Relationships

(a) Complete the table below for y = 3x – 2.

x 1 2 3

y

y = 3 X 1 – 2

1 4

y = 3 X 2 – 2

7

(b) Draw the line y = 3x – 2

3

2 Line AB is shown on the grid below.Write down the equation of line AB.

-10

-5

-5-10 1050

5

10

BA

y

x

(1 , 2) (5 , 2)(-4 , 2)y = 2

1

3 Solve the following equation: 2y + 3 = –5

2y + 3 = -5

2y = -5 – 3

2y = -8

y = -4

2

4 For the formula F = ma

Change the subject of the formula to m.

ma = F

m = F a

5 Change the subject of the formula

y = 7m + 5 to m.

7m + 5 = y

m = y – 5

7m = y – 5

7

Standard 1.1

Need 5 out of 9

3

6 Triangle KLM is a right-angled triangle as shown in the diagram below. KM is 17 metres long and KL is 8 metres long.

8 m17 m

ML

K

Calculate the length of LM (in metres).

x2 = 172 – 82

= 225

x = √225

= 15m

x

3

7 Copy the diagram below, then draw an enlargement of the given shape using a scale factor of

2

3

.

14

21

8

12

4

6

6

9

12

18

2

119°

57°

>

>

GE

B

SQDC

RPA

F

8 In the diagram below, lines AB and CD are parallel. Lines EF and GF intersect AB and CD at the points P, Q, R and S as shown.Angle APQ is 57° and angle DSR is 119°. Calculate the size of angle EFG.

570 1190610

6201 Interpret

1

O

D

77°

BA

9 AB is the diameter of a circle, centre O.

D is a point on the circumference of the circle. Angle BAD is 77°.

130

2

10 On the grid shown, the end-points of a line are (1, 3) and (7,9).Calculate the length of the line.Calculate the length of the line.

6

6

x2 = 62 + 62

= 72

x = √72

= 8.5 unitsx

1

1 Interpret

Standard 1.2

Need 5 out of 9

Interpret

Need 1out of 2

11 Calculate the length of side x in the right-angled triangle below.

38°

24 m

x HO

SOHCAHTOA

Tan = O/A

Tan 380 = x/24

x/24 = Tan 380

x = 24 X Tan 380

A

x = 18.8cm 3

12 A ramp 50 m long slopes at an angle of x° from level 1 to level 2.The height between levels is 7 metres.

Level 2

Level 17 metres

x°

(a) Calculate x°.(b) For safety reasons angle xº should be less than 10 degrees.

Can the angle of the ramp be considered safe? (Justify your answer.)

O

A

Sin = O/H

Sin x = 7/50

= 0.14

x = 8.00

H

a)

b) The ramp is safe as the angle is less than 100

SOHCAHTOA

2

Standard 1.3

Need 3 out of 5

Explain 1

13 A class of students sat two tests in the same subject.Here are the marks for six of the students who sat the tests:

Student Test A Test B

Allan 30 30

Margaret 50 75

Kirandeep 25 20

Ahmed 62 80

Simon 48 60

Susan 40 50

(a) Draw a scattergraph of these marks on the grid provided.

Marks

Test B

Test A1009080706050403020100

10

20

30

40

50

60

70

80

90

100

(b) Draw a best fitting straight line for this scattergraph.

(c) Karen scored 55 marks for Test A. Use your line to estimate the number of marks she scored in Test B.

(d) Brian scored 65 for Test B but was absent for test A. His teacher estimated his mark to be 40 for test A. Is this a reasonable estimate?

Estimate is too low. 50 would be a better estimate

70

Standard 1.4

Need 2 out of 4

Explain 1Explain Need 1 out of 2