mrjacksonmaths higher calc paper 1
TRANSCRIPT
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8/13/2019 MrJacksonMaths Higher Calc Paper 1
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8/13/2019 MrJacksonMaths Higher Calc Paper 1
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GCSE Mathematics
0ormulae: igher Tier
olume of a !rism2 area o$ cross section length
olume of s!here2
4
- r-
olume of cone2
1
- r*
hSurface area of s!here2 4r* Curved surface area of cone2 rl
In any triangle A"C The #uadratic Equation
The solutions o$ ax*3 bx3 c2 %here a , are gi'en !
x2 bb*4ac
*a
Sine $ulea
sin A2
b
sinB2
c
sinC
Cosine $ule a*2 b*3 c* *bccos A
Area of triangle21
*absin C
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sectioncross
length
r
l h
r
c B
C
A
b a
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#%
#&
+.* cm
*.7 cm
4.8 cm
Ans'er A(( T)E*T+ SEE* questions.
)rite your ans'ers in the s!aces !rovided.
+ou must 'rite do'n all the stages in your 'or,ing.
%. 9ar plas t%o games o$ ta!le tennis.ach game is either %on or lost.
The pro!a!ilit that he loses !oth games is .*7The pro!a!ilit that he %ins e#actl one game is .-
"or out the pro!a!ilit that he %ins !oth games.
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-Total & mar,s
&. /iagram */Taccuratel dra%n
The diagram sho%s a replacement !lade $or a ni$e.The !lade is in the shape o$ a trape
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#0
0ront
0. The diagram sho%s a -=/ shape made $rom cu!es.
(a) >n the grid, dra% the $ront ele'ation o$ the shape $rom the direction sho%n.
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(!) >n the grid, dra% the plan o$ the shape.
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-Total 1 mar,s
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#1
#2
1. Angela recorded the resting pulse, in !eats per minute, o$ * people.
ere are her results.
+* 8- 54 84 7 8 8+ 8- +5 +7
81 +7 +* 5+ 8- 5+ 88 7- +1 8?
/ra% an ordered stem and lea$ diagram to sho% her results.@ou should include a e.
-Total 0 mar,s
2. (a) se our calculator to %or out the 'alue o$ -.1-
;;;;;;;;;;-%
(!) Bath sas
s&uaring a num!er al%as maes it !iggerD.
9i'e an e#ample to sho% that Bath is %rong.
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-Total 0 mar,s
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#3
3. ere are $our $air spinners.
pinner A pinner 6 pinner C pinner /
n each part o$ this &uestion a statement is made.
"rite do%n the letter o$ the spinner $or %hich the statement is true.
(a) The pro!a!ilit o$ getting a 4 is1
*.
pinner ;;;;;;-%
(!) t is impossi!le to get a -.
pinner ;;;;;;-%
(c) The pro!a!ilit o$ getting a * is the same as the pro!a!ilit o$ getting a 5.
pinner ;;;;;;-%
(d) The pro!a!ilit o$ getting a 4 is t%ice the pro!a!ilit o$ getting a 8.
pinner ;;;;;;-%
-Total 1 mar,s
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1*
44
-
4
11
48
*
-
**
58
-
5
14
58
4
5
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#4
#5
4. (a) se our calculator to %or out the 'alue o$ ?.8 *.-
*
.18
"rite do%n all the $igures on our calculator displa.
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(!) "rite our ans%er to part (a) correct to an appropriate degree o$ accurac.
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-Total 0 mar,s
5. The ta!le sho%s the heights o$ pupils in a class.
eight (hcm) 0re&uenc
1 E h 11 8
11 E h 1* ?
1* E h 1- 7
1- E h 14 5
14 E h 15 1
0ind the class inter'al in %hich the median lies.
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-Total & mar,s
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#6
*x3 1
-x *
*x 1
x
6. /iagram */Taccuratel dra%n
The diagram sho%s a &uadrilateral.
The lengths o$ the sides are gi'en in centimetres.
(a) 0ind an e#pression, in terms o$x, $or the perimeter o$ the &uadrilateral.9i'e our ans%er in its simplest $orm.
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The perimeter o$ the &uadrilateral is -4 cm.
(!) 0ind the length o$ the longest side o$ the &uadrilateral.
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-Total 2 mar,s
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4 m
*.5 m
8 m
* m
1 m
#%7
%7. 6ill and 6en are decorators.
6ill charges F+ per %all to hang %allpaper.
6en charges F8 per s&uare metre co'ered to hang %allpaper.
/iagram */Taccuratel dra%n
The diagram sho%s the dimensions o$ 6rianGs dining room.e %ants %allpaper hung on all $our %alls e#cept $or the door %hich is shaded.
"or out %ho %ill charge less to hang the %allpaper, 6ill or 6en, and ! ho% much.@ou must sho% all our %oring.
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-Total 2 mar,s
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#%%
%%. The e&uation
x- x2 1
has a solution !et%een 4 and 5.
se a trial and impro'ement method to $ind this solution.9i'e our ans%er correct to 1 decimal place.@ou must sho% allour %oring.
x2 ;;;;;;;;
-Total 1 mar,s
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#%&
1 * 4- 5 8 + 7 x
1
*
4
-
5
8
+
7
y
O
C
"
A
%&.
/escri!e $ull the single trans$ormations %hich %ill map
(a) triangle Aonto triangle ",
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-&
(!) triangle Aonto triangle C.
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-Total 2 mar,s
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#%0
#%1
1+ cm
8* cm
%0. (a) ol'ex -
42 *
x2 ;;;;;;;;-&
(!) 0actorise ? y*
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-Total 1 mar,s
%1. /iagram */Taccuratel dra%n
A rectangle has sides o$ length 1+ cm and 8* cm.
Calculate the length o$ a diagonal o$ the rectangle.9i'e our ans%er correct to - signi$icant $igures.
;;;;;;;;;; cm
-Total 0 mar,s
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#%2
a b
D
A CB
O
%2. /iagram */Taccuratel dra%n
OABis a triangle.
OA 2 a and OB 2 b.
(a) #pressAB in terms o$ aand b.
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Cis the point on ABe#tended such that AB: BC2 - : *
Dis the midpoint o$ OC.
(!) 0indOD in terms o$ aand b.
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-Total 1 mar,s
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#%3
P
R
1-*
S
Q
O
8-
%3. /iagram */Taccuratel dra%n
P, Q, Rand Sare points on a circle, centre O.
AnglePQR2 1-*.Angle ORQ2 8-.
(a) (i) "or out the si
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#%4
A
C
Y
B
X
45
%4. /iagram */Taccuratel dra%n
The diagram sho%s a 'ertical mast ABC.The mast is supported ! ca!les attached to the hori
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#%5
#%6
%5. ol'e the simultaneous e&uations
-x3 *y2 11
*x5y2 *
x2 ;;;;;;;;
y2 ;;;;;;;;
-Total 1 mar,s
%6. /iaGs %eight is 7H less than it %as a month ago.e no% %eighs 5*.? g.
"or out ho% much %eight /ia has lost in the last month.
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-Total 0 mar,s
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#&7
1 * 4- 5 8 + 7 x
1
*
4
-
5
8
+
7
y
O
&7. (a) 4 E *n 8
nis an integer.
"rite do%n all the possi!le 'alues o$ n.
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(!) yI , yE -x, y3 *xE 8
xand yare integers.
>n the grid, mar %ith a cross ( ) each o$ the threepoints %hich satis$ allthesethree ine&ualities.
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-Total 2 mar,s
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#&%
&%. Jind collects data on ho% pupils usuall get to school.
The ta!le sho%s her results.
Transport to school Num!er o$ pupils
Car -416us *1+
Train -*
6ie 85
"al 158
Jind %ants some pupils to ans%er more &uestions a!out their Kourne to school.
he decides to as a strati$ied sample o$ 8 pupils.
(a) "or out the num!er o$ pupils tra'elling to school ! car %ho should !e in hersample.
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Jind needs 18 pupils tra'elling to school ! !us in her sample.
(!) /escri!e a method she could use to o!tain a random sample o$ 18 $rom the *1+pupils %ho tra'el ! !us.
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-Total 1 mar,s
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8/13/2019 MrJacksonMaths Higher Calc Paper 1
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#&&
#&0
x
7.4 cm
+.1 cm
5.8 cm
&&. A car Kourne taes 1 hour 1 minutes, correct to the nearest minute.
The carGs a'erage speed on the Kourne is +* mLh, correct to * signi$icant $igures.
"or out the least distance the car could ha'e tra'elled.
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-Total 1 mar,s
&0. /iagram */Taccuratel dra%n
The diagram sho%s a triangle %ith sides o$ length 5.8 cm, +.1 cm and 7.4 cm.
0ind the si
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#&1
Amount spent (FA)
1 * 4- 5
&1. Richard carried out a sur'e on the amount o$ mone people spent online in a %ee.
The ta!le sho%s his results.
Amount spent (FA) 0re&uenc
AE 5 85 AE 1 *5
1 AE * -7
* AE - 1+
- AE 5 17
/ra% a histogram $or the in$ormation gi'en in the ta!le.
-Total 0 mar,s
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#&2
#&3
&2. A mug o$ %arm co$$ee is le$t on a ta!le outside.
The temperature o$ the co$$ee, TC, decreases ! PH each minute. ts temperature a$ternminutes is gi'en ! the $ormula
T2 85 (.?+5)n
(a) "rite do%n the 'alue o$ T%hen n2 .
T2 ;;;;;;;-%
(!) "rite do%n the 'alue o$ P.
P2 ;;;;;;;-%
(c) 0ind the temperature o$ the co$$ee a$ter * minutes.9i'e our ans%er correct to 1 decimal place.
;;;;;;;; C
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-Total 1 mar,s
&3. impli$ $ull* x x
*
8 +x x*
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-Total 0 mar,s
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y
xO
CB
A
&4.
The diagram sho%s a setch o$ the cur'e %ith e&uation y2 4 x*
The ma#imum point o$ the cur'e is the point A.The cur'e crosses the x=a#is at the points Band C.
(a) 0ind the coordinates o$ the points A, Band C.
A( ;; , ;; )
B( ;; , ;; )
C( ;; , ;; )-0
(!) >n the set o$ a#es on the ne#t page, setch and la!el the cur'es %ith e&uations
(i) y2 *(4 x*)
(ii) y2 4 (x3 *)*
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#&4
1
*
1
-
4
5
8
y
* 1 1 * - 4 5 x5 4 - O
*
+
?
7
-0
-Total 3 mar,s
T/TA( 8/$ 9A9E$: %77 MA$;S
E*