National 5 Mathematics Formal Homework Block 1 - Fractions

You must not use a calculator for questions 1 – 5: 1. This year, Jamie paid £260 for his car insurance. This is an increase of 30% on last year’s payment. How much did Jamie pay last year? 2. Round the following numbers to 2 significant figures:

(a) 675403.6 (b) 9.03955 (c) 99806 (d) 0.0050599 3. Work out the answers to the following:

(a) 10

7

4

33 (b)

4

3

8

5

4

12 2,4

4. Calculate the circumference of a circle with diameter m312 . Let

722 .

Give your answer as a mixed number in its simplest form.

5. A farmer has 3 fields which cover an area of 218 acres of land.

Two of the fields have areas of 322 acres and

431 acres.

What is the area of the third field? You may now use a calculator for questions 6 – 8

6. Carry out the following calculations, writing your answer in Scientific Notation.

(a) 6.7 x 106 x 2 (b) 4.18 x 10-5 x 7

7. Calculate 6

32

103

)105(4)102(3

giving your answer in standard form 2

8. Due to fire damage, the value of a painting has fallen by 34% and is now valued at

£4158. What was its value before the damage?

3

3

2

Total = 26

3

3

45

National 5 Mathematics Formal Homework Block 1 - Algebra

You must not use a calculator for this homework

1. Expand the brackets and simplify

(a) 3a – 5(1 + 2a) (b) 4(2b – c) – 6(3c – d)

2. Solve the following equations

(a) 8x +6 = 10x – 1 (b) 2(3y - 2) + 4y + 1 = 5y + 32

3. Solve the inequality 2(a + 4) > 5(a 2)

4. A function is defined by the formula g(x) = 12 5x

(a) Calculate the value of g(5) + g(2) (b) If g(k) = 14, find k.

5. A function is defined as f(x) = 2x – 3x2. Find the value of f(-2).

6. Solve the equation 2x - ¼(3x – 1) = 4 7. (a) Find an expression with brackets for the area of this rectangle.

(b) If the area is 87cm², form an equation and then solve it to find x . (c) What are the dimensions of this rectangle?

3

3

5

Total = 29

2,2

3

3 cm

(2x+3) cm

3,3

3,2

National 5 Mathematics Formal Homework Block 1 –

Straight Line& Simultaneous Equations 1. Calculate the gradient of the following lines: 2. Calculate the gradient of the line joining each pair of points below. a) A(4,3) , B(8,11) b) C(-2,6) , D(8,-2) 3. For each line, write down the gradient and the coordinates of the point where it

Crosses the y axis:

(a) 3y = 5x 12 (b) 3x = y 10

4. Find the equation of the line passing through P(4, 6) which is parallel to the line

with equation 4x 2y + 6 = 0.

5. Find the point of intersection of the lines with equations: 3x + 2y = 5 2x – 3y = -14

6. A rectangular window has length, l centimetres and breadth, b centimetres. A security grid is made to fit this window. The grid has 5 horizontal wires and 8 vertical wires. a) The perimeter of the window is 260 centimetres.

Use this information to write down an equation involving l and b. 1

b) In total, 770centimetres of wire are used.

Write down another equation involving l and b. 1

c) Find the length and breadth of the window. 3

Total = 25

5

2,2

2,2

4

3

National 5 Mathematics Formal Homework Block 2 - Algebra

You must not use a calculator for questions 1 – 4: 1. Remove brackets and simplify:

(a) (2a + 5)(a + 9) (b) (4x 3)2 (c) (x – 2)(2x² – 3x – 2) 2. Simplify the following:

(a) 50 (b) 35147 (c) 6)23(2

3. Express as a fraction with a rational denominator:

(a) 32

5 (b)

34

5

4. A formula is given as P = R3 b – 5.

Change the subject of the formula to R. You may now use a calculator for question 5

5. A spinning toy consists of two identical cones base-to-base on a string.

The toy’s volume is given by :

where w cm is its width and L cm its length.

(a) Change the subject of the formula to L.

(b) Calculate the length of the spinning toy with a volume of 250 cm³ and a width of 5 centimetres.

1,2,2

3

3,2

Total = 25

LwV 2

12

1

2,2,3

2,3

National 5 Mathematics Formal Homework Block 2 – Percentages and Statistics

You must not use a calculator for questions 1 – 2: 1. A house bought at £80000 increases in value by 20% over the

1st year. The next year the value increases by a further 25%. What is the value of the house after the 2 years?

2. A group of smokers were asked how many cigarettes they smoked in a day and

how many chest infections they had suffered in the last ten years. The results are shown in the scattergraph with the line of best fit drawn.

(a) Find the equation of the best fit line in terms of I and C.

(b) Use your equation to estimate the number of chest infections for someone who smokes 60 cigarettes a day.

2

2

4

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35 40 45

Number of cigarettes smoked in a day ( C )

Num

be

r o

f ch

est

infe

ction

s in

la

st

10

ye

ars

( I

)

You may now use a calculator for questions 3 – 7 3. A trumpet bought for £120 was later sold for £135.

Calculate the profit as a percentage of cost price. 4. The ages of the players in a local football team are given below: 19 23 30 24 19 25 31 27 28 30 19

Calculate the mean, median, mode and range for the above data.

5. Three football teams play in the same town. Team A have won 7 out of their 10 games. Team B have won 9 out of their 13 games. Team C have won 11 out of their 16 games. Which team has the best winning record? Justify

your answer by calculation.

6. In 2015 a house was valued at £210,000 and the contents were valued at £30,000. The value of the house appreciates by 5% each year. The value of the contents depreciates by 8% each year. What will be the total value of the house and contents in 2018?

Give you answer correct to 2 significant figures.

7. Mary puts £1200 into an account where the annual rate of interest is 5∙5%. How long will it be before she has at least £1400 in her account?

2

4

3

Total = 24

4

3

National 5 Mathematics Formal Homework Block 3 Algebra

You must not use a calculator for this homework

1. Factorise each expression in the following:

(a) 12a2 16ab (b) 5s2 20 (c) 3m2 11m 4

2. Simplify: (a) 2

2 23

a

aa (b) 328 )( kk (c)

)

1(2

1

aaa

3. Evaluate (a) 32 (b) 4

3

16

4. Simplify:

(a) x

x

36

12 2

(b) )3(

652

x

xx

5. Express each of the following in its simplest form.

(a) 45

mm (b)

3

14

xx

(c) 21

9

3

7 k

k (d)

aa

212

2,2

Total =28 marks

2,2,2,

2,2,2

2,2

2,2,2,2

National 5 Mathematics Formal Homework Block 3 Geometry

You must not use a calculator for this homework

1. Calculate the value of x in the diagram. 3 2. Two tube of toothpaste are mathematically similar in shape. Their price is proportional to their volume. Given that the cost of the small

tube of toothpaste is 35p calculate the cost of the large tube.

3a) In the diagram triangle ABC is

isosceles and BD is a diameter of the circle. 3

Calculate the size of angle ACD. 3

b). The diagram opposite shows a circle centre O.

AB is a tangent to the circle at A OB intersects the circle at C Angle OCA = 610

Calculate the size of angle OBA

3

120mm 240mm 3

46

A

BC

D

A B

C

O

o61

J K

L

N M 270cm

x cm

600cm 640cm

720cm

4. Use the diagram opposite to name a vector equal to:

a) a + 2b 1 b) c – b 1 c) a – d 1

5. Vector a has components

p

1

8. If |a|= 9, calculate the value(s) of p.

6. The first four levels of a stepped pyramid are shown.

Each level is a square-based cuboid with a height of 3m. The shaded parts indicate the steps which are 1m deep. With coordinate axes as shown, and 1 unit representing 1m, P is (12,0,0) and A is (24,0,0).

Find the coordinates of Q and R.

Total =20 marks

3

2

National 5 Mathematics Formal Homework Block 3 – Trgonometry and Pythagoras

1. 2. Calum is making a picture frame . It is 25 cm high and 21·5 cm wide.

To check whether the frame is rectangular, he measures the diagonal, d. It is 31·5 cm long. Is the frame rectangular?

3. Calculate the perimeter of this field,

which consists of a rectangle and a right angled triangle.

4.

A camera is positioned at the top of a 90 metre high tower. Two cars are viewed from the camera with angles of depression of 31° and 41°. How far apart are the cars?

5. The figure shows the cross section

of a tunnel with a horizontal floor AB which is 2.4 metres wide. The radius OA of the cross section is 2.5 metres. Find the height of the tunnel .

4

3

4

4

Total = 20

40 m

70 m

80 m

5

. O

2.5m

A B

Height of the tunnel