ALTERNATE Paper 1 (Non - calculator) - · PDF file · 2015-03-26Give reasons for...

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ALTERNATE

Paper 1 (Non - calculator) November 2014 HIGHER

Name: _______________________

Total Marks: ___________

Q. Max Actual RAG Q. Max Actual RAG

1 3 14 4

2 2 15 4

3 3 16 4

4 3 17 4

5 4 18 5

6 4 19 4

7 4 20 5

8 4 21 2

9 4 22 6

10 2 23 4

11 4 24 4

12 9 25 3

13 5


1. Using the information that

9.8 × 67 = 656.6

find the value of

(i) 9.8 x 670

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

(ii) 98 x 0.67

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

(iii) 6566 ÷ 6.7

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

(Total for Question 1 is 3 marks)

____________________________________________________________

*2. Karen got 48 out of 60 in a maths test.

She got 81% in an English test.

Karen wants to know if she got a higher percentage in maths or in English.

Did Karen get a higher percentage in maths or in English?



3. Here are the heights, in cm, of 18 children.

9.8 9.0 8.4 10.2 11.5 9.1

8.8 9.1 10.8 11.0 9.7 9.3

9.0 8.9 10.3 9.5 9.2 10.6

Show this information in an ordered stem and leaf diagram.



4. Kalinda buys x packs of doughnuts and y boxes of muffins.

There are 8 currant buns in a pack of doughnuts.

There are 10 iced buns in a box of muffins.

Kalinda buys a total of T cakes.

Write down a formula for T in terms of x and y.

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


5. (a) Solve the inequality 7y - 3 < 25

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

(2)

(b) Here is an inequality, in x, shown on a number line.

Write down the inequality.

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

(2)



*6. Steve wants to put a hedge along one side of his garden.

He needs to buy 31 plants for the hedge.

Each plant costs £4.48

Steve has £140 to spend on plants for the hedge.

Does Steve have enough money to buy all the plants he needs?



7. The diagram shows the plan of a floor.

The area of the floor is 155 m2.

Work out the value of x.



*8.

ABC is parallel to EFGH.

GB = GF

Angle BFG = 68°

Work out the size of the angle marked x.

Give reasons for your answer.



9. Jack wants to find out how many newspapers people read.

He uses this question on a questionnaire.

(a) Write down two things wrong with this question.

1....................................................................................................................

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

2....................................................................................................................

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

(2)

Jack also wants to find out how much people spend on newspapers.

(b) Write a question Jack could use on his questionnaire to find out how much

people spend on newspapers

(2)


How many newspapers do you read?

0 to 2 2 to 3 3 to 4 5 to 6


10. Use ruler and compasses to bisect the angles BAC.

You must show all your construction lines.



11. Ria is going to buy a caravan.

The total cost of the caravan is £6000 plus VAT at 20%.

Ria pays a deposit of £4000.

She pays the rest of the total cost in 6 equal monthly payments.

Work out the amount of each monthly payment.

£..............................



12. (a) Factorise 5m2 – 12m

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

(1)

(b) Solve 3(t – 4) = t + 8

t = ..........................................

(3)

(c) Expand and simplify (3y + 4)(y – 1)

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

(2)

(d) Solve 5−2𝑚

4= 1

m = ..........................................

(3)



13. (a) Express 56 as a product of its prime factors.

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

(3)

Martin thinks of two numbers.

He says,

“The Highest Common Factor (HCF) of my two numbers is 5.

The Lowest Common Multiple (LCM) of my two numbers is a multiple of 100.”

(b) Write down two possible numbers that Martin is thinking of.

........................ , ........................

(2)



14. Suha has a full 500 ml bottle of wallpaper remover.

She is going to mix some of the wallpaper remover with water.

Here is the information on the label of the bottle.

Suha is going to use 500 ml of water.

How many millilitres of wallpaper remover should Suha use?

You must show your working.

..........................................ml


Wallpaper remover

500 ml

Mix 1

5 of the wallpaper remover with

4000 ml of water


15. The students in a class kept a record of the amount of time, in minutes, they

spent doing homework last week.

The table shows information about the amount of time the girls spent doing

homework last week.

Minutes

Least amount of time 60

Inter-quartile range 120

Median 170

Lower quartile 100

Highest amount of time 290

(a) On the grid, draw a box plot for the information in the table.

(2)

The box plot below shows information about the amount of time the boys spent

doing homework last week.

*(b) Compare the amount of time the girls spent doing homework with the amount

of time the boys spent doing homework.

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

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

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

(2)



16. There are 200 workers at a factory.

The frequency table gives information about their ages.

Age (a years) Frequency

0 < a ≤ 20 25

0 < a ≤ 30 45

0 < a ≤ 40 68

0 < a ≤ 50 37

0 < a ≤ 60 11

0 < a ≤ 70 8

0 < a ≤ 80 6

(a) On the grid opposite, draw a cumulative frequency graph for this information.

(2)

(b) Graham says,

“40% of workers at the factory are younger than 30”

Is Graham correct?

You must show how you get your answer.

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

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

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

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

(2)


17.

ABCDEFGH is a regular octagon.

BCKFGJ is a hexagon.

JK is a line of symmetry of the hexagon.

Angle BJG = angle CKF = 140°

Work out the size of angle KCD.

You must show all your working.

..........................................°



18.

ABCD and AEFG are mathematically similar trapeziums.

AE = 5 cm

EF = 12 cm

BC = 18 cm

(a) Work out the length of BE.

.........................................cm

(2)

Trapezium AEFG has an area of 36 cm2.

(b) Work out the area of the shaded region.

.........................................cm2

(3)



19. (a) Complete the table of values for y = 2

𝑥

x 0.5 1 2 4 5 8

y 0.5 1

(2)

(b) On the grid, draw the graph of y = 2

𝑥 for 0.5 ≤ x ≤ 8

(2)



20. The diagram shows a solid shape.

The solid shape is made from a cylinder and a hemisphere.

The radius of the cylinder is equal to the radius of the hemisphere.

The cylinder has a height of 10 cm.

The curved surface area of the hemisphere is 8π cm2.

Work out the total surface area of the solid shape.

Give your answer in terms of π.

.......................................... cm2



2 221. Expand (6 + )(1 + )

2bGive your answer in the form a + where a and b are integers.

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


____________________________________________________________


22. (a) Simplify fully (5m2)0

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

(1)

(b) Simplify (81𝑥8

16𝑥4)−1

2

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

(2)

(c) Write 3

𝑥+1−

2

𝑥+5 as a single fraction in its simplest form.

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

(3)



23. Paul has 8 cards.

There is a number on each card.

Paul takes at random 3 of the cards.

He adds together the 3 numbers on the cards to get a total T.

Work out the probability that T is an even number.

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



*24. A is the point with coordinates (1, 3).

B is the point with coordinates (4, –1).

The straight line L goes through both A and B.

Is the line with equation 3y = -2x + 12 perpendicular to line L?

You must show how you got your answer.



25.

The diagram shows part of the curve with equation y = f(x).

The coordinates of the minimum point of this curve are (2, –5).

Write down the coordinates of the minimum point of the curve with equation

(i) y = f(x) + 2

(....................... , .......................)

(ii) y = f(3x)

(....................... , .......................)

(iii) y = f(–x)

(....................... , .......................)


TOTAL FOR PAPER IS 100 MARKS

ALTERNATE Paper 1 (Non - calculator) - · PDF file · 2015-03-26Give reasons for...

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