10 steps to (edexcel) certificate...

PiXL Maths Associates

10 steps to (Edexcel)

Certificate Success!

A PiXL 10-session Booster Resource aimed at E/F/G Borderline candidates


Contents Session 1 Basic Arithmetic & BODMAS 1.1 Write a number in words / place value

Use of Basic Arithmetic Reading number lines and scales Reading timetables 1.2 Using a calculator BODMAS Simple index numbers

Session 2 Transformations & Coordinates 2.1 Reflect simple shapes using a mirror line

Order of rotational symmetry Translate a shape using a description such as 4 units right and 4 units down Enlarge a shape by a positive scale factor 2.2 Find the coordinates of the midpoint of the line segment AB, given the points A and B Plot points in all 4 quadrants

Session 3 Displaying Data 3.1 Bar Chart Pictograms 3.2 Interpreting Pie Charts Combinations

Session 4 Formulae & equations 4.1 Substitute numbers into simple formulae and expressions Rearrange linear formulae such as s = 4q - 7 Use formulae expressed in words 4.2 Solve simple linear equations

Session 5 2D and 3D Shapes 5.1 Know the name of standard 3D shapes Find the area of a triangle and rectangle Find the area and perimeter of compound shapes Session 6 Sequences & Basic Algebra 6.1 Generate terms of a sequence using term-to-term methods Generate terms of a sequence in pictures 6.2 Multiply out brackets expressions with brackets such as 5(3x-2) Collecting like terms

Session 7 Probability & Averages 7.1 Calculate the mean, mode and median for small data sets 7.2 Understand that probabilities must be written as fractions, decimals or percentages Use the fact that the probabilities of mutually exclusive events add up to 1


Be able to calculate Expected Frequency

Session 8 Angles & Travel Graphs 8.1 Angles on a straight line, intersecting lines. Angle properties of triangles and quadrilaterals 8.2 Travel graphs

Session 9 Fractions & Decimals 9.1 Fraction of a shape shaded

Convert between fractions, decimals and percentages Order fractions, decimals and percentages Understand the effects of multiplying and dividing by numbers between 0 and 1

Session 10 Percentages 10.1 Work out a percentage of a shaded shape Express one quantity as a percentage of another


Session 1 Basic Arithmetic & BODMAS Test 1.1 Write a number in words / place value Use of Basic Arithmetic Reading number lines and scales Question 1


Question 2 Cinema tickets

Adult ticket: £8.65 Child ticket: £4.90 Senior ticket: £5.85

Tony buys one child ticket and one senior ticket. (a) Work out the total cost.

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

Stephanie buys adult tickets only. The total cost is £60.55 (b) How many adult tickets does she buy?

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

(Total 2 marks)

Question 3 The chart below shows the distances, in miles, between pairs of cities by the fastest route. For example,

the distance between Cardiff and Edinburgh is 400 miles by the fastest route.

London

155 Cardiff

212 245 York

413 400 193 Edinburgh

(a) Write down the distance between London and Edinburgh by the fastest route.

..…………….. miles (1)


Question 4

(a)

Write down the number marked by the arrow.

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

(b) Find the number 110 on the number line. Mark it with an arrow ( ↑ ).

(1)

(c) Find the number 0.27 on the number line. Mark it with an arrow ( ↑ ).

(1)

(Total 3 marks)

Total Mark /10


Test 1.2

Using a calculator BODMAS Simple index numbers

Question 1

Question 2

(a) Work out 51.62.3

85.36.42

Write down all the numbers on your calculator display.

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

(b) Give your answer to part (a) correct to 1 significant figure.

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

(Total 4 marks)


Question 3

(a) Work out 4 × 5 – 8

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

(1) (b) Work out 18 + 2 × 3

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

(1) (c) Work out (4 + 3) × 7

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

(1) (Total 3 marks)

Total Mark /10


Session 2 Transformations & Co-ordinates Test 2.1

Reflect simple shapes using a mirror line Order of rotational symmetry Translate a shape using a description such as 4 units right and 4 units down Enlarge a shape by a positive scale factor

Question 1 This question is about transformations of triangle A.

(a) Describe fully the single transformation that takes triangle A onto triangle B. ………………………………………………………………………………………….. …………………………………………………………………………………………..

(2 marks)

(b) Translate triangle A, 2 units to the left and 3 units down. Label the new triangle C. ………………………………………………………………………………………….. …………………………………………………………………………………………..

(2 mark) (Total 4 marks)


Question 2


Question 3

On the grid, draw an enlargement, scale factor 2, of the shaded shape.

(2)


Question 4 (a) Shade one more square to make a pattern with 1 line of symmetry.

(1)

(b) Shade one more square to make a pattern with rotational symmetry of order 2

(1)

(Total 2 marks)

Total Mark /10


Test 2.2

Find the coordinates of the midpoint of the line segment AB, given the points A and B Plot points in all 4 quadrants

Question 1


Question 2 Points A, B and C are three corners of a square ABCD. Write down the coordinates of A, B and C.

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7

×

×

×

A

B

C

x

y

A (............... , .................) B (............... , .................) C (............... , .................) (2 marks)


Question 3

(a) Write down the coordinates of the point P.

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

(b) Write down the coordinates of the point Q.

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

M is the midpoint of the line from Q to P. (c) Find the coordinates of M.

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

(Total 4 marks)

Total Mark /10


Session 3 Statistics & Probability

Test 3.1

Bar Chart Pictogram

Question 1 Emma asks her friends what type of TV programme they like best.

Type of TV programme Frequency

Cartoons 4

Drama 2

Quizzes 1

Soaps 6

(a) Draw a bar chart to show Emma’s results.

7

6

5

4

3

2

1

0Cartoons Drama Quizzes Soaps

Frequency

(2)

(b) Emma chooses one of her friends at random. What is the probability that this friend chose cartoons?

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

(Total 5 marks)


Question 2

(2)

(Total 5 marks)

Total Mark / 10


Test 3.2

Interpreting Pie Charts Combinations

Question 1

Total 3 marks


Question 2

Total 3 marks


Question 3

Total 4 marks

Total Mark /10


Session 4 Formulae & Equations

Test 5.1

Substitute numbers into formulae Rearrange linear formulae such as s = 4q - 7 Use formulae expressed in words

Question 1 (a) Work out the value of 2a +ay when a =5 and y = -3

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

(b) Work out the value of 5t2 – 7 when t = 4

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

(Total 5 marks)


Question 2 Make y the subject of the formula 5x + 3y =7

y = ..................... (2 marks)

Question 3 The cost, in pounds, of hiring a car can be worked out using this rule. The cost of hiring a car for n days is C pounds. Write down a formula for C in terms of n.

………………… (3 marks)

Total Mark /10

Add 3 to the number of days’ hire Multiply your answer by 10


Test 5.2

Solve linear simple equations Question 1 Solve 4y + 2 = 9

y = …………………………. (2)

Question 2

Question 3

(3) Question 4

(3)

Total Mark /10


Session 5 2D/3D Shapes

Test 5.1 Know the name of standard 3D shapes Find the area of a triangle & rectangle Find the area and perimeter of compound shapes

Question 1 Write down the name of each of these 3-D shapes

(i) ………………………. (ii) ……………………… (Total 2 marks)

Question 2

The diagram shows a shaded shape drawn on a centimetre grid. (a) Work out the perimeter of the shaded shape.

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

(b) Work out the area of the shaded shape. State the units of your answer.

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

(Total 3 marks)

(i) (ii)


Question 3 Here is a shape drawn on a centimetre grid.

(a) Find the perimeter of the shaded shape.

………………. cm (1)

(b) Find the area of the shaded shape. State the units of your answer.

…………………………. (2)

(Total 3 marks) Question 4 Here is a rectangle. 3.5cm Diagram NOT drawn accurately 5.6cm (a) Work out the perimeter of the rectangle.

……………. cm (1)

(b) Work out the area of the rectangle.

……………… cm3 (1)

(Total 2 marks)

Total Mark /10


Session 6 Sequences & Basic Algebra

Test 6.1

Write the terms of a sequence in pictures Generate terms of a sequence using term-to-term methods

Question 1. (a) Write down the next two terms in the number pattern

3, 7, 11, 15, …, …

(b) Write down, in words, the rule for finding the next number in the pattern from the one before.

(4 marks) Question 2

Copy and complete the table

Shape number 1 2 3 4 5 Number of dots 5 8 11 … …

(2 marks)


Question 3 Chi Sam is making patterns with dots.

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

. . . . . . . . . . . . Pattern 1 Pattern 2 Pattern 3 (a) In the space below, draw Pattern 4.

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

(b) Complete the table for the number of dots in each pattern. Pattern number 1 2 3 4 5 Number of dots 5 8 11

(2)

Total Mark /10


Test 6.2 Content:

Multiply out brackets expressions with brackets such as 5(3x-2) Collecting like terms

Question 1 Simplify 8c + 5d –c – 3d

…………………. (2)

Question 2

(a) Simplify m + m + m + m .........................

(1)

(b) Simplify p×q×4 .........................

(1)

(c) Expand 5(3x – 2)

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

(d) Expand 3y( y + 4)

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

(Total 5 marks)


Question 3 (a) Simplify 8x – 4x

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

(b) Simplify y × y × y

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

(c) Simplify 4x + 3y – 2x + 5y

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

(Total 3 marks)

Total Mark /10


Session 7 Probability & Averages Test 7.1

Calculate the mean, mode & median for small data sets Question 1

The sizes of the first eleven pairs of shoes sold in a shop one morning are

8 5 4 5 7 10 9 5 11 5 6

(a) What is the mode of the data?

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

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

(b) What is the median shoe size?

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

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

(c) Which of the mode or median would be more useful to the shopkeeper when he is ordering more shoes? Explain your answer.

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

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

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

(2)

(Total 6 marks)


Question 2

Total Mark /10


Test 7.2 Understand that probabilities must be written as fractions, decimals or percentages Use a probability scale Use the fact that probabilities add up to 1 Be able to calculate Expected Frequency

Question 1


Question 2


Question 3

Total Mark /10


Session 8 Angles & Travel Graphs Test 8.1

Angles on a straight line, intersecting lines Angle properties of triangles and quadrilaterals

Question 1

ABC is a straight line. (a) (i) Work out the size of the angle marked x (ii) Give a reason for your answer. ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………….

(2 marks) (b) (i) Work out the size of the angle marked y

..……………….. (ii) Give a reason for your answer ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………….

(2 marks)

(Total 4 marks)


Question 2:

Total Mark /10


Test 8.2

Travel graphs

Question 1

(2)


Question 2 Rana cycled from his home to the supermarket. Rana did his shopping in the supermarket. Then he cycled back home. The graph below is a distance-time graph of Rana’s complete journey.

(a) At what time did Rana leave his home?

…….. (2)

(b) What is the distance from Rana’s home to the supermarket? ……..

(2) (c) How long, in minutes, did Rana spend in the supermarket?

…….. (2)

(Total 6 marks)

Total Mark /10


Session 9 Fractions & Decimals

Test 9.1

Fraction of a shape shaded Convert between fractions, decimals & percentages Order fractions, decimals & percentages Understand the effects of multiplying and dividing by numbers between 0 and 1

Question 1

Question 2 Write these fractions in order of size. Start with the smallest fraction.

………..

(1)


Question 3

Change into a decimal

………..

(1) Question 3 Write 60% as a decimal

………..

(1) Question 4 Write 0.85 as a percentage

………..

(1) Question 5

Question 6 (a) Calculate 1 0.2

………..

(1)

(b) Calculate 2.4 0.6 ………..

(1)

Total Mark /10


Session 10 Percentages Test 10.1

Work out a percentage of a quantity Work out percentages of a shaded shape Express one quantity as a percentage of another

Question 1 Work out 70% of £340

£ ………………………… (3 marks)

Question 2

(2)


Question 3 Andrew got 42 out of 60 marks in a history test. He got 48 out of 50 marks in a geography test. The marks for each test were changed to a percentage. In which test did Andrew get the higher percentage mark? You must show all your calculations.

…….. (4 marks)

Question 4


Total Mark /10

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