Linwood High School

Added Value Practice

National 4 Calculator

DO NOT WRITE ON THIS BOOKLET!

Algebra: Linear Equations and Simplifying

Core skills

Q1: Multiply out the brackets

a) 3(x + 1) b) 5(y – 3)

Q2: Simplify and solve

a) 4x + x + 12 = 22 b) 2y + 18 + 3y = 38

c) 5m – m – 9 = 3 d) x + 60 + 2x – 30 = 180

Q3: Solve these equations

a) 9a + 3 = 2a + 17 b) 8x + 4 = 5x + 28

b) 13 + 20r = 11r + 76 d) 37 + 2c = 100 – 5c

In Context

Q1: The straws in each pair are equal in length. All measurements are in centimetres. For each pair:

i) Write an equation

ii) Solve the equation

iii) Find the length of the straws

a) 4x 3x + 5 b) 30 – x 2x

Q2: Lisa is making pendants in the shape of stars out of wire.

1 star 2 stars

5 pieces of wire 10 pieces of wire

a) Copy and complete the table

No of stars (s)

1 2 3 4 11

No of pieces of wire (w)

5

b) Create the formula connecting s and w.

c) If Lisa is making 16 stars how many pieces of wire does she need?

Q3: Joe is building a fence.

2 fence posts 3 fence posts

3 panels 6 panels

a) Copy and complete the table

No of fence posts (F)

2 3 4 5 20

No of panels (P)

3

b) Create the formula connecting F and P.

c) Joe has 25 panels, (i) how many fence posts does he need?

(ii) how many panels will he have left over?

Area:

Core skills

5cm Q1: find the area of this square

Q2: find the area of a rectangle which has length 12cm and breadth 4cm.

Q3: find the area of a circle which has radius of 6cm.

Q4: find the area of a triangle which has a base of 10cm and height of 13cm.

In Context

Q1: Sam’s desk top is 87cm long and 62cm broad.

Calculate its area

Q2: Calculate the areas of these shapes:-

a)

3 cm

8cm 9 cm

6cm b)

5cm 11 cm

18cm

Q3: The sign for the Little Diamonds Nursery is in the shape of a rhombus. The diagonals of the rhombus are 80 cm and 96 cm long.

What is the area of the sign?

The

Little Diamonds Nursery

Q4: 98cm

Scott is entering a kite flying competition.

The rules of the competition state that the

188 cm area of the kite must be no more than

9500 cm2.

a) Calculate the area of the kite. b) Can he enter the competition?

Q5:

Garnet Street 26 cm

37 cm

The road sign is in the shape of a rectangle and a semi-circle combined.

a) Calculate the area of the rectangle. b) Calculate the area of the semi-circle (to 1dp). c) Calculate the total area of the sign.

Volume:

Core skills

Find the volume of each

Q1: Cuboid with length 5cm, breadth 3cm and height 4cm

Q2: Cube with length 6m

Q3:Cylinder with radius 10cm and height 25cm

In context (answers to 1dp where required)

Q1: Calculate the volume of the tin of beans. 8cm

Beans 12cm

Q2: Calculate the volume of the each box.

a) b)

12cm

20cm

12cm

8cm 3.2cm 7cm

Q3: A tank, in the shape of a cuboid, holds oil.

a) Calculate the volume in cm3 b) How many litres can it hold?

5 litre

c) How many 5 litre oil cans can be filled from the tank when it is full?

d) The tank has to be insulated against the weather by placing padding on all surfaces.

What is the Total Surface Area of the tank?

50 cm

120 cm

80 cm

Q4: Ava has a vase which is a glass cuboid and it holds 539cm3 of water.

If the base is a square with length 7cm what height is the vase?

Distance, Speed, and Time:

Core skills

Find the missing value:

Q1: speed = 70 km/hr, time = 4 hours; Distance =.............?

Q2: distance = 120 km, time = 5 hours; Speed =.................?

Q3: distance = 180 km, speed = 60 km per hour; Time =...............?

In context

Q1: Dave drove an average speed of 60 mph for 2½ hours.

What distance did he cover?

Q2: Emily has learnt to fly a light aircraft and on her latest trip she flew with an average speed of 150km/hr for 337.5 km.

How long was she flying? (Give your answer in hours and minutes)

Q3: Hazel can walk to school in 30 minutes.

The distance from her house to the school is 2 miles.

a) Calculate Hazel’s average speed in mph.

She can cycle twice as fast as she can walk

b) How many minutes will it take her to cycle to school?

Q4: On a stretch of road the speed limit is 30 mph.

Who is obeying the law? (Give good reasons)

a) Tom, covering 6 miles in 15 minutes

b) Andy, covering 12 miles in 20 minutes

c) Kirsty, covering 5.5 miles in 10 minutes

Pythagoras:

Core skills

1.

In Context:

2.

3.

7.

8.

9.

A is the point (1,1) and B is the point (7,9).

Plot these points and find the length of the line AB.

Trigonometry:

Core skills

In Context:

2.

3.

4.

5.

Co-ordinates 1. (a) On the grid below, plot the points A(2, 6), B(8, 2) and C(6, –1).

(b) Plot a fourth point D so that ABCD is a rectangle.

(c) Find the length of the line AD to 1 decimal place. (Hint – Pythagoras) 2. The coordinates of 3 corners of a square are: ( 3 , 1 ), ( –1 , 1 ) and ( 3 , –3 ). (a) What are the coordinates of the 4th corner? (b) Calculate the length of the diagonal. (1dp) 3. The vertices of a shape have coordinates: A ( 3 , 3 ) ,B ( 5, –1 ) , C( 3 , –5 ) and D ( 1 , –1 ).

(a) Plot the points on a co-ordinate diagram and join them in order. (b) What is the name of the shape? (c) By considering the diagonals of this quadrilateral, calculate the length of each side.

Comparing Data Sets:

Core skills

Q1: For this set of data:

3, 4, 7, 3, 3, 8, 9, 5

Find a) the mean b) the mode c) the median d) the range

e) Which of the averages least represents the data, and why?

In context

Q1:

(a) The pie chart shows the favourite flavour of

crisps from a sample of 40 pupils.

Using the information in the table below calculate

Prawn cocktail Salt &

Vinegar

Plain

the sector angles of the pie chart.

Crisp flavour No of people Angle Salt and vinegar 22 Prawn cocktail 10 Plain 8

(b) If one of the pupils from the above sample was chosen at random, what would be the Probability that their favourite flavour of crisps was Plain?

Q2: The ages of children at Youth Club A are listed below:

7, 10, 11, 12, 9, 8, 7, 8, 10, 9, 9, 9, 7, 11, 8

a) Construct a frequency table showing these ages

b) What is the mean age of the children?

c) Youth Club B had the same number of children, but the mean age was 10. Make a comment comparing the two means.

ADDED VALUE ASSESSMENT - A

Paper 1 Time: 20 minutes Marks

No calculator is permitted Answers without explanation may receive no credit;

Make sure all your working is clear.

All questions must be attempted.

1 Sports4u.com has a sale on all sports shoes.

Original Price £80

20% Discount!!

(a) How much money will be saved on the above sports shoes? (1) (b) What is the new price of these sports shoes? (1)

2 During one week in winter the midday temperatures in Edinburgh were recorded as shown in the table below.

Day Sun Mon Tue Wed Thurs Fri Sat Temp (oC) 1 2 4 1 1 4 3

Calculate the mean midday temperature for the week correct to 2 decimal places (3)

3 240 pupils are going on a school trip to Alton Towers. Only 83 of these pupils were brave

enough to ride the Nemesis rollercoaster.

(a) How many pupils had a ride on the Nemesis rollercoaster? (2)

(b) How many pupils did NOT have a ride on Nemesis? (1)

4 Laura collects her paper round money on a Sunday. She has to collect £12.75 in total from her Brown Street customers and £18.20 from her High Street customers.

(a) How much should she collect altogether? (2) (b) Including tips she received £40.

How much of this money was made up in tips? (2)

5 Paul cycles 2.3 miles for 6 days. What is the total distance he cycled? (3)

Total (15)

End of Paper 1

ADDED VALUE ASSESSMENT - A

Paper 2 Time: 40 minutes Marks

You may use a calculator. Answers without explanation may receive no credit;

Make sure all your working is clear.

All questions must be attempted.

1 It took Kate 5 hours and 20 minutes to drive from Edinburgh to Liverpool at an average speed of 45 miles per hour. How far is it from Edinburgh to Liverpool?

(3)

2 A hotel charges a set fee of £200 for the use of their function room AND an additional £15 per guest for weddings.

(a) Let x be the number of guests and write down a formula in x for the total cost of a wedding. (1)

(b) How much would it cost for a wedding with 55 guests? (1)

(c) Ian and Jill have £1400 to pay for their wedding function.

Form an equation in x and solve it to find the maximum number of guests they can invite. (3)

25m

10m

3.5m

1.5m 3

This swimming pool is 25m long and 10m wide.

It is 1.5m deep at the shallow end and 3.5m deep at the deep end.

Calculate the volume of water in cubic metres in the pool when it is full. (5)

4 The sides of a bridge are constructed by joining sections. The sections are made of steel girders.

3 sections 2 sections 1 section

Number of Sections (s) 1 2 3 4 ………. s Number of Girders (g) 3 7

(a) Write down a formula for the number of girders, g, required when the number of sections, s, is known. (2)

(b) How many girders will be needed for 10 sections? (1)

(c) How many sections can be constructed from 87 girders? (2)

5 ABCD is a RHOMBUS with an area of 24 square units. What are the coordinates of B and D?

(2)

6 A banner for a parade is to be edged all around with gold braid.

The banner (shown above) is in the shape of a rectangle with an isosceles

triangle below it.

Calculate the total length of gold braid needed. (6)

32cm

56cm 86cm

7 Alice, whose eyes are 4.5 feet above ground level, is attempting to measure the height of a clock tower. She is standing 23 feet away from the clock tower looking at the top at an angle of 67o to the horizontal.

Calculate the height of the clocktower correct to 2 decimal places.

(4)

Total (30)

End of Paper 2

ADDED VALUE ASSESSMENT - B

Paper 1 Time: 20 minutes Marks

You may use a calculator. Answers without explanation may receive no credit;

Make sure all your working is clear.

All questions must be attempted.

Q1 : Mrs Young bought a new Volkswagen Polo for £9000. In the first year it lost 20% of its value.

(a) How much did it loose in the first year? (1) (b) What is it now worth? (1)

Q2 : Harry downloads music each week to his MP3 player. The number of downloads is shown for the first 6 weeks is shown in the table below:

Week 1 2 3 4 5 6

Downloads 9 7 12 10 15 5

Calculate the mean number of downloads per week correct to 2 decimal places. (3)

Q3 : A brown bear weighs 900kg before it hibernates for the winter.

During the winter it loses 10

3 of its body weight.

(a) How much weight did the bear loose during hibernation? (2) (b) How much did he weigh at the end of his hibernation period? (1)

Q4 : A decorator knows that he usually he can get 3 strips from a roll of wallpaper. For a hallway he uses 2 strips of length 2.3m and 2.75m. The roll of wallpaper is 7.4metres long.

(a) What length of wallpaper has he used in the first two strips? (2) (b) Does he have enough left in the same roll to cover a length of 2.2m? (2)

Q5 : For a chemistry experiment each group of pupils needs to measure 24.4ml of an acid. If there are 6 groups in the class, how many millilitres of acid is used altogether? (3)

END OF PAPER 1

ADDED VALUE ASSESSMENT - B

Paper 2 Time: 40 minutes Marks

You may use a calculator. Answers without explanation may receive no credit;

Make sure all your working is clear.

All questions must be attempted.

Q1: Mr Campbell takes his family on a holiday to York. If he drives the 180 miles in 4 hours 30 minutes, what is his average speed for the journey?

(3)

Q2: A BMX start ramp is shown opposite:

(a) Calculate the area of paint needed to cover side A. (3) (b) What volume of concrete would be needed to create the whole of the start ramp?

(2)

Q3: Triangle ABC is shown below. A is the point (-2, -1) and B is the point (4, -1).

Find the co-ordinates of C.

(5)

(-2,-1) (4,-1)

Q4: In a Greek café the tables are triangular in shape.

Tables (T) 1 2 3 4 5

People (P) 3 4

(a) Copy and complete the table above. (1)

(b) Write down a formula which will give P, the number of people, when you have T, the number of tables. (1)

(c) How many people can be seated at 13 tables? (1)

(d) How many tables would be needed for 21 people? (2)

Q5: A Swedish home store sells glasses in packs of 3.

Each shelf in the warehouse can hold x number of packs.

(a) Make an expression in x for the number glasses that can be held on each shelf. (1) (b) If there are 5 shelves in each warehouse stocking these glasses, write another

expression in x for the number of glasses that are held in the warehouse. (1) (c) If the warehouse knows that in total there are 1800 individual glasses in stock, (i) Form an equation in x (1) (ii) Solve it to find the number of packs of glasses in the warehouse. (1)

Q6: The plan for a section of a church 50 metres high and 10 metres wide is shown opposite.

Regulations state that the angle xo of the steeple cannot exceed 70o.

(a) Calculate the angle and state whether this complies with regulations. (3) (b) Find the length, l, of the slanted roof. (3)

Q7 : The time of a swimmer’s race over 50m for two swim teams is shown below.

Freestyle Time over 50 metres

Team South Team North

5 2 3 7

4 4 2 0 3 0 4 8

7 5 2 1 4 1 6 9 9

1 5 6

2 7 means 27seconds

(a) What is the modal swim time ? (1) (b) Which team has the fastest time ? (1) (c) What is the median swim time for each team ? (3)

END OF PAPER 2

Answers - Calculator

Solving Linear Equations and Simplifying

Core Skills

1) a) 3x + 3 b) 5y -15

2)a) x = 2 b) y = 4 c) m = 3 d) x = 50

3)a) a = 2 b) x = 8 c) r = 7 d) c = 9

Context

1)a) i) 4x = 3x + 5 ii) x = 5 iii) 20 cm

b) i) 30 – x = 2x ii) x = 10 iii) 20 cm

2)a)

No of stars (s)

1 2 3 4 11

No of pieces of wire (w)

5 10 15 20 55

b) w = 5s c) 80 pieces of wire

3)a)

No of fence posts (F)

2 3 4 5 20

No of panels (P)

3 6 9 12 57

b) P = 3F – 3 c)i) 9 fence posts ii) 1 panel

Area

Core Skills

1) 25cm2 2) 48 cm2 3) 113.1 cm2 ( to 1 decimal point) 4)65 cm2

Context

1) 5394 cm2 2)a) 67 cm2 b) 231 cm2 3) 3840 cm2

4)a) 9212 cm2 b) Yes, because his kite is 288 cm2 less than 9500 cm2

5)a) 962 cm2 b) 265.5 cm2 ( to 1dp) c) 1227.5 cm2

Volume

Core Skills

1)60 cm3 2) 216 cm3 3) 7854 cm3 (to the nearest whole number)

Context

1) 603.2 cm3 (to 1dp) 2)a)1680 cm3 b) 307.2 cm3

3)a) 480000 cm3 b) 480 litres c) 96 d) 39 200cm²

4) 11 cm

Distance, Speed, Time Problems

Core Skills

1) 280 km 2) 24 km per hr 3) 3 hours

Context

1) 150 miles 2) 2 hr 15 mins 3)a) 4 mph b) 15 mins

4) Tom was obeying the law, he had an average speed of 24mph. Andy and Kirsty were not obeying the law, their speeds were 36 mph and 33 mph.

Pythagoras

Core skills

1a) 32.7 b) 63.6 c) 12.8 d) 60.0 e) 20.7

Context

2a) AB = 1m b) DC = 2.4m

3. 9.57cm

4.a b. 1.03m

2m 2.25m

5. 3.79m 6. 9.17m 7. 20.9m

8a 8.5cm b. 4.25cm 9. 10 units

Trigonometry

Core skills

1a. 9.9 b. 3.7 c. 53º d 16.2

Context

2. 25.6m 3. 24.4º

4. 76.0º 5. DF = 16.1cm

Co-ordinates

1) a) Diagram Drawn

b) D (0,3) c) 3.6 units

2) a) (-1,-3) b) 5.7 units (1dp)

3) a) Pupils diagram

b) Rhombus

c) 4.5 units

Comparing Data Sets

Core Skills

1)a) 5.25 b) 3 c) 4.5 d) 6 e) the mode- lowest number

Context

1) Crisp flavour No of people Angle Salt and vinegar 22 198o Prawn cocktail 10 90 o Plain 8 72 o

2)a) b) 9 years old

c) The mean age at Youth Club A is lower than Youth Club B. This shows that there were more younger people there than at YCB

Age Frequency 7 3 8 3 9 4 10 2 11 2 12 1

Assessment A

Paper 1

1(a) 20% of £80 = 0.2 x 80 = £16 Knowing how to find 20%

(b) £80 -£16 = £64 Knowing to subtract 2 1+2+4+1+1+4+3 =16

16 7 = 2.2857

2.29 to 2dp

Knows to add Divides correctly by 7 Rounds correctly

3(a) 1/8 of 240 = 2408 = 30

3/8 of 240 = 30 x 3 = 90

Finds an eighth Finds 3 eighths

(b) 240 – 90 = 150 pupils Knows how to use result 4(a) £12.75 +£18.20

= £30.95

Knows to add Adds decimals correctly

(b) £40 - £30.95 = £9.05 Has a strategy to tackle differing no of decimal places

Subtracts decimals correctly

5 2.3 x 6 = 13.8 miles Know 6 times table Knows how to carry Handles decimal point correctly

Paper 2

1 T = 5 1/3 hours

D = SxT

D = 45 x 5 1/3

= 240 miles

Converts time to hours only Uses appropriate formula Calculates D

2(a) 15x + 200 Devises expression (b) 15 x 55 + 200 = £1025 Calculates cost (c) 15x + 200 = 1400

15x = 1200

x = 80

Forms equation Performs operations correctly solution

3 A of rectangle = 25 x 1.5

= 37.5m2

A of triangle = ½ x 25 x 2

calculates area of rectangle

Area of triangle

= 25m2

Area Total = 37.5 + 25

= 62.5 m2

V = A x h

= 62.5 x 10

= 625 m3

Adds to find area of composite

shape

Knows how to find volume

solution 4(a) TABLE NOT REQUIRED

g = 4s -1

identifies steps of 4 completes formula

(b) g – 4 x 10 -1

= 39 girders

solution

(c) g = 87

4s -1 = 87

4s = 88

S = 22

appropriate reasoning solution

5 B(1,2)

D(7,2)

one coordinate 2nd coordinate

6 Width of right angled triangle = 16cm

Height of triangle = 86cm -56cm = 30cm

X2= 302 + 162

X = 34cm

Total = 32 + 56 + 34 + 34+ 56

= 212cm

Finds width of triangle Knows height of triangle Knows to use Pythagoras’ Theorem Length of sloping edge Know to add lengths solution

7 Tan 67 = O/23

O = 23 x tan67

= 54.1846

= 54.18 feet to 2 dp

Total Height = 54.18 + 4.5

= 58.68 feet

knows to use tangent ratio operation height of triangle total height of tower

Assessment B

Paper 1

Question Solution Comments 1 £9000 ÷ 5 = £1800

£9000-£1800 = £7200

Knows how to find 20% Subtracts to get correct

answer 2 9+7+12+10+15+5 = 58

58 ÷ 6 = 9.6666....

Mean = 9.67 to 2dp

Knows to find sum Divides by 6 Rounds correctly

3 (a)1/10 of 900 = 90kg

3/10 = 270kg

(b)900 – 270 = 630kg

Finds a tenth Finds 3 tenths Knows to subtract

4 2.3 + 2.75 = 5.05

7.4 – 5.05 = 2.35

Yes as 2.35 >2.2

Knows how to add Subtracts correctly Answers correctly with reason

5 24.4 x 6 = 146.4 Knows 6 times table Knows how to carry Knows how to handle decimal

point Paper 2

Question Solution Comments 1 T = 4.5 hours

S = D ÷ T

= 180 ÷ 4.5

= 40mph

Makes time into hours only Knows relationship S = D ÷ T

Calculates S

2 (a) As = 2x2 = 4m2

At = 0.5 x 1 x 2 = 1m2

Total area = 1 + 4 = 5 m2

(b) V = Ah = 5 x 4

= 20m3

Finds area of square Finds area of triangle Adds to find total area Knows how to find volume Calculates V

3 (a) (T, P ) : (3,5), (4,6), (5,7)

(b) P = T + 2

(c) P = 13 + 2 = 15

(d) P = 21

=> 21 = T + 2

=> T = 19

Completes table Constructs formula Uses formula Reasoning Steps

4 (a) 3x

(b) 5 x 3x = 15x

(c) (i) 15x = 1800

(ii) x = 1800 ÷ 15 = 120

Interprets Interprets Operation 1 Finds answer

5 (a) tanx = 0pp/adj = 20/5

tan-1x = 4 = 75.964o

No as 75.96>70

(b) L2 = 202 + 52

= 425

L = √425

= 20.6 metres

Reasoning Inverse tangent Clear reasoning with

comparison Strategy

Finds square root Finds answer

6 52 = h2 + 42

h2 = 25-16 = 9

h = 3

C(-2+4, -1+3)

= C(2,2)

Strategy Sets Pythagoras rule up

correctly Finds height of triangle Knows to add distances Correct answer

7 34 seconds

Team North ( 23 sec )

Team South ( 34 + 41)/2

= 37.5sec

Team North = (38+41)/2

= 39.5 sec

Correct answer Correct answer Knows how to find median Finds answer

Correct answer