Year 10 Maths Foundation Ark Globe Academy Remote Learning ... 10... · Area and Perimeter -...

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Year 10 Maths Foundation Ark Globe Academy

Remote Learning Pack Phase II

Monday 20 April –Friday 1 May

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Year 10 Foundation Revision Booklet

Day Title Work to be completed Resource provided

Outcome On-Line Support

1 Day 1 Test Lines, angles and shapes Foundation Test Booklet

Tasks completed and ready for submission

Hegartymaths Students’ VLE

2 Day 2 Test Area and Perimeter Foundation Test Booklet



3 Day 3 Test Fractions, Decimals and Percentages

Foundation Test Booklet



4 Day 4 Test Probability Foundation Test Booklet



5 Day 5 Test Simplifying and Substituting




6 Day 6 Test Ratio & Proportion Foundation Test Booklet



7 Day 7 Test Calculation & Accuracy Foundation Test Booklet



8 Day 8 Test Sequences, Functions and Graphs




9 Day 9 Test Inequalities Foundation Test Booklet



10 Day 10 Test Forming and solving Equations




Guidance/Instructions:

1. Each test consists of 20 marks. You are allowed 30 minutes for each test. 2. One test is to be completed each day. 3. Answers will be provided when you email daily.

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Day 1 Test Name: ____________________________ TOPIC: Lines, Angles and Shapes - FOUNDATION 1. (a) The diagram shows a regular octagon. Not drawn

accurately. The base line of the octagon is extended. Work out the size of angle y. ……………………………………………………………….. ……………………………………………………………….. ………………………………………………………………..

Answer …………………………………………………° (2)

(b) ABCD is a parallelogram. BD is a diagonal. Not drawn accurately. Work out the size of angle w.

………………………………………… …………………………………………

…………………………………………………………………………………………………..

Answer …………………………………………………° (3)

(Total 5 marks) 2. Three triangles are shown on the

centimetre grid. (a) Which triangle is not

isosceles?

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

(b) Work out the area of the triangle with the greatest area. State the units of your answer.

…………………………………………………………………………………………………

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

(Total 4 marks)

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3. (a) Work out the size of angle x. Not drawn accurately. ………………………………………………………………… ………………………………………………………………… …………………………………………………………………

Answer …………………………………………………° (2)

(b) Not drawn accurately. Give a reason why, if drawn accurately, ABC would be a straight line.

………………………………… …………………………………

………………………………………………………………………………………………… (1)

(Total 3 marks) 4.

(a) Which angles are vertically opposite? Circle your answer

a and b a and c b and c b and d c and d (1)

(b) Which angles are alternate? Circle your answer


(c) Which angles are corresponding? Circle your answer


(Total 3 marks)

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5. AD is parallel to BC. AE = DE. Not drawn accurately. Work out the size of angle BAE.

…………………………………………………… …………………………………………………… …………………………………………………… …………………………………………………… …………………………………………………… ……………………………………………………

Answer …………………………………………………° (Total 3 marks)

6. (a) These triangles are congruent. Not drawn accurately

State the condition they satisfy.

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

(b) These triangles are congruent. Not drawn accurately

State the condition they satisfy.

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

(Total 2 marks)

(Total for test = 20 marks)

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Day 2 Test Name: ____________________________ Area and Perimeter - FOUNDATION 1. The shape below is drawn on a centimetre grid. Estimate the area of the

shape.

Answer ............................................................... cm²

(Total 1 mark) 2. Field A is a rectangle with sides of 30 m and 70 m.

Field B is a square with the same perimeter as Field A. Not drawn accurately

How much bigger in area is Field B than Field A? You must show your working. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ............................................................................. m2

(Total 4 marks)

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3. This diagram shows Adam’s garden. It is in the shape of two rectangles joined together. Not

drawn accurately.

Work out the area of the garden.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ................................................................. m² (Total 4 marks)

4. Calculate the area of the triangle. Not drawn accurately.

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

Answer ............................................................... cm2

(Total 2 marks)

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5. ABCD is a trapezium. Not drawn accurately.

Calculate the area of ABCD. State the units of your answer.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ...................................................................... (Total 3 marks)

6. (a) The radius of this circle is 4 cm. Not drawn accurately

Work out the area. Use 𝜋 = 3.1. ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………………………………………

Answer ............................................................................ cm²

(3)

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(b) The diameter of this semicircle is 16 cm. Not drawn accurately

Work out the perimeter of the semicircle. Use 𝜋 = 3.1. ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………………………………………

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

(Total 6 marks)


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Day 3 Test Name: ____________________________ Fractions, Decimals and Percentages - FOUNDATION 1. (a) Write 30% as a fraction. ………………………………………………………………………………………………… …………………………………………………………………………………………………

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

(b) Write 80% as a decimal. ………………………………………………………………………………………………… …………………………………………………………………………………………………

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

(c) Circle the two values that are equivalent to 2

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66

100 0. 6̇ 60%

66

99 0.6

(2) (Total 4 marks)

2. Which of 2

5 or

5

8 is closer in value to

1

2 ? You must show your working.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ................................................................................... (Total 3 marks)

3. A gym has 275 members. 40% are bronze members. 28% are silver members. The rest are

gold members. Work out the number of gold members. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ............................................ (Total 3 marks)

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4. Put these in order starting with the smallest value.

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4 3

1

2 3.15 √9

You must show your working.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Smallest ....................................................................

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

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

Largest .................................................................... (Total 3 marks)

5. Work out the sale price. ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… …………………………………………………………

Answer £ ...................................................................... (Total 3 marks)

6. 120 men and 80 women were asked if they drive to work. Altogether 1

4 of the people said

yes. 1

3 of the men said yes. What fraction of the women said yes?

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………



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Day 4 Test Name: ____________________________ Probability - FOUNDATION 1. Here are three events for an ordinary fair dice.

A Roll an odd number B Roll a number greater than 6 C Roll an even number less than 3

Draw and label arrows to show the probabilities of events B and C on the probability scale.

(Total 2 marks)

2. Four teams A, B, C and D play matches against each other. The teams play each other

once. Complete the list of matches. One match has been done for you.

A plays B……………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

(Total 2 marks) 3. There are 25 counters in a bag. 12 are red, 5 are green and the rest are white. A counter is

chosen at random. Work out the probability that it is white.

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………


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4. A spinner has four sections A, B, C and D. The table shows the probabilities of the spinner

landing on A, B or C.

Outcome A B C D

Probability 0.2 0.3 0.15

Work out the probability of landing on D.

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

Answer ...................................................................................

(Total 2 marks) 5. A game is played with a fair spinner. The player spins the spinner

twice. The score is the difference between the two numbers. (a) Complete the table to show the scores.

First spin

1 2 3 4

Second spin

1 2

2

3 2

4

(2)

(b) The player loses if the score is 0 or 1. The player wins if the score is 2 or 3. Amy says,

“Two scores win and two scores lose, so the chance of winning is evens.” Is Amy correct? Tick a box.

Yes No

Give a reason for your answer.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(2) (Total 4 marks)

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6. Fay is testing an ordinary six-sided dice to see if it is biased. She throws the dice 120 times. (a) Work out the number of times the dice is expected to land on 1

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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

(b) Here are the actual results.

Number on dice 1 2 3 4 5 6 Total

Frequency 5 19 17 20 21 38 120

Is the dice biased? Tick a box.

Yes No Could not tell

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(2) (Total 3 marks)

7. (a) In a statistical experiment a fair, an ordinary die is rolled. Tick a box to show the

correct ending to the sentence below.

When this statistical experiment is repeated you will:

always get the same outcome

usually get the same outcome

usually get a different outcome

always get a different outcome

(1)

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(b) Tick a box to show the correct ending to the sentence below. An estimate of probability based on a statistical experiment is more reliable with

more trials

fewer trials

more time between trials

less time between trials (1)

(Total 2 marks) 8. An ordinary fair dice is rolled.

(a) Complete the tree diagram for the dice landing on 4

First spin Second spin

(1)

(b) Work out the probability of the dice landing on 4 both times.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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

(Total 3 marks)


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Day 5 Test Name: ____________________________ Simplifying and Substituting - FOUNDATION 1) In each part, match the statement to the expression. Circle your answer.

(a) Two more than x.

2x x + 2 x – 2 x2

(1) (b) Four less than x.

4 – x 4x 𝑥

4 x − 4

(1) (c) Three times x.

3x 𝑥

3 x + 3 x3

(1) (d) Half of x.

x ÷ 0.5 2

𝑥

𝑥

2 2x

(1) (Total 4 marks)

2) Which of these can be written as 𝑎

𝑏? Circle your answer.

b ÷ a a – b a ÷ b b − a

(Total 1 mark) 3) (a) Circle the expression that is equivalent to 4 × m m4 4m 4m m x m x m x m

(1) (b) Circle the expression that is equivalent to y × y × y

3y y2 3y2 y3

(1) (c) Circle the expression that is equivalent to a + b

b + a ab ba 2ab

(1) (Total 3 marks)

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4) You are given that a = 3 and b = 5. Tick whether each statement is true or false. Give a

reason for each answer.

Statement True False Reason

ab = 35

2b2 = 100

(Total 2 marks)

5) (a) Simplify fully 4x + 7y + 5x – y ………………………………………………………………………………………………….. …………………………………………………………………………………………………..

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

(b) Multiply out 4(x + 3)

…………………………………………………………………………………………………..

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

(c) Factorise x2 − 5x

…………………………………………………………………………………………………..

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

(Total 4 marks)

6) Here is a formula: 𝑉 = 1

2𝑥2ℎ

Work out the value of V when x = 11 and h = 6 ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………


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7) (a) Expand and simplify (x + 5)(x + 9) ………………………………………………………………………………………………….. …………………………………………………………………………………………………..

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

(b) Factorise fully 5x2 − 10xy

…………………………………………………………………………………………………..

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

(Total 4 marks) (Total for test = 20 marks)

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Day 6 Test Name: ____________________________ Ratio and Proportion - FOUNDATION 1) A drink is mixed in the ratio

lemonade : orange : cranberry = 6 : 3 : 2 What fraction is orange? Circle your answer.

3

8

2

11

3

11

6

11

(Total 1 mark)

2) 120 adults complete a survey. 45 are men. Write the ratio of men : women in its simplest form.

………………………………………………………………………………………………………… …………………………………………………………………………………………………………


3) Divide 270 in the ratio 3 : 2 : 1 ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ............... : ............... : ...............

(Total 3 marks) 4) At a school, number of boys : number of girls = 9 : 7. There are 116 more boys than girls.

Work out the total number of students at the school. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………


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5) Here are the ingredients to make 8 biscuits. 75 g flour

50 g sugar 40 g butter

2 egg yolks Work out the ingredients to make 20 biscuits.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

............................................................................... g flour

............................................................................... g sugar

............................................................................... g butter

............................................................................... egg yolks (Total 3 marks)

6) Here are two offers for batteries.

Zak wants to buy 40 batteries. Which is the cheaper offer? You must show your working.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………


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7) Laura buys a saddle in the UK for £950. Delivery is free. Steve buys the same saddle from Holland for 990 Euros. He pays 30 Euros for delivery.

£1 = 1.10 Euros Including the delivery charge, whose saddle is cheaper? You must show your working.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………



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Day 7 Test Name: ____________________________ Calculations and Accuracy - FOUNDATION Q1. Here is a list of numbers.

−9 −5 −3 −1 0 3 4 6 (a) Write down two numbers from the list that add up to 5

................................ and ................................

(1) (b) Write down two numbers from the list that have a difference of 13

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

(c) Write down two numbers from the list that multiply to give −15

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

(d) Use three different numbers from the list to make the following calculation correct.

20 ÷ ..................... = ..................... ÷ ..................... (1)

(Total 4 marks) Q2. (a) Write in figures the number: thirty thousand and sixteen

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

(b) Write in words the number 0.43

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

(c) Write down the value of the digit 9 in the number 41 982

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

(Total 3 marks)

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Q3. This is a bill for coffee and buns. The bill has coffee spilt on it.

How many buns were bought? You must show your working. ………………………………………………………………………………………………………

………………………………………………………………………………………………………

………………………………………………………………………………………………………

………………………………………………………………………………………………………

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

(Total 3 marks) Q4. Put signs in the boxes to make these calculations correct.

You may use the signs +, −, × and ÷

(a) 1 2 3 = 0 (1)

(b) 1 2 3 = 5 (1)

(c) 1 2 3 = − 4 (1)

(Total 3 marks)

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Q5. These cars are for sale.

(a) Which car is the cheapest?

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

(b) The price of each car is rounded to the nearest £100. Which price changes by the greatest amount? You must show your working.

…………………………………………………………………………………………………..

…………………………………………………………………………………………………..

…………………………………………………………………………………………………..

…………………………………………………………………………………………………..

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

(Total 4 marks) Q6. Use approximations to estimate the value of

………………………………………………………………………………………………………

………………………………………………………………………………………………………

………………………………………………………………………………………………………

………………………………………………………………………………………………………


Q7. x = 2500 to the nearest 100. Circle the smallest possible value of x.

2449 2450 2495 2499

(Total 1 mark) (Total for test = 20 marks)

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Day 8 Test Name: ____________________________ Sequences, Functions and Graphs - FOUNDATION 1. The diagram shows patterns made with sticks.

Pattern 1 Pattern 2 Pattern 3 (a) How many sticks are in Pattern 3?

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

(b) Draw Pattern 4.

(1) (c) How many sticks are in Pattern 6?

…………………………………………………………………………………………………..

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

(Total 4 marks) 2. Here is a linear sequence.

46 40 34 28 22 ...... Work out the nth term of the sequence.

………………………………………………………………………………………………………….. …………………………………………………………………………………………………………..


3. Here is the graph of y = 5 − x for values of x from 0 to 5

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(a) On the same grid, draw the graph of y = x + 1 for values of x from 0 to 5

(2) (b) Use the graphs to solve the

simultaneous equations y = 5 − x and y = x + 1

x = ............................................ y = ............................................

(1) (Total 3 marks)

4. Here is a straight-line graph. (a) Use the graph to work out the value of x when

y = 8

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

(b) Work out the gradient of the line. …………………………………………………… …………………………………………………… …………………………………………………… …………………………………………………… ……………………………………………………

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

(Total 4 marks) 5. Circle the equation of a line that is parallel to y = 5x – 2

y = 2x – 5 y = 5x + 2 y = 3x – 2 y = – x – 2

(Total 1 mark)

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6. (a) Complete the table of values for y = 2 + x − x2

x -3 -2 -1 0 1 2 3

y -10 0 2 0 -4

(2) (b) Draw the graph of y = 2 + x − x2 for

values of x from −3 to 3 (2)

(c) Draw the line y = −3 on the same grid. (1)

(d) Write down the solutions to the equation 2 + x − x2 = −3

Answer ……………………………………… (1)

(Total 6 marks)


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Day 9 Test Name: ____________________________ Inequalities - FOUNDATION 1. Put the correct symbol in each box. Choose from < > =

11 × 12

22 × 6

32

23

10

0.5

10

(Total 3 marks) 2. Circle the inequality shown by the diagram.

−7 < 𝑥 < 6 −7 ≤ 𝑥 < 6 −7 < 𝑥 ≤ 6 −7 ≤ 𝑥 ≤ 6

(Total 1 mark) 3. (a) 𝑥 is an integer.

−7 ≤ 𝑥 < 9

Work out the largest possible value of 𝑥2.

……………………………………………………………………………………………

……………………………………………………………………………………………

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

(b) 𝑦 is an integer. −4 < 𝑥 < 3 Work out the smallest possible value of y3

……………………………………………………………………………………………

……………………………………………………………………………………………

Answer .................................................................................

(1) (Total 2 marks)

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4. 10 < 5𝑥 ≤ 35 List the possible integer values of x.

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

Answer ......................................................................

(Total 3 marks)

5. Solve 2𝑛 + 1 ≤ 15 …………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

………………………………………………………………………………………………………… …………………………………………………………………………………………………………

…………………………………………………………………………………………………………

Answer ......................................................................

(Total 2 marks) 6. (a) Solve 4𝑥 − 7 ≤ 13

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

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

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(b) Show 3 < 𝑥 ≤ 8 on the number line.

(2)

(Total 4 marks)

7. (a) Write down all the integers that satisfy −3 ≤ 𝑛 < 2

……………………………………………………………………………………………

……………………………………………………………………………………………

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

(b) Show 2 < 𝑥 ≤ 10 on the number line.

(2)

(Total 3 marks) 8. Solve 5𝑥 − 2 > 3𝑥 + 11 …………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………

…………………………………………………………………………………………………………



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Day 10 Test Name: ____________________________ Forming and Solving Equations - FOUNDATION 1) (a) Here is a number machine.

Work out the output when the input is 9. Answer ......................................................................

(1) (b) Here is the same number machine.

Work out the input when the output is 9. Answer ......................................................................

(1) (Total 2 marks)

2) (a) Solve 6x = 54

…………………………………………………………………………………………………

x = ............................................................................. (1)

(b) Solve 3y + 15 = 9

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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

(c) Solve 4w + 2 = 2w + 7

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

w = ............................................................................ (3)

(Total 6 marks)

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3) (a) Rearrange the formula to make w the subject of y = 3w + 8

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

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

(b) Solve 5(x + 4) = 3x + 23

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

x = .............................................................................

(3) (Total 5 marks)

4) Solve the simultaneous equations 5x + 6y = 3 2x – 3y = 12

Do not use trial and improvement. You must show your working. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

Answer ................................................................................. (Total 3 marks)

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5) The area of the rectangle and the area of the triangle are equal. Not drawn accurately.

Work out the value of x. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… …………………………………………………………………………………………………………

x = .......................................................................................... (Total 4 marks)


You have completed the tasks. Well Done!

Year 10 Maths Foundation Ark Globe Academy Remote Learning ... 10... · Area and Perimeter -...

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Transcript of Year 10 Maths Foundation Ark Globe Academy Remote Learning ... 10... · Area and Perimeter -...