mrjacksonmaths higher calc paper 1

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.

;;;;;;;;;

-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.

-&

(!) >n the grid, dra% the plan o$ the shape.

-&

-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.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;-&

-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.

;;;;;;;;;;;;-&

(!) "rite our ans%er to part (a) correct to an appropriate degree o$ accurac.

;;;;;;;;;;-%

-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.

;;;;;;;;;;;;

-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.

;;;;;;;;; cm-&

The perimeter o$ the &uadrilateral is -4 cm.

(!) 0ind the length o$ the longest side o$ the &uadrilateral.

;;;;;;;;; cm-0

-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.

;;;;;;;;;;;;;;;;;;;;;;;;;

-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 ",

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

-&

(!) triangle Aonto triangle C.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;-0

-Total 2 mar,s

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#%0

#%1

1+ cm

8* cm

%0. (a) ol'ex -

42 *

x2 ;;;;;;;;-&

(!) 0actorise ? y*

;;;;;;;;;;;;-&

-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


OABis a triangle.

OA 2 a and OB 2 b.

(a) #pressAB in terms o$ aand b.

;;;;;;;;;;-%

Cis the point on ABe#tended such that AB: BC2 - : *

Dis the midpoint o$ OC.

(!) 0indOD in terms o$ aand b.

;;;;;;;;;;-0

-Total 1 mar,s

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#%3

P

R

1-*

S

Q

O

8-


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


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.

;;;;;;;; g

-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.

;;;;;;;;;;;;-&

(!) 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.

-0

-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.

;;;;;;;;-0

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.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;-%

-Total 1 mar,s

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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.

;;;;;;;;;; m

-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

-&

-Total 1 mar,s

&3. impli$ $ull* x x

*

8 +x x*

;;;;;;;;;;

-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*

mrjacksonmaths higher calc paper 1

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