# Stonelaw Mathematics Department Green Course Revision Sheets Block E

 Date 05.01.2017 Size 113.92 Kb. #7293

Stonelaw Mathematics Department

Green Course

Revision Sheets

Block E

GE 0 Fractions and Percentages

GE1 Algebra

GE2 Probability

GE3 Statistics

GE4 Special Numbers

Revision 1 – Fractions, Decimals & Percentages
1. Write each percentage as a fraction and as a decimal:

a) 50% b) 25% c) 75% d) 20% e) 10%

2. Write the following percentages as fractions:

a) 33% b) 66% c) 40% d) 60% e) 80%

3. Write each percentage as a fraction and as a decimal:

a) 67% b) 29% c) 57% d) 61% e) 37%

f) 91% g) 41% h) 11% i) 1% j) 7%

4. Write each decimal as a fraction and as a percentage:

a) 0∙63 b) 0∙79 c) 0∙27 d) 0∙19

e) 0∙43 f) 0∙89 g) 0∙51 h) 0∙01

5. Write each fraction as a percentage and as a decimal:

a) b) c) d)

e) f) g) h)
 6. Change each fraction into a percentage (calculator), a) b) c) d) e) f) g) h) i) j)

Revision 2 (a) – Fractions
1. a) b) c)

d) e) f)

g) h) i)
2. Simplify the following fractions:-

a) b) c) d)

e) f) g) h)

i) j) k) l)

m) n) o) p)

q) r) s) t)

3. Copy and complete the following to make equivalent fractions:-

a) b) c)

d) e) f)

g) h) i)

j) k) l)

m) n) o)

p) q) r)

4. Copy each of the following and complete:-

a) b) c) d)

e) f) g) h)

i) j) k) l)

m) n) n) o)

5. Copy each of the following and complete:-

a) b) c) d)

e) f) g) h)

i) j) k) l)

m) n) n) o)

Revision 2 (b) – Percentages

(Non –Calculator)
1.Write down the simplest fraction for each of the following percentages :-
(a) 50% (b) 20% (c) 100% (d) 25% (e) 40% (f) 5% (g) 10% (h) 1% (i) 75%

(j) 30% (k) 80% (l) 70% (m) 33% (n) 66 % (o) 60% (p) 30%

2. Find without a calculator :-
(a) 50% of £9 (b) 10% of 360 metres (c) 80% of 90 €

(d) 25% of 300p (e) 60% of 240 p (f) ) 33% % of 120 kg

(g) 70% of 520 cm (h) 75% of 9600 kg (i) 75% of £440
(j) 30% of 3100 km (k) 75% of £5 (l) 66% of 1·2 kg
3. Explain how you might (mentally) calculate 15% of £80.
4. Explain how you might (mentally) calculate 12 % of £80.

5. In a sale 12% is deducted off all items. Find the sale price of a wrist watch originally priced at £240.

(Calculator)

1.Calculate :-

(a) 22% of £60 (b) 47% of 250 kg (c) 62% of £150 (d) 18% of 120 g

(e) 8% of £66 (f) 38% of 500 cm g) 12.5% of £80 (h) 37.5% of 240 €

2. Eighty five percent of the 560 videos in a shop are rated 15.

How many videos are rated 15 ?

3. On holiday, Calvin spent 95% of his £450 spending money.

How much did Calvin spend ?

4. Margaret took £350 on holiday and returned with 15% of her money.

How much money did Margaret spend on holiday ?
5. Of the 380 goals scored in a season,

15% were scored by penalties and

65% were scored by the home team.
(a) How many penalties were scored ?

(b) How many were scored by the away team ?

6. An advert makes 2% of an hours television.

How long is the advert (to the nearest second) ?

Revision 3 – Algebra

1. Copy and simplify

(a) 8x + 4x (b) 3y – 2y (c) 9h + h
(d) 12p – p (e) 5x + 3x + 4x (f) 9w + 5w + w
(g) c + c + c (h) 8k + 5k – 10k (i) 15q + 9q – 19q
(j) 83d + 22d – 91d (k) 20z – 17z + z (l) 31h – 25h – 6h

2. Simplify by gathering like terms

(a) (b)

(c) (d)

(a) 18x + 14x – 27x (b) 7y – y + 8y

(c) 12i + 7i – 14i (d) 26t – t – t – t
(e) v + 11v + 4v – v (f) 90j2 + 5j2 – j2
(g) h + 13h + 12h – 23h (h) 7u + 6u – 12u

(i) 5g2 + 9g2– 4g2 (j) 51e3 + 29e3 – 79e3

(k) z – 5z + 7z (l) 31x – 35x – 6x

3. (i) If a = 4 and b = 5, find the value of

(a) a + b (b) a – b (c) ab (d) 5a – 3b
(e) 8b ÷ 4 (f) 7a ÷ 2 (g) 4xy ÷ 20 (h) xy ÷ 40
(ii) For w = 2, x = 3, y = 1 and z = 6, calculate
(a) 2w + 3 + x (b) 1 + 2z – 2x (c) 5y + 2w (d) 30 – 5z
(e) z – 3w + y (f) w + 3x – y (g) 2wx – 2 (h) 25 – 3yz
(i) 2z + 4y – x (j) 2x – 4y + 2w (k) wz + x (l) zw – xy
(m) 10 – 2z + y (n) 5 + 3yw– wyz (o) 2y – 5w + z (p) 50 – 2wxyz

4. For each statement below use the information given to construct a formula in symbols.

(a) Profit can be calculated by subtracting costs from sales.

(b) The total number of pupils in a class can be found by adding the number of boys and the number of girls.

(c) The area of a rectangle can be found by multiplying the length by the breadth.
5. Use the information in the diagram below to write a formula for calculating the perimeter of the shape.

6. A regular decagon has side of length k cm.

(a) Find an expression for the perimeter.
(b) If k = 3, what is the perimeter ?

Revision 4 – Algebra (Equations)

1.Copy each equation and solve

(a) x + 4 = 7 (b) y + 2 = 12 (c) 7 + y = 8
(d) p – 4 = 6 (e) 5 – x = 13 (f) 9 – w = 6
(g) c – 12 = 16 (h) 14 – g = 0 (i) 15 + e = 17
(j) 8 + x = 7 (k) z – 3 = –1 (l) 31 + a = –10

2. Copy and simplify

(a) 2a = 10 (b) 3y = 15 (c) 9h = 81
(d) 12p = 0 (e) 5x = 75 (f) 19w = 76
(g) 11z = 121 (h) 8k = 864 (i) 15q = 300
(j) 10k = 3000 (k) 20z = 6000 (l) 6h = 27

3. Five calculators (c) are priced at a total of £30

(a) Form an equation in c to show this.

(b) Solve the equation to find the cost of one calculator.

4.Find the value of each variable by solving the equations
(a) 2x + 4 = 16 (b) 3y + 1 = 13 (c) 5y + 4 = 9
(d) 8p – 1 = 23 (e) 2x – 7 = 13 (f) 9 + 2w = 15
(g) 7c – 12 = 9 (h) 14 – 5g = 4 (i) 15 – 4e = –1
(j) 8 + 4x = 0 (k) 12z – 3 = 57 (l) 31 – 2a = –2

For each question, use the information to construct an equation, then solve your equation and give the answer to the question.

5. A rectangle with area 45 cm2, has length y cm and breadth 5 cm.

1. Write an equation to show this information.

(b) Solve the equation to find y.

6. Look at the diagram below

Find the value of x.

7. I think of a number (let number = n), multiply it by 5, then add 42. The answer is 57.

What is my number?

8. Zoe goes shopping with a friend and buys five bangles and one pair of earrings.

She knows the earrings cost £3 and she pays £13.

How much does one bangle cost?

Extension Work
(a) 4x = 3x + 8 (b) 4x = x + 18 (c) 9x = 4x + 45
(d) 10x = 9x + 41 (e) 3x = x + 17 (f) 5x – 26 = 3x
(g) 7x – 48 = x (h) 3x + 17 = x (i) 10x – 30 = 6x.

10. Solve for x

(a) 5x + 3 = 3x + 5 (b) 8x + 9 = 7x + 17 (c) 7x – 1 = 3x + 15
(d) 5x – 3 = 2x + 18 (e) 12x – 5 = 8x + 7 (f) 10x – 1 = 8x + 6
(g) 6x + 4 = 3x + 4 (h) 9x – 1 = 4x + 34 (i) 7x – 8 = x + 1

11. The two shapes below have the same perimeter.

Find the value of x.

Revision 5 – Algebra (Distributive Law)
1.Multiply out the brackets
(a) 3(x + 2) (b) 4(t + 4) (c) 5(a – 1) (d) 10(w – 2)
(e) 2(2a + 1) (f) 3(4e + 5) (g) 7(2g – 1) (h) 9(5k – 3)
(i) 3(2a + b) (j) 5(x + 2y) (k) 2(4a  3) (l) 6(4y  3)

(m) 3(2x  5) (n) 4(5c  6) (o) 7(2a  1) (p) 2(8x  3)

(q) 5(6  7y) (r) 3(8t  5) (s) 3(9x  4) (t) 8(7  5y)

(u) 7(2b  9) (v) 2(12x  7) (w) 8(2h + 4g – 1) (x) 5(v – 3w + y – 5)

2. A rectangular card has length 3x + 1 centimetres and breadth 5 centimetres. Find two expressions for its area
3x + 1

5

3. Multiply out the brackets and simplify

(a) 2(x + 3) + 1 (b) 3(y + 4) + 5 (c) 7(k + 1) + 10
(d) 5(t + 2) – 5 (e) 3(2g + 4) + 8 (f) 6(3x + 1) – 6
(g) 8(3e + 2) + 5 (h) 9(4h + 7) – 60 (i) 4(w + 1) – 4w

4. Expand and simplify

(a) 2(f + 3) + 3(f + 1) (b) 4(y + 2) + 7(y + 1) (c) 6(b + 3) + 2(b – 5)
(d) 5(2g + 2) + 4(g – 3) (e) 7(p + 3) + 5(p + 1) (f) 7(2q + 3) + 4(3q – 5)
(g) 5(3m + 2) + 3(2m – 6) (h) 4(3p + 4) + 3(4p – 5) (i) 5u(2u + 3) + 2u(u –7)

Revision 6 – Probability
1. A bag contains red, green, blue, yellow and white balls.

There are 10 of each colour, numbered from 1 to 10.

The balls are placed in a drum and one is drawn out.

1. What is the probability that it is a 7 ?

2. What is the probability it is a blue 7 ?

2. Roy and Zara go to the fairground. A stall has a card game where a goldfish can be won if anyone can turn over a face card from a pack of 52 cards which are placed face down. Calculate the probability, in its simplest form, of Zara winning the goldfish.

3. A box contains 5 red, 6 green, 7 blue and 2 yellow coloured pencils.

1. What is the probability that it is a green pencil?

2. She does NOT replace the pencil, but draws another one.

What is the probability that this is a blue pencil?
4. A ten sided spinner, numbered 1 to 10, is spun.

1

2

3

4

5

6

7

8

9

10

Work out each of the following probabilities.

1. The probability that the spinner will land on an odd number.

1. The probability that the spinner will land on a square number.

1. The probability that the spinner will land on a prime number.

5. A bag contains 10 red, 25 green, 9 blue and 6 yellow marbles.

Sam picks one out of the bag, replaces it and then picks another one.

What is the probability that he picked a Green marble followed by a Red one?

6. Two dice are thrown. What is -

(a) The probability that the sum of the two dice is 7.

(b) The probability that the difference is 2.

(c) The probability of the product being a multiple of 5.

Revision 7 – Statistics

1. Find the mean, median, mode and range of :-

1. 2, 3, 6, 5, 2, 9, and 8 (b) 41, 37, 53, and 45

1. 13, 12, 12, 15, 14 and 15 (d) 12, 11, 14, 14, 16, 21 and 10

2.Calculate the mean, median, mode and range of :-

(a) 3·1, 2·5, 3·8, 3·4 and 3·9 (b) 8·8, 8·7, 7·9, 8, 9·1, 8·6 and 7·7

3. In a swimming competetion the following times were recorded :-

18·7 secs, 22·4 secs, 19·7 secs, 20·1 secs, 20·3 secs, 18·9 secs, 21·3 secs.
How many swimmers were faster than the mean time ?

4. In the first six months of the church lottery, £6360 in prizemoney was paid out. How much on average was paid each month ?

5. Josh is a computer games whizkid. He completed each level of DEATHGAME in the following times (in minutes) :- 8·6, 9·5, 8·8, 7·9, 10·1, 8·9, 8·1, 8·3 and 9. What was his mean time per level ?

6. In the first four weeks of selling ice-cream, Tony had

made a profit of £876.

1. How much was the average profit each week ?

2. How much was the average profit per day ?

7. A group of 18 year old boys and girls were surveyed about how old they were when they went out on their first date. The results of the survey are shown below.

Age at first date

Frequency

1. How many boys took part in the survey?

1. What was the modal age for the girls?

1. What was the range of ages for the boys?

1. Can you draw any conclusions about the dating ages of the boys and girls who took this survey?

8. The following list of numbers represents the number of goals scored by Manchester United in the 2010/11 Champions League.

0 1 1 3 1 1 0

2 1 2 2 4 1

1. What was the mean number of goals scored? (answer to 2 d.p’s)

2. What was the modal number of goals scored?

3. What was the median number of goals scored?

4. What was the range of goals scored?

9. In the last five home games the following scores were recorded at Hawick rugby club :

15 - 10, 12 - 5, 0 - 25, 21 - 15, 7 - 5 (In all home games Hawick scores come first)
(a) Find the range of the (i) home scores, (ii) away scores.

(b) Find the average points Hawick scored.

(c) Find the average points of the away teams.

(d) Why do you think the away teams average is higher ?

10. The mean weight of 3 boys is 37 kg.

Andy weighs 36 kg, Bill weighs 34 kg. Calculate the weight of Colin.

Revision 8 – Multiples & Factors

1. List the first TEN multiples of the following numbers:

a) 1 b) 2 c) 3 d) 4 e) 5

f) 6 g) 7 h) 8 i) 9 j) 10

2. Find the lowest common multiple (LCM) of:

a) 2 and 5 b) 4 and 6 c) 5 and 9 d) 6 and 9 e) 8 and 10

f) 4 and 10 g) 5 and 8 h) 3 and 7 i) 2 and 9 j) 5 and 6

k) 13 and 3 l) 2, 3 and 5 m) 3, 6 and 7

3. List all the factors of the following number.

a) 12 b) 15 c) 10 d) 24 e) 11 f) 14

g) 28 h) 30 i) 21 j) 36 k) 42 l) 120
4. Baby frog croaks every 3 seconds.

Mummy frog croaks every 6 seconds.

Daddy frog croaks every 9 nine seconds.

How many seconds pass before they all croak together ?

5. Find the highest common factor (HCF) of the following numbers

a) 4 and 6 b) 10 and 15 c) 9 and 27 d) 8 and 20 e) 12 and 18 f) 10 and 15

g) 18 and 30 h) 14 and 21 i) 24 and 32 j) 15 and 36 k) 6, 8 and 12 l) 14, 35 and 42
6. Investigate the factors of the following numbers.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

What do you notice?

What name do we give to these types of numbers?

Revision 9 – Prime Numbers

1. Investigate the factors of the following numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

What do you notice?

What name do we give to these types of numbers?

 2. Write down the prime numbers from a) 14, 9, 38, 31, 21 b) 77, 81, 95, 47, 93 c) 78, 79 , 99, 63

3. Write the following as products of prime factors (prime decomposition)

a) 12 b) 18 c) 20 d) 32 e) 40 f) 27

g) 45 h) 50 i) 72 j) 98 k) 120 l) 680

Revision 10 – Powers
1.Do NOT use a calculator. Find the values of :-
(a) 52 (b) 102 (c) 82 (d) 112 (e) 122 (f) 202

(g) 23 (h) 33 (i) 43 (j) 53 (k) 32 + 22 (l) 62 - 42

(m) 13 +72 (n) 32 -23 (o) 53 -43 (p) 103+13

2. Use a calculator to find the values of :-

1. 132 (b) 212 (c) 342 (d) 3002 (e) 93 (f) 153

(g)203 (h) 1503 (i) 422 - 202 (j) 272 + 652 (k) 253-252 (l) 133+112

(m) 183 - 123

3.Calculate the area of the following squares using the formula;

Area = (length)2

A = l2

(a) (b) (c)

10m

1cm

6cm

6cm

4. A chessboard has 64 squares.

If we are going to place £1 in the first square, £2 in the second square, £4 in the third square, so that the amount keeps doubling, how much money do we need to fill all the 64 squares?