St Paul’s Catholic School Mathematics GCSE …...(c) The temperature, in C, at midday at the theme...
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Page 1 St Paul’s Catholic School Mathematics GCSE Revision MAY HALF TERM PACK 1 – NUMBER TOPICS TO GRADE 4/5 Name: ______________________________________ Maths Teacher:_______________________________
Transcript of St Paul’s Catholic School Mathematics GCSE …...(c) The temperature, in C, at midday at the theme...
Page 1
St Paul’s Catholic School Mathematics GCSE Revision
MAY HALF TERM
PACK 1 – NUMBER TOPICS TO GRADE 4/5 Name: ______________________________________ Maths Teacher:_______________________________
Page 2
Percentages, Fractions, Decimals Q1. Three students take the same test.
The test has 20 questions.
Each question has one mark.
The pass mark is 70%.
(a)
Did Elena pass the test?
Explain your answer.
.....................................................................................
.....................................................................................
..................................................................................... (1)
(b)
Did Clyde pass the test?
Explain your answer.
.....................................................................................
.....................................................................................
..................................................................................... (1)
(c)
How many questions did Alfie answer correctly?
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Answer ................................................. (2)
(Total 4 marks)
Q2. Karl sees this advertisement in a shop window.
HOCKEY KIT
Shirt £16.50
Pair of Shorts £8.50
SPECIAL OFFER!
Buy both items and receive a 10% reduction in price
Karl buys both items.
How much does he pay?
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Answer £ ................................................. (Total 3 marks)
Page 3
Q3. Here is an advert for a summer holiday.
(a) Martha books a 14-night holiday in May.
She books for herself, husband Billy and daughter Mary (aged 11).
She books the holiday online.
Explain clearly why the total cost will be £990.
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………................................................................................... (4)
(b) Salima books a 7-night holiday in April for two adults.
The travel agent adds a percentage surcharge to the cost of the holiday for booking fees.
Salima’s final bill is £642.60
What was the percentage surcharge?
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Answer ............................................... % (3)
(Total 7 marks)
Q4. In a school there are 800 students and 70 teachers.
10% of the students are left handed.
20% of the teachers are left handed.
How many left-handed students and teachers are there altogether?
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Answer ................................................. (Total 3 marks)
Page 4
Q5. Work out 45% of 330.
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Answer ........................................... (Total 2 marks)
Q6. (a) A triangle on this grid is shaded.
What percentage of the grid is shaded?
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Answer .............................................% (2)
(b) This shape consists of 3 equal squares.
What fraction of the shape is covered by the triangle?
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Answer .................................................. (2)
(Total 4 marks)
Q7. The price of a roll of film is reduced from £4 to £3.50
Calculate the reduction as a percentage of the original price.
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Answer ................................................. % (Total 3 marks)
Page 5
Q8. (a) Write 0.8 as a fraction. Give your answer in its simplest form.
.............................................................................................. ..............................................................................................
Answer ................................................ (2)
(b) (i) Work out 3/10 of 270.
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Answer ................................................ (2)
(ii) Kaye has 270 magazines.
She sells 30% of them.
How many magazines does she have left? ................................................................................... ...................................................................................
Answer ................................................ (2)
(Total 6 marks)
Q9. Work out the value of .............................................................................................. .............................................................................................. Answer ................................................
(Total 2 marks)
Q10. The table shows Ann’s marks in two tests.
Test Mark
1 60 out of 80
2 70 out of 100
In which test did Ann do better?
You must show your working.
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Answer ................................................. (Total 3 marks)
Q11. Write 65%, 0.7 and in order of size starting with the smallest.
You must show your working.
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Answer ................................................ (Total 3 marks)
Page 6
Q12. Tom works 12 hours each week.
He earns £4 per hour.
Tom saves of his earnings each week.
How many weeks does it take Tom to save £80?
You must show all your working.
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Answer ................................................. weeks (Total 4 marks)
Q13. (a) Circle the two fractions in the list that have the same
value as .
(2)
(b) Write as a percentage.
Answer .............................................. % (1)
(Total 3 marks)
Q14. Two bottles are on a shelf. The 3 litre bottle, A, is 55% full of water. The 2.5 litre bottle, B, is three-quarters full of water. Which bottle contains more water? You must show all your working.
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Answer ............................................
(Total 4 marks) Q15. Tom has £2 200.
He gives ¼ to his son and 2/5 to his daughter.
How much does Tom keep for himself?
You must show all your working.
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Answer ................................................. (Total 3 marks)
Page 7
Powers and Roots
Q1. (a) Work out the value of
………................................................................................................
...........................................................................................................
Answer .................................................. (2)
(b) (i) Write down the value of 92.
Answer .................................................. (1)
(ii) Tick the box for the statement that is true.
The sum of the squares of two odd numbers is always odd
The sum of the squares of two odd numbers is always even
The sum of the squares of two odd numbers could be odd or even
Give an example to justify your choice.
…………………....................................................................................
………………….................................................................................... (2) (Total 5 marks)
Q2. Work out the difference between the two square numbers in this list of numbers. 6 11 15 21 27 36 48 64
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Answer ................................................. (Total 2 marks)
Q3. (a) Write down the square of 11.
Answer .................................................. (1)
(b) Given that x = 12
Write down the value of x2
Answer.................................................. (1)
(c) Given that y3 = 125
Write down the value of y.
Answer .................................................. (1)
(Total 3 marks)
Q4. (a) Work out 74 × 74
Give your answer as a power of 7.
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Answer ................................................. (1)
(b) Work out 64 ÷ 64
Give your answer as a whole number.
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Answer ................................................. (1)
(Total 2 marks)
Page 8
Q5. Show that there are no square numbers between 9100 and 9200
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........................................................................................................ (Total 3 marks)
Q6. Glynn says that is the same as Show that Glynn is wrong.
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........................................................................................................ (Total 2 marks)
Q7. (a) Two square numbers under 50 have a difference that is also a square number. Which two square numbers are they?
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Answer .................... and ........................... (2)
(b) Three consecutive square numbers have a total greater than 50 but less than 100.
Which three square numbers are they?
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Answer ............ and .............. and .............. (2) (Total 4 marks)
Ratio
Q8. Divide £7200 in the ratio 2 : 3 : 7
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Answer £............. £ ............ £ ............ (Total 3 marks)
Q9. Jim’s class and Rosie’s class go on a trip to the zoo. Each pupil pays the same amount.
What is the total cost for Rosie’s class?
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Answer £ ................................................. (Total 3 marks)
Page 9
Q10. Packets of chocolate biscuits are sold in two sizes.
Which size is the better value for money?
You must show your working.
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Answer ................................................. (Total 2 marks)
Q11. Mohsin invests some money in a cash ISA (c) and in a savings account (s).
The ratio of the amounts of money invested is c : s = 3 : 7
He invests £3600 in the cash ISA.
How much money does he invest altogether?
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Answer £ ..............................................
(Total 2 marks)
Q12. Here are two rectangles, A and B.
Not drawn accurately
Is rectangle B an enlargement of rectangle A?
Tick the correct box.
Yes No
Explain your answer.
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........................................................................................................ (Total 3 marks)
Page 10
Rounding and Estimation
Q13.The table shows the size of population for five Derbyshire villages.
Village Population
Ashover 1796
Bamford 1184
Clowne 7447
Darley Dale 5167
Eckington 16684
(a) Write the population of Darley Dale in words.
Answer .....................................................................................................
….............................................................................................................. (1)
(b) Write the population of Clowne correct to the nearest 100.
Answer …..............................................................................................................
(1) (c) Write the population of Eckington to the nearest 1000.
Answer …..............................................................................................................
(1)
(d) How many more people live in Eckington than Bamford?
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……………................................................................................................ (2)
(Total 5 marks)
Q14. (a) A plant costs £4.99
How many of these plants can be bought for £50?
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Answer ....................................................................... (2)
(b) Jill writes £4.99 × 20 = £998
Is she correct?
Explain your answer.
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.................................................................................................................. (2)
(Total 4 marks) Q15. The area of a square is 387.5cm2.
(a) Work out the length of one side of the square. Give all the figures on your calculator display.
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Answer ......................................... cm (2)
(b) Give your answer to 1 decimal place.
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Answer ......................................... cm (1)
(Total 3 marks)
Page 11
Factors and Multiples
Q16. (a) From this list of numbers
65 5 25 70 75 34
(i) Write down a multiple of 10.
Answer ............................................... (1)
(ii) Write down a factor of 35.
Answer .............................................. (1)
(iii) Write down a square number.
Answer .............................................. (1)
(iv) Write down three-quarters as a percentage.
Answer .......................................... % (1)
(b) Work out 70 ÷ (65 – 5 – 25) × 75
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Answer .............................................. (2)
(Total 6 marks)
Q17. Here is a list of numbers.
3 4 6 8 9 12 18
(a) Write down four different numbers from the list that add up to 30.
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Answer .................... , ...................... , ..................... , ..................... (1)
(b) Write down one number in the list that is a multiple of 6.
Answer ....................................................................... (1)
(c) Write down all the numbers in the list that are factors of 18.
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Answer ....................................................................... (2)
(d) There are two square numbers in the list.
Work out the difference between them.
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Answer ....................................................................... (2)
(Total 6 marks)
Page 12
Q18. Here is a list of numbers
6 8 11 15 25 28 30 33
From this list, write down
(a) a multiple of 7,
Answer ................................................. (1)
(b) the two factors of 24,
Answer ................................................. (2)
(c) a square number,
Answer ................................................. (1)
(d) a prime number.
Answer ................................................. (1)
(Total 5 marks)
Q19. Find a multiple of 4 & a multiple of 5 that add to make a multiple of 6.
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Answer ...................... + ...................... =...................... multiple of 4 multiple of 5 multiple of 6
(Total 2 marks)
Q20. Romana picks a number. (a) One number that she could pick is 36.
Write down the other two numbers that Romana could pick.
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Answer ..................... , ..................... , ........36........ (2)
(b) Romana gives some more clues about the number.
What number does Romana pick? You must show your working.
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Answer ................................................. (2) (Total 4 marks)
Page 13
Q21. Complete the following table.
Put a tick ( ) next to the statements that are right.
Put a cross ( ) next to the statements that are wrong.
(Total 3 marks)
Statement or
8 is a factor of 56
8 is a square number
8 million = 80 000
20 is a multiple of 8
When you divide a whole number by 8 the greatest possible remainder is 7
Page 14
Negative Numbers Q22. In a quiz there are ten questions.
Each correct answer gains five points. Each wrong answer loses two points.
(a) Liz gave ten correct answers.
How many points did she get altogether?
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Answer ................................................. (1)
(b) Glen gave seven correct answers and three wrong answers.
How many points did he get altogether?
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Answer ................................................. (3)
(c) Iqbal answered all ten questions.
Explain how Iqbal could get 43 points altogether.
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.................................................................................................................. (2)
(Total 6 marks)
Q23. Here is a pyramid pattern.
Each number is found by adding the two numbers directly below. For example, 7 = 2 + 5
Complete the following pyramid pattern.
10 –8 5
(Total 3 marks)
15
7 8
2 5 3
Page 15
Q24. (a) The entry prices at a theme park are
Adults £5.25 each Children £3.40 each
Find the cost for 2 adults and 4 children to visit the theme park.
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Answer £................................................. (2)
(b) The entry prices for a group are
Adults £5.00 each Children £3.00 each
(i) A group of adults and children goes to the theme park for a cost of £44. There are 4 adults in the group. How many children are in the group?
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Answer ................................................. children (2)
(ii) Another group also pays £44. Find a different answer for the number of adults and children.
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Answer ................. adult(s) ................. children (2)
(c) The temperature, in °C, at midday at the theme park on 6 winter days was recorded.
Day Monday Tuesday Wednesday Thursday Friday Saturday
Temperature – 3 –2 0 –4 –1 1
(i) Which day was the warmest at midday?
Answer ................................................. (1)
(ii) Which day was the coldest at midday?
Answer ................................................. (1)
(d) The temperature, in °C, at midday at the theme park on 6 summer days was recorded.
21 17 25 30 21 18
Work out the mean temperature at midday for these 6 days.
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Answer ................................................. °C (3)
(Total 11 marks)
Page 16
General Number
Q25. (a) A shopkeeper uses this method to work out VAT. Use this method to work out the VAT for an item with a price of £120 before VAT. You must show your working.
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Answer £ ................................................... (4)
(b) A different shopkeeper uses a table to work out the price of items including VAT.
Price excluding VAT £1 £5 £10 £20 £50
Price including VAT £1.18 £5.88 £11.75 £23.50 £58.75
Use the table to work out the price including VAT of an item that costs £61 excluding VAT.
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Answer £ ................................................... (3)
(Total 7 marks)
Q26. (a) Work out 352 + 352
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Answer ............................................ (1)
(b) Given that 748 + 748 + 748 + 748 = 2992
complete the following.
(i) 748 × = 2992 (1)
(ii) 74.8 × = 29920 (1)
(Total 3 marks)
Write down the price before VAT
Divide by 10
Divide your answer by 4
Multiply your new answer by 7
The answer is the VAT
Page 17
Q27. Three whole numbers have a mean of 30.
(a) The numbers are all different.
Write down three possible numbers.
……………..............................................................................................
Answer ............ and .............. and .............. (1)
(b) Two numbers are equal and the third number is smaller than the other two.
Find three possible numbers.
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Answer ............ and .............. and .............. (1)
(c) Two numbers are equal and the third number is half the size of the other two. Work out the three numbers.
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Answer ............ and .............. and .............. (2)
(Total 4 marks)
Q28. The following tiles fit into the grid below so that the column and row totals add up to the numbers shown.
The two shaded tiles have been fitted for you.
Fit the other four tiles into the grid.
(Total 3 marks)
Page 18
Page 19
M1. (a) No and reference to 10 being 50%
Accept 70% is 14 correct B1
(b) Yes and 75% > 70%
Accept 75% is 15 correct
or = 75% B1
(c) 70 × 20 ÷ 100
70 ÷ 5 M1
14 A1
[4]
M2.
and
worked out separately M1
(16.50 + 8.50) – their 2.5(0)
16.50 – their 1.65 (= 14.85) and 8.50 – their 0.85 (= 7.65)
is M2 or
of each worked out separately is M2
M1 dep
22.50
Do not accept 22.5 but M2 implied
SC1 Answer 14.85 or 7.65 A1
[3]
M3. (a) 400 + 400 + 300 (= 1100) M1
Total £1100 A1
10% of 1100 = 110 B1
990 = 1100 – £110
oe B1
Page 20
(b) 642.60 – 630 M1
Their 12.6 ÷ 630 M1
2 A1
[7]
M4. 800 ÷ 10 (= 80)
oe M1
70 ÷ 5 (= 14)
oe M1
94 A1
[3]
M5. 0.45 × 330
oe build up method must be complete
M1
148.5
SC1 149 A1
[2]
M6. (a) (× 100)
oe M1
25 A1
(b) × 2 × 2 (= 2)
or states 2 out of 3 shaded
Identifies 1 square unshaded
or 4 quarters unshaded
or 2 squares shaded oe
M1
A1
[4]
M7.
or M1
Page 21
100 – above or above × 100 M1 dep
12.5 A1 [3]
M8. (a)
B1 seen B2
(b) (i) 270 ÷ 10 × 3
oe M1
81 A1
(ii) 270 – their 81
0.7 × 270 oe M1
189
Correct or ft A1 ft
[6]
M9. 12 or any common denominator used
eg, or M1
A1
[2]
M10. or
oe
or Two fractions with the same denominators and one correct numerator
eg, M1
75 (%) or 0.75
and or and oe M1
75 (%) and 70 ( %) and Test 1 or 0.75 and 0.7(0) and Test 1
Correct fractions and Test 1 A1
[3]
M11. One correct conversion
Decimals 0.65, 0.7 and 0.64 M1
All 3 numbers correct in same form
Percentages 65%, 70% and 64%
M1
Page 22
, 65%, 0.7
SC1 Correct answer no working
A1
[3]
M12. 4 × 12
or 48 M1
(their 48) ÷ 3 or 16
oe M1
80 ÷ their 16
oe M1
5
SC2 for 5 with no working A1
[4]
M13. (a) and
B1 One correct (and one incorrect)
B1 Two correct and one incorrect
Accept any indication B2
(b) 25 B1
[3]
M14. 55/100 × 3 M1
1.65 (litres) A1
3/4 × 2.5
oe only penalise once for repeated error
M1
1.875 (litres) + (B or 2.5 litre)
oe A1
[4]
M15. × 2200 or 2/5 × 2200
13/20 or 1/4 + 2/5 7/20 on its own
M1
2200 - their (550 + 880)
(1 – their 13/20) × 2200 gets M2
DM1
770 A1
[3]
Page 23
M1. (a) 5 (×) 4
At least one correct M1
20 A1
(b) (i) 81 B1
(ii) Always even ticked and a valid example eg, 92 + 32 = 90
B1 if example incomplete eg, 92 + 32
B2
[5]
M2. 28
B1 36 and 64 identified B2
[2]
M3. (a) 121 B1
(b) 144 B1
(c) 5 B1
[3]
M4. (a) 78
B1
(b) 1
Not 18
B1
[2]
Page 24
M5. = 95.3(...) or 95.4
952= 9025 B1
= 95.9(...)
962 = 9216 B1
No whole numbers between 95.4 and 95.9 oe
952 < 9100 and 962 > 9200 oe E1
[3]
M6. (√25 =) 5 B1
(√16 + √9 =) 7 B1
[2]
M7. (a) Evidence of 2 square numbers other than one M1
25 and 16 or 25 and 9 A1
(b) Evidence of summing any three consecutive square numbers
or 77 seen M1
36, 25 and 16 A1
[4]
M8. 7200 ÷ (2 + 3 + 7) M1
Their 600 × 2 or × 3 or × 7 M1dep
1200, 1800, 4200
All correct A1
[3]
Page 25
M9. 90 ÷ 30 or (£)3 M1
25 × their (£)3 M1
75 A1
[3]
M10. Large is 3 times standard
Or standard is large
Price per biscuit 9...p and 8...p M1
Which costs 3 × £1.09 = £3.27 Large is better
Which is £1.05 or £1.06 Large is better
A1
[2]
M11. 1200
or 8400 seen B1
12000 B1
[2]
M12. 12.5 ÷ 5 or 16.5 ÷ 7 or 2.5 or 2.3(....) or 2.4
oe M1
12.5 ÷ 5 and 16.5 ÷ 7 or 2.5 and 2.3(....) or 2.4
or their 2.5 × 7 or 17.5
or their 2.3(....) or 2.4 × 5 or 11.5 - 12 inc
M1
No ticked and 12.5 ÷ 5 ≠ 16.5 ÷ 7 or 2.5 ≠ 2.3(....) or 2.4
or 17.5 ≠ 16.5
or 11.5 - 12 inc ≠ 12.5
oe eg, the lengths are different A1
[3]
Page 26
M13. (a) Five thousand one hundred and sixty seven B1
(b) 7400 B1
(c) 17 000 B1
(d) 16 684 – 1184 M1
15 500 A1
[5]
M14. (a) 50 ÷ 4.99 or 50 ÷ 5 M1
10 A1
(b) 20 × (£) 5(.00) without error
Sight of 49.9 or 99.8 or 4 × 20 M1
No and valid explanation
eg, Decimal point in wrong place
About (£) 100
4 × 20 = 80
5× 20 = 100
Correct answer is (£) 99.8(0)
Arithmetic errors made is M1A0 A1
[4]
M15. (a) √387.5
or length2 = 387.5
M1
19.685(01969) A1
(b) 19.7 B1ft
[3]
M16. (a) (i) 70 B1
(ii) 5 B1
(iii) 25
Page 27
B1
(iv) 75 B1
(b) 150
oe B1 for or 2 seen
B2
[6]
M17. (a) 4, 6, 8 and 12 or 3, 6, 9 and 12
Any order
B1
(b) 6 or 12 or 18 B1
(c) 3, 6, 9 and 18
B1 2 correct with 0 incorrect
or 3 correct with 0, 1 or 2 incorrect
or 4 correct with 1 or 2 incorrect B2
(d) 9 (–) 4 M1
(±) 5 A1
[6]
M18. (a) 28 B1
(b) 6 and 8
– 1 eeoo
B2
(c) 25 B1
(d) 11 B1
[5]
M19. Any correct values eg, 8 + 10 = 18
B1 For meeting 3 of the following 4 correct multiples of 4, 5, 6 except 4, 5 and 6 Correct addition
eg, 8 + 15 = 23, 16 + 8 = 24, 16 + 10 = 26, 16 + 10 = 24
or Four or more multiples for two of 4 or 5
or 6 listed
eg, 4, 8, 12, 16..., 5, 10, 15, 20...
B2
[2]
Page 28
M20. (a) 1, 2, 3, 4, 6, 9, 12, 18, 36 seen
oe eg, 1 × 36, 2 × 18, 4 × 9, 3 × 12, 6 × 6 seen Allow up to 2 errors or omissions
M1
12 and 18 A1
(b) 1 + 2 and 1 × 2 or 1 + 8 and 1 × 8 or 3 + 6 and 3 × 6
or ft Their 2-digit factors M1
18
SC1 any value that satisfies both conditions eg, 88
A1
[4]
M21. Fact 1
Fact 2
Fact 3
Fact 4 Fact 5
B2 3 or 4 correct
B1 1 or 2 correct B3
[3]
M22. (a) 50 B1
(b)
35 M1
subtracted from their 35 M1
29 A1
(c) 9 questions right or 1 question wrong
Page 29
or 45 right 2 wrong
B1 45 correct 1 wrong or 9 correct 2 wrong or 45 and 2 seen
B2
[6]
M23. 2 –3 B1 + B1
–1
ft with at least 1 negative number used
B1 ft
5 B1
[3]
M24. (a) £10.50 adults or £13.60 children
5.25 × 2 or 3.40 × 4 M1
24.10 A1
(b) (i) (44 – 4 × 5) ÷ 3 M1
8 A1
(ii) 7 adults
1 adult B1
3 children
13 children SC1 for both numbers reversed
B1
(c) (i) Saturday
or 1 B1
(ii) Thursday
or -4
B1
(d) Attempt at Ʃx
At least 3 additions M1
Their 132 ÷ 6 DM1
22 A1
[11]
Page 30
M25. (a) 120 ÷ 10 or 12
120 ÷ 10 ÷ 4 × 7 M1
Their 12 ÷ 4 or 3 M1dep
Their 3 × 7 M1dep
21 A1
(b) Correct build up seen (exc VAT)
eg, 50 + 10 + 1 20 + 20 + 20 + 1
M1
Correct build up seen (inc VAT)
eg, 58.75 + 11.75 + 1.18 23.5 × 3 + 1.18
M1dep
[71.68, 71.98]
SC2 For [10.68, 10.98] A1
[7]
M26. (a) 704 B1
(b) (i) 4 B1
(ii) 400 B1
[3]
M27. (a) Any 3 different numbers that total 90 B1
(b) Any 2 equal numbers and a third smaller with total 90 B1
(c) Evidence of searching for 2 equal and one half the other
x + x + x = 90 or 2.5x = 90 M1
36, 36, 18
SC 12, 12, 6 B1 A1
[4]
Page 31
M28.
3 6 4 2 2 1 18
2 1 7 6 4 5 25
5 4 3 8 9 6 35
1 2 5 1 8 7 24
11 13 19 17 23 19
Top left B1
Bottom right B1
Both Middle B1 B3
[3]
