A grade B student can …

GCSE Foundation Revision

Grade D to C

Name: ______________

a grade D student can …

Number

Estimate answers to calculations involving division

Use the terms square, positive and negative square root, cube and cube root

Recall integer squares from 2×2 to 15×15 and the corresponding square roots

Recall the cubes of 2, 3, 4, 5 and 10

Multiply two decimals such as 2·4 × 0·7

Convert decimals to fractions and fractions to decimals

Do calculations with simple fractions involving subtraction

Increase or decrease a quantity by a given percentage

Algebra

Multiply out expressions with brackets such as 5(3x – 2)

Factorise expressions

Write the terms of a sequence or a series of diagrams given the nth term

Draw lines such as y = 2x + 3

Solve problems involving straight lines

Solve linear equations with unknowns on each side such as 3x – 4 = 5 + x

Solve linear equations with brackets such as 2(5x + 1) = 28

Substitute numbers into more complicated formulae such as

Solve problems involving graphs, such as finding where the line y = x + 5 crosses the line y = 1

Draw graphs of simple quadratic functions such as y = 2x2 and y = x2 + 2

Shape and Space

Find the area of a triangle, parallelogram, kite and trapezium

Find the area and perimeter of compound shapes

Calculate the circumference of a circle to an appropriate degree of accuracy

Calculate the area of a circle to an appropriate degree of accuracy

Reflect shapes in lines such as x = 2 or y = –1

Rotate shapes about the origin

Describe fully reflections and rotations about the origin

Identify reflection symmetry in 3-D solids

Translate a shape using a description such as 4 units right and 3 units down

Enlarge a shape by a positive scale factor from a given centre

Calculate simple average speeds from distance–time graphs

Draw a quadrilateral such as a kite or a parallelogram with given measurements

Construct and recognise the nets of 3-D solids such as pyramids and triangular prisms

Draw plans and elevations of 3-D solids

Data Handling

Calculate the mean for a frequency distribution

Construct a stem-and-leaf diagram (ordered)

Construct a frequency diagram

Interpret a time series graph

Draw a scatter graph by plotting points on a graph

Interpret the scatter graph

Classify and know the difference between various types of data

Design and use data collection sheets and questionnaires

Use a variety of different sampling methods

Use a two-way table to find a probability

Understand mutually exclusive events

Use the fact that the probabilities of mutually exclusive events add up to 1

a grade C student can …

Number

Find the least common multiple (LCM) and highest common factor (HCF) of two simple numbers

Write a number as a product of prime factors

Solve numerical problems using a calculator efficiently and appropriately

Find minimum and maximum values

Divide a number by a decimal such as 1 ÷ 0·2

Work out a percentage increase or decrease

Express one quantity as a percentage of another

Do calculations with mixed numbers and simple fractions involving division

Solve complex ratio problems, such as sharing out money between two groups

Solve ratio and proportion problems using the unitary method

Algebra

Multiply out expressions with brackets such as y(3y – 8)

Expand and simplify two expressions of the form (x + n)

Use index notation and index laws for positive and negative powers

Write the nth term of a sequence or a series of diagrams

Solve more complex linear equations such as 3x – 12 = 2(x – 5)

Form and solve equations such as x3 + x = 12 using trial and improvement methods

Rearrange linear formulae such as s = 4q - 7

Find the gradients of straight-line graphs

Solve inequalities such as 3x < 9 and 4x – 3 < 10 and 4x < 2x + 7

Represent sets of solutions on the number line

Shape and Space

Solve problems involving circles such as finding the area and perimeter of a semicircle

Calculate volumes of triangular prisms, parallelogram-based prisms and cylinders

Solve problems involving surface areas of prisms

Convert between measures of area and volume

Classify a quadrilateral by geometric properties

Use angle and symmetry properties of polygons and angles in parallel lines

Calculate exterior and interior angles of a regular polygon

Find the midpoint of a line segment

Use and understand coordinates in three dimensions

Reflect shapes in the lines y = x and y = –x

Rotate shapes about any point

Describe fully reflections and rotations about any point

Find the centre of a rotation and describe it fully

Combine reflections and rotations

Translate a shape by a vector such as

Transform shapes by a combination of translation, reflection and rotation

Understand and use compound measures such as speed and density

Construct a perpendicular bisector of a line, from a point to a line, from a point on a line

Construct angles of 60° and 90° and the bisector of an angle

Identify congruent shapes

Use Pythagoras’ theorem

Construct loci

Data Handling

Find the mean, median class and modal class for grouped data

Use measures of average and range to compare distributions

Draw a line of best fit on the scatter graph by inspection

Identify possible sources of bias in the design and use of data collection sheets & questionnaires

Understand relative frequency as an estimate of probability

Use relative frequency to compare outcomes of experiments

Number D

1. Estimate the value of:

38 197

83

(4)

2. For only this question use a calculator work the answer to:

2∙24 16∙8

(6∙8 – 1∙9)

Write down all the numbers on your calculator display

(2)

3. Given that 67 112 = 7504, write down the answers for:

a) 6∙7 1∙12

(1)

b) 7504 ÷ 670

(1)

4. A computer is reduced by 15% in a sale. The original price is £560. Calculate the sale price.

(3)

5. Fred can’t decide which microwave to buy. The ‘Burnyourmouth’ model is £60 + 17∙5% VAT but the ‘PingPingPing’ model is £70 including VAT. Which is the better deal?

(4)

6. Sheila got 183 out of 300 in a test. Bob got 24 out of 40 on a different test. Who got the higher percentage?

(3)

7. Bert runs of a mile every day. What is the number of miles Bert runs in a week to the nearest mile?

(3)

8. Calculate

(3)

9. Calculate simplifying your answer.

(4)

10. Grandma Margaret's Butterfly Cakes (for 12 people)

2 eggs

100g of sugar

120g of flour

150g of margarine

What ingredients are needed for 18 people?

eggs

g of sugar

g of flour

g of margarine

------- ------ -------- ------

(4)

11. Albert and Ethel share £240 in the ratio 3 : 5 . How much does Ethel receive?

(3)

12. Buzz travels 150 kilometres in 1hour 30 minutes. Calculate Buzz’s speed in km/h.

(3)

13. Write these numbers in order of size.Start with the smallest number.

65%0.72

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

(2)

Number C

1.

a) Write 60 as a product of prime factors

(3)

b) Write 45 as a product of prime factors

(3)

c) Find the HCF of 45 and 60

(2)

d) Find the LCM of 45 and 60

(2)

2. If x = 5, write down the value of 2x²

(2)

3. Work out 4 - 1

(4)

4. Hannah measures the length of her train. She says it is about 21cm to the nearest cm. What is the greatest and least value of the length of the train?

(2)

5. Calculate the % increase from 45cm² to 54cm².

(3)

6. Calculate the compound interest on £2500 for 3 years at 5% p.a. Use a calculator

(4)

7. A coach carries 54 passengers. How many coaches are needed to transport 528 supporters to the Man United match?

(3)

Algebra D

1. Write down the first three terms of the sequence described by the nth term n² - 3.

(3)

2. P = F(B -1) . Calculate the value of P when B = -5 and F = 20.

12

(2)

3. a) Write down an expression for the total cost in pence of x chocolate bars at 80p and y ice creams at 75p each.

(2)

b) Write down a formula for the total cost, C, in pence.

(1)

4. Sam buys t Spiderman toys at 60p and 3 at £1.20. The total cost is £6.

a) Construct an equation.

(3)

b) Solve the equation to find the value of t.

(2)

5.

x + 5

x

a) Write down an expression for the perimeter,P, of the rectangle in terms of x.

(2)

b) If the P = 30cm, find the longest side of the rectangle.

(3)

6. Find the value of the largest angle.

2x+60º

x

x+20º

120º

Diagram not drawn to scale

(4)

7. Simplify:

a) 5a + 2b – 3a + b

(2)

b) p² + p² + p²

(2)

8.Expand 3(x – 4)

(2)

9. Factorise completely:

a) 5a – 20

(2)

b) p² - 5p

(2)

10. Solve:

a) 2x – 4 = 14

(2)

b) + 3 = 18

(2)

c) 4(3x + 2) = 44

(3)

d) 5x + 3 = 13 + 3x

(3)

11.

a) Complete the table of values for y = x² + 3.

x

-2

-1

0

1

2

y

7

4

(3)

b) Draw the graph of y = x² + 3

y

x

(2)

12. Draw the graph of y = 2x – 4.

y

x

(2)

13. Hannah likes to feed the ducks at her local park. She leaves the house at 11.00a.m. The distance time graph shows her journey:

(min)

a) On the way to the park, Hannah stops to have a snack. At what time did this occur?

(1)

b) How long did Hannah stay at the park?

(1)

c) What was Hannah’s average speed on the way home?

(3)

Algebra C

1. Simplify the following:

a) p³ p²

b) 2t² 5t4

c) b7

b³

d) 24k6

3k²

e) (y3)2

(10)

2.

a) Simplify 3(x + 4) + 2(x +3)

(4)

b) Simplify 5(y + 3) – 4(y – 6)

(4)

3. Make x the subject of the y = 3x -6

(2)

x + 5

4.

Diagram not drawn to scale

x

x

x - 2

The perimeter of the trapezium is 13cm. Calculate the longest side.

(4)

5. Find the value of the smallest angle.

2x+60º

x

x+20º

120º

Diagram not drawn to scale

(3)

6. Solve 4x – 5 7.

(2)

Show your answer on the number line below:

(2)

Shape D

1. Rotate triangle EFG 90º clockwise about the origin. Label

y

the new triangle E’F’G’.

x

G

E

F

(3)

2. Reflect triangle PQR in the line y = -1. Label the image P’Q’R’.

y

x

R

Q

P

(3)

3. Describe the transformation of shape A to shape B.

y

A

B

x

(3)

4. Enlarge the triangle by a factor of 2 from centre P.

y

P

x

(3)

5. Find the missing angle in each diagram giving reasons for your answers:

a)

x = Reasons:

(3)

b)

x = Reasons:

(2)

c)

s = Reasons:

(3)

6. Calculate the interior angle of a regular hexagon

(3)

7. Draw a plane of symmetry on the solid:

(1)

8. Find the area and perimeter of the following shapes:

a)

3cm

4cm

5cm

Perimeter =

Area =

(4)

6cm

b)

6cm

10cm

Perimeter =

Area =

8cm

(5)

c)

Perimeter =

Area =

5cm

4cm

(4)

9. Find the area and circumference of the circle given below:

20cm

(Take π = 3)

Area:

(3)

Circumference:

(3)

10. Dorothy is painting her shed. 1 litre of paint covers 2m². How much paint does she need?

2m

3m

2m

(4)

11. You are looking at a solid from the side. Draw the front elevation and plan.

FRONT

(3)

Shape C

1. Calculate the areas of the following shapes:

(Take π=3)

a)

2m

(3)

b)

2m

(4)

2. Calculate the volume of the world’s largest Toberlone piece shown below:

50cm

10cm

50cm

(5)

“SUCCESS comes in ‘cans’ not ‘can’ts’”

3.

Calculate the volume of ‘success’ in the can shown.

(Height = 10cm and radius = 3cm - take π=3)

(4)

4. Find the missing sides of the following triangles:

a)

12cm

5cm

x

(3)

b)

x

6cm

10cm

(3)

5. Find the surface area of the solid shown below:

4cm

2cm

3cm

(6)

6. A ship leaves harbour A and sails on a bearing of 050º to harbour B. What is the bearing of harbour A from harbour B?

(2)

7. The Great Western Don’tStandSoCloseToMe (which looks like a cute bunny but isn’t!!!) has a nasty sting which it uses if people get too close to it. The zookeeper is trying to feed him. It is a particularly bad day and The Great Western Don’tStandSoCloseToMe is only happy if:

- the zookeeper doesn’t get any closer than 50cm to him

- the zookeeper stays closer to the North wall than him.

Shade on the diagram below the areas where the zookeeper is ‘safe’.

Use a scale of 1:20 and show all construction lines.

NORTH WALL

(5)

8. Construct a perpendicular bisector through point A. Show all construction lines.

B

A

(3)

9. Bisect the angle below. Show all construction lines.

(3)

Data D

1. The number of silly mistakes a student makes in the first

10 questions of their Maths GCSE are shown in the table below:

Silly Mistakes

Frequency

1

0

2

8

3

2

4

2

5

3

a) Calculate the mean number of silly mistakes.

(4)

b) Calculate the mode for the silly mistakes

(1)

2. The pie chart shows information on how students travel to school.

a) What is the modal form of transport?

(1)

b) If 320 students travel to school, how many use the bus?

(2)

3. Sam was counted the number of sweets in ten ‘Millions’ packets. The number of sweets he counted are as follows:

35, 42, 33, 55, 63, 29, 37, 48, 43, 51

(he was very upset to find that there wasn’t a million sweets even though it did say so on the packet!?!)

Represent this information using a stem and leaf diagram.

(3)

4. a) ‘Only intelligent people think that smoking should be banned in

public places.

Do you think smoking should be banned in public places? Yes No

Is this question appropriate to use in a questionnaire?

Give a reason to support your answer.

(2)

b) Mr Healthy visits a school and asks the first 10 students he can find a question about their lunch. They are all in Year 7 and he is delighted to hear that they all eat healthy sandwiches and no chips. He goes home happy knowing that all students eat healthily.

Is he correct?

(2)

5. The following data was collected - number of hours revision doing past paper questions and the final GCSE %.

Hours

7

6

5

7

9

6

4

8

9

10

GCSE %

58

55

35

65

90

45

35

75

83

95

a) Represent this information using a scatter diagram

GCSE

%

Hours Revision

(2)

b) Draw the line of best fit on your scatter diagram.

(1)

c) Describe the correlation

(1)

6. A bag has 4 colours of sweets. George loves blue sweets. The probability of getting the other colours in the bag are:

Colour

Red

Yellow

Green

Blue

Probability

0∙3

0.25

0.12

?

a) What is the probability of getting a blue sweet

(2)

b) If the bag contains 200 sweets, estimate how many sweets would be red.

(3)

Data C

1. The number of silly mistakes a student makes in the their Maths

GCSE papers are shown in the table below:

Silly Mistakes (m)

Frequency

0m<4

6

4m<8

8

8m<12

4

a) Estimate the mean number of silly mistakes.

(4)

b) In which class interval is the median number of silly mistakes?

(2)

2. Describe the type of correlation in the scatter diagram given below:

(1)

3. Mr Healthy hates fast food. He is interested to find out the eating habits of students at his local school. Design a suitable question for a questionnaire that he could use to collect the data.

(2)

4. Tina rolls a die and records the numbers she gets.

a) Write down the relative frequency of getting a 2.

(2)

b) If Tina rolls the die 450 times, approximately how many times would the number 4 occur?

(3)

5.

What is the probability of getting double six when rolling two dice?

(Hint: draw a sample space)

(3)

÷

÷

ø

ö

ç

ç

è

æ

-

3

4

´

3

5

31

43

-

14

35

+

4

3

3

2

5

3

3

4

1

3

3

x

´

£

£

9

)

1

(

D

A

C

+

=