1. Test 1 - Standard - Units 1 to 7

7/29/2019 1. Test 1 - Standard - Units 1 to 7

1/20

mep

School

Surname

Other names

Mathematics Test 1

MEP Units 1-7 STANDARD

For examiner's

use

Total

In addition to this paper you will need

A calculator

Mathematical instruments

Time1 hour 45 minutes

Instructions to candidatesWrite your name and other details in the spaces provided

above.

You should attempt as many questions as you can.

Write your answers in this combined question

paper/answer book.

Show your working in the space provided and make sure thatyour answer is clear.

Information for candidatesThe number of marks is given in brackets at the end of each

question or part-question.

You may be given marks for method even if your answer is

wrong.

You are reminded of the need for good English and clear

presentation.

Additional answer sheets, graph paper and tracing paper will beissued on request and must be fastened securely to the answer

book.

CIMT, University of Exeter

Summer ..........


2/201

MEP: Units 1-7, Test 1, STANDARD

1. Consider the following numbers:

2, 4, 8, 16, 32.

(a) Using ONLY these numbers write down

(i) a square number,

................................................................................................................. (1)

(ii) a prime number.

................................................................................................................. (1)

(b) Which of these numbers are factors of 8?

........................................................................................................................... (2)

(c) These numbers form part of a sequence.

Write down the next TWO numbers of this sequence.

........................................................................................................................... (2)

(SEG)

2. This formula is used to change degrees Fahrenheit to degrees Celsius.

C F= ( )5

932

Crepresents the temperature in degrees Celsius and Frepresents the temperature in

degrees Fahrenheit.(a) Calculate the value ofCwhen F = 60.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(b) Make Fthe subject of the formula.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(LON)


3/202


3. Staircases are designed using TREADS and RISERS as shown in the diagram.

Risers have a height of 20 cm. Treads have a length of 23 cm. There is one tread

for every riser.

HeightBetweenFloors

280 cm

h

Not to scale

TREAD23 cm

RISER20 cm

(a) In a house the height between floors is 280 cm. How many risers are needed

to make the staircase?

............................................................................................................................

............................................................................................................................ (2)

(b) Calculate in centimetres the length h, shown in the diagram.

............................................................................................................................ (2)

(SEG)

4. My bank account was 21.65 in credit.

From my account I wrote a cheque to pay a bill for 17.90

I then paid 20.00 into my account.

How much is now in my account?

......................................................................................................................................

...................................................................................................................................... (2)

(SEG)


4/203


5.

The length of a sink unit is 1200 mm. The length of a base unit is 930 mm.

(a) What is the total length of the two units in millimetres?

............................................................................................................................

............................................................................................................................ (1)

(b) What is the total length in metres?

............................................................................................................................ (1)

(SEG)

6. Do not use a calculator to answer this question.

The cash price of a car is 5870.

The hire purchase terms are 36 monthly payments of 197.

(a) Calculate how much more it will cost to pay for the car on hire purchase than

to buy it for cash.

(Write down all your working to show that you have not used a calculator.)

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(b) Use estimation to check that your answer to part (a) is reasonable.

Show all your working.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(NEAB)

Not to scale


5/204


7. The speed, v, in miles per hour, of an aircraft is given by the formula

v m p=

Calculate the value ofv, when m p= =0 41 761. and .

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(LON)

8. The diagram shows a section of trellis fencing.

a

b

Not to scale

All the quadrilaterals in the fence have four equal sides and two pairs of equal angles.

(a) What name is given to these quadrilaterals?

............................................................................................................................ (1)

(b) Angle a is 50 . What is the size of angle b?

............................................................................................................................ (2)

(SEG)


6/205


9. In the right-angled triangle ABC, the hypotenuse AC is 35 cm,

and the angle ACB is 48.

Not to scale

Calculate the length of the shortest side of the triangle.

.....................................................................................................................................

.....................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(LON)

10.

Diagram NOT

accurately drawn

Calculate the size of the angle marked x .

Give your answer correct to one decimal place.

.....................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(LON)

A

C B

35 cm

48

A

B C

15 m12 m

x


7/206


11. There are 454 grams in 1 lb. There are 16 ounces in 1 lb.

Change 34

ounce to grams.

Give your answer correct to 1 decimal place.

.....................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(LON)

12. A square lawn has an area of 144 square metres.

(a) Calculate the perimeter of the lawn.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

A path 2 metres wide surrounds the lawn.

(b) Calculate the area of the path.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(SEG)

LAWN PATH

Not to scale


8/207


13. Trevor rears turkeys to sell at Christmas.

He estimates that the cost, C, of rearing each turkey is given by the formula

C W W= +0 1 0 05 2. . ,

where Wkilograms is the weight of a turkey.

(a) What is the estimated cost of rearing a 9 kilogram turkey?

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(b) He advises his customers that they should cook their turkeys using the formula

T W= +40 20 ,

where Tminutes is the cooking time for each turkey.

(i) Re-arrange the formula to make Wthe subject.

.................................................................................................................

.................................................................................................................

.................................................................................................................

................................................................................................................. (2)

(ii) Anne uses this formula and cooks her turkey for 7 hours.

What is the weight of the turkey which Anne cooks?

.................................................................................................................

.................................................................................................................

.................................................................................................................

................................................................................................................. (3)

(NEAB)


9/208


14. For homework, John is asked to throw two pennies 500 times and record the number

of heads.

These are his results.

(a) Comment on whether you think the coins are fair.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(b) If the coins are fair, and John threw them 2000 times, how many times should

he expect to get at least one head?

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(NEAB)

15. The probability that a GCSE candidate, chosen at random, will obtain a grade C or

higher in English is 0.55.

Calculate the probability that a GCSE candidate, chosen at random, will obtain a

grade lower than grade C in English.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(LON)

0 heads 126

1 head 254

2 heads 120

Total 500


10/209


16.

Not to scale

ABCD is a square.

BEC is an equilateral triangle.

(a) Write down the size of

(i) angle ABC, ..................................................................... (1)

(ii) angle EBC. ..................................................................... (1)

(b) Calculate the size of

(i) the angle markedx, .....................................................................

................................................................................................................. (1)

(ii) the angle markedy. .....................................................................

................................................................................................................. (1)

(c)

Not to scale

AC is parallel to FE.

(i) What is the size of the angle markedz?

................................................................................................................. (1)

(ii) Give a reason for your answer.

................................................................................................................. (1)

(NEAB)

x

y

A

D C

B

E

F

z

x

y

A

D C

B

E


11/2010


17. The diagram shows an isosceles triangle of base 10 mm

and height 12 mm.

(a) Calculate the area of the triangle.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)(b) Write down the value oftan x , giving your answer as a decimal.

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(c) Calculate the size of anglex.

............................................................................................................................

............................................................................................................................ (1)

(NEAB)

x

10 mm

12 mm


12/2011


18. The diagram shows a stack of crates.

(a) Each crate is a cuboid. The dimensions of a crate are shown.

6 m

2 m

2.5 m

Not to scale

What is the volume of a crate?

............................................................................................................................

............................................................................................................................ (1)

(b) The crates are filled with cartons. Each carton is a cube of side 0.5 m.

How many cartons are in one crate?

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(c) The cartons contain kitchen rolls. Each kitchen roll is a cylinder with radius

5 cm and height 25 cm.

The stack contains eighteen crates.

How many kitchen rolls are included in the stack of crates?

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(SEG)


13/2012


19. The diagram shows the top of a block of height 1 cm.

On the grid, complete a three dimensional drawing of the block.

One line has already been drawn for you.

(2)

(SEG)


14/2013


20. Judith has a ride on a roundabout. On her ride she goes round in a circle of

diameter 3 m.

How far does she travel in one complete circle?

Take to be 3.14 or use the key on your calculator.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(SEG)

21.

A table has a top in the shape of a circle with a radius of 45 centimetres.

(a) Calculate the area of the circular top of the table.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

The base of the table is also in the shape of a circle. The circumference of this circle

is 110 centimetres.

(b) Calculate the diameter of the base of the table.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(LON)

Not to


15/2014


22. John keeps a weather chart. He records each day as either wet or dry.

If it is dry one day, the probability that it will be dry the next is4

5.

If it is wet one day, the probability that it will be wet the next day is2

5.

The 31st March is dry.

(a) Complete the tree diagram. (1)

Dry

Wet

Dry

Wet

Dry

Wet ( )

4

5( )

( )

( )( )

( )

1st April 2nd April

(b) Calculate the probability that 2nd April will be dry.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(c) Calculate the probability that at least one of the days, 1st and 2nd April,

will be dry.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(NEAB)


16/2015


23. The CN tower in Toronto is the world's tallest free-standing structure.

The following information is given about the tower.

Height: 1815 feet 5 inches (553.33 metres),equivalent to five football pitches stacked end to end.

(12 inches = 1 foot)

Structure: 130 000 tons (132 080 metric tonnes), equivalent to

23 214 large elephants. (2240 pounds = 1 ton)

Use this information to calculate (showing your method),

(a) the number of centimetres equivalent to one inch,

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (3)

(b) the length, in feet, of a football pitch,

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(c) the number of pounds in a metric tonne,

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)

(d) the weight of a large elephant, in pounds.

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................ (2)


17/201

MEP: Units 1-7, Test 1, STANDARD, Marking SchemeMEP: Units 1-7, Test 1, STANDARD Marking Scheme

1. (a) (i) 4 (or 16) (ii) 2 B1 B1

(b) 2, 4, 8 (B1 for 2, 4) B2

(c) 64, 128 B1 B1

6

2. (a) C = = =5

960 32

5

928 15 6( ) . (allow 16) M1 A1

(b)9

532

CF= B1

FC

= +329

5B1

4

3. (a) number = =280

2014 M1 A1

(b) h = =14 23 322 cm M1 A1

4

4. . . .21 65 17 90 3 75 = B1

. . .3 75 20 00 23 75+ = B1

2

5. (a) 1200 930 2130+ = mm B1

(b) 2.13 m B1

2

6. (a) 36 197 7092 = M1 A1

7092 5870 1222 = A1

(b) 35 200 7000 = M1 A1

5

7. v = =0 41 761 312 01. . M1 A1

2

8. (a) rhombus B1

(b) 2 360 2 50 130b b= = M1 A13


18/202

MEP: Units 1-7, Test 1, STANDARD, Marking Scheme

9. CB = 35 48cos M1

= =35 0 66913 23 419. . A1 A1

3

10. cos .x = =12

150 8 M1 A1

x = 36 9. (to 1 d.p.) A1

3

11.3

4ounce lbs=

3

64B1

3

64454 21 3 = . g M1 A1

3

12. (a) length = 12 m B1

perimeter = =4 12 48 m B1

(b) total area = 16 16 B1

area of path = =256 144 112 m2 M1 A1

5

13. (a) C = + =0 1 9 0 05 81 4 95. . . M1 A1

(b) (i) T W =20 40 M1

WT

= 2040

A1

(ii) T = =7 60 420 B1

W = =

400

40 10 kg M1 A1

7

14. (a) Yes as you would expect about 125, 250, 125 B1 B1

(b) approximately3

42000 1500 = M1 A1

4

15. 1 0 55 0 45 =

. . M1 A12


19/203


16. (a) (i) 90 (ii) 60 B1 B1

(b) (i) 15 (ii) 30 B1 B1

(c) (i) 30 (ii) alternateangles (or equivalent) B1 B16

17. (a) area = =1

210 12 60 mm

2 M1 A1

(b) tan .x = =12

52 4 M1 A1

(c) 17 4. B15

18. (a) 30 m3

B1

(b) 12 4 5 240 = M2 A1

(c) In one carton, there are 5 5 2 50 = kitchen rolls B1

Total = =50 240 18 216 000 kitchen rolls M1 A1

7

19.

(Minor errors B1) B2

2

20. distance = = 2 2 1 5 r . M1 A1

= 9 42. m A1

3

21. (a) area = = r2 2

45 M1 A1

= 6361 7. cm2 A1

(b) d = 110 M1

d = =110

35 01

. cm A1 A1

6

22. (a)

(Fully correct) B1

D

W

4

5( )

( )15

D

W

4

5( )

( )15

D

W

( )

( )25

3

5


20/20


(b)4

5

4

5

1

5

3

5

+

M1 A1

=19

25A1

(c) 11

5

2

51

2

25

= M1 A1

=23

25A1

7

23. (a) 155333

1815 12 52 54inch cm cm

+( )= . M2 A1

(b) lengthfeet 5 inches

feet= = =1815

5

1815

5363 1

512 (. ) M1 A1

(c) 2240130 000

132 0802204 7 = . lbs (Allow 2205) M1 A1

(d)130 000

23 2142240 12 544 = lbs M1 A1

9

TOTAL 100

1. Test 1 - Standard - Units 1 to 7

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