - H Definition of the Derivative
6/11
Jill$Gough$in$collaboration$with$Sam$Gough$for$AP$Calculus$ July,$2013$
$$
A$Definition$of$the$Derivative$ $ Name$Table$of$Specifications$$ $ $ $ Date$ $ $ $ Period$
$
Circle%the%number%of%each%question%where%you%missed%something.%In%the%Percent%Correct%
column,%record%the%percent%of%questions%worked%correctly%for%each%category.%
Content$ Question$Number$Simple$
Mistake$
Study$
needed$
Percent$(%)$
Correct$
EL:%%I$can$find$ f (x) $using$the$ limh0
f(x + h) f(x)
h$limit$definition$of$a$derivative.$
I$can$evaluate$functions$using$function$
notation$when$ x $is$a$constant.$1,$2,$3,$4$ $ $ $
I$can$simplify$polynomial$and$rational$
expressions.$5,$6,$7,$8$ $ $ $
I$can$evaluate$functions$using$function$
notation$when$ x $is$a$variable$expression.$9,$10,$11,$12$ $ $ $
I$can$find$
f (x) $using$the$
limh0
f(x + h) f(x)
h$limit$definition$of$a$
derivative.$$%
13,$14,$15,$16$ $ $ $
I$can$find$a$function,$ f(x) ,$when$given$its$
derivative, f (x) .$$$17,$18,$19,$20$ $ $ $
$
Identify%the%level%where%your%work%is%most%consistently%correct.%
I%am%here% Level% Knowing%the%content.%
$ 4% I$can$find$a$function,$ f(x) ,$when$given$ f (x) .$$%
$ 3% I$can$find$ f (x) $using$the$ limh0
f(x + h) f(x)
h$limit$definition$of$a$derivative.$$ %
$ 2%I$can$evaluate$functions$using$function$notation$when$ x $is$a$variable$expression.$
I$can$simplify$polynomial$and$rational$expressions. %
$ 1% I$can$evaluate$functions$using$function$notation$when$ x $is$a$constant.%
%
Identify%the%level%where%your%work%is%most%consistent.%
I%am%here% Level% Showing%your%work:%
$ 4% I$have$the$correct$answer.$$I$have$stated$the$formula$where$applicable.$$I$have$shown$enough$work$to$indicate$my$thinking.$$My$work$is$organized$and$easy$follow.$
$ 3% I$have$the$correct$answer.$$My$work$is$organized$and$easy$follow.$
$ 2% I$have$an$answer$with$some$work,$but$my$work$is$messy$or$difficult$to$follow.$
$ 1% I$have$an$answer$without$any$supporting$work.$
$
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