Algebra

Achievement Criteria

Q

Evidence

Code

✓

Judgement

Sufficiency

Achievement

Solve number problems.

1

0.18, 19%, [pic 1], 35%, [pic 2], 0.39

A

A

✓

✓✓

Award 1 ‘A’ if there is 1 mistake.

5 A

2

A

A

✓

✓

Accept sensible rounding

3(a)

$64.50

A

✓

3(b)

53.5 Euro

A

✓

Accept 53 or 54

3(c)

399.1 Rand

A

✓

Accept 399

3(d)

$ 125 Singapore

A

✓

Merit

Solve number problems in context.

4(a)

3.822 × 1021

M

✓

✓

Number

Standard form

Achievement

plus

4 M

4(b)

4.9156 × 1012

M

✓

✓

Number

Standard form

4(c)

4.89922 × 1012

M

✓

✓

Number

Standard form

5

$149.00

M

✓

working

✓

answer

6(a)

Least 10.35

Most 10.45

M

✓

✓

Accept

10.35 ≤ t < 10.45

6(b)

Least 99m 95cm

Most 100m 5 cm

M

✓

✓

Accept

99.95 ≤ d < 100.05

7

21.3 g

(21.28125)

M

✓

working

✓

answer

✓

rounding

Excellence

Solve number problems in context involving several steps or reversing processes.

8

14 cm ×

21 cm ×

42 cm

E

✓

✓

✓

Merit

plus

2 E

9

Amount available:

2500 × 0.95

2375 mL

Bottles filled:

2375 ÷ 200

11 (11.875)

Need to charge:

35 × 1.4 ÷ 11

$4.45

(4.45454545…)

E

✓

✓

✓

✓

✓

Must be supported by working, including annotations stating what is being calculated.

Achievement Criteria

Q

Evidence

Code

✓

Judgement

Sufficiency

Achievement

Solve simple angle problems and give reasons.

1

f = 110°

B = 55°

g = 55°

A

A

A

Each

✓

angle

✓

reason

Reasons not required.

Do not award if reason is isosceles triangle.

4 A

2

p = 108°

q = 72°

r = 72°

A

A

A

Each

✓

angle

✓

reason

Reasons not required.

Merit

Solve angle problems and give reasons.

3(a)

Isosceles

M

✓

Achievement

plus

2 M

3(b)

[pic 3][pic 4]

[pic 5][pic 6][pic 7]

M

✓

angles

✓

sides

Both correct.

4(a)

90o

Square

M

✓ both

(a) and (b) plus one of (c) and (d)

4(b)

60o

Equilateral triangle

✓ both

4(c)

15o

Isosceles triangle

✓ angle

✓ reason

4(d)

30o

Square

✓ angle

✓ reason

Excellence

Calculate angles giving reasons.

5

a = 90o

b = 85o

c = 85o

d = 47o

E

Each

✓

angle

✓

reason

Reasons depend on order.

ALL angles and reasons correct.

Merit

E

Achievement Criteria

Q

Evidence

Code

✓

Judgement

Sufficiency

Achievement

Plot and Interpret simple linear graphs

1(a)

$70

A

✓

3 A

1(b)

2 hours

A

✓

1(c)

A

✓

All correct

1(d)

Line starts at $15 and intersects PHHP line at 2 hours

A

✓

Merit

Write equations of simple linear graphs.

Draw simple parabolas

1(e)

C = 20H + 15

M1

✓

Must be equation (with =)

Achieved plus

3 M1

and

1 M2

1(f)

Two points:

1. Same price for 2 hours.

2. HHHC cheaper for <2 hours

3. PHHP cheaper for >2 hours

M1

✓✓

One for each point

Must have 2 points

2(a)

y = 3x + 3

M1

✓

Must be equations (with =)

2(b)

x = 2

M1

✓

2(c)

y = -x – 1[pic 8][pic 9]

M1

✓

3(a)

[pic 10]

M2

✓

3(b)

M2

✓

Excellence

Write equations of parabolas

4

y = (x-1)(x-3) or
y = (x+2)2-1

E

✓

Oops.  Sorry this is the same as 3(a)!!!

Merit plus

E

Achievement Criteria

Q

Evidence

Code

✓

Judgement

Sufficiency

Achievement

Carry out simple algebraic manipulations (A1).

Solve straightforward algebraic equations (A2).

Describe simple arithmetic or geometric patterns (A2).

1(a)

8r

A1

✓

No alternative

4 A1

plus

both A2
plus

both A3

1(b)

13x - 5z

A1

✓

Or equivalent

1(c)

a5

A1

✓

No alternative

1(d)

b4

A1

✓

No alternative

2(a)

3x + 18

A1

✓

Or equivalent

2(b)

8x2 + 4x

A1

✓

Or equivalent

3(a)

x = 3

A2

✓

3(b)

x = 7

A2

✓

4(a)

[pic 11]

A3

✓

4(b)

13

16

19

A3

✓

ALL

Merit

Find terms and rules for patterns (M1).

Carry out more complex algebraic manipulations (M2).

Solve equations (M3).

Interpret linear graphs (M4).

4(c)

L = 3F + 1

M1

✓

Achievement

Plus

2 M1

6 M2

3 M3

3 M4

Replacement

M2 for A1

M3 for A2

M1 for A3

4(d)

67

M1

✓

4(e)

51

M1

✓

5(a)

6

M2

Working ✓

Answer ✓

No alternative

5(b)

50

M2

Working ✓

Answer ✓

No alternative

6

p4

M2

✓

No alternative

7(a)

9x - 4

M2

Expand ✓

Simplify ✓

Or equivalent

7(b)

x2 + 3x - 10

M2

Expand ✓

Simplify ✓

Or equivalent

7(c)

6x2 - x - 35

M2

Expand ✓

Simplify ✓

Or equivalent

8(a)

2(x + 4)

M2

✓

No alternative

8(c)

(x + 2)(x + 9)

M2

(x + 2)✓

(x + 9)✓

9(a)

x = 1.5

M3

Working ✓

Answer ✓

Or equivalent

9(b)

x = 9

M3

Working ✓

Answer ✓

No alternative

10(a)

90 - 8x

M3

✓✓

Or equivalent

10(b)

(30 - 2x)(15 - 2x)

M3

✓✓

Or equivalent

12(a)

$ 15.20

M4

Working ✓

Answer ✓

Excellence

Solve algebra problems using graphs and manipulation.

12(b)

Cook for 40 minutes per kg

E

✓

Merit

plus

2 E

12(c)

[pic 12]

✓✓

Or equivalent

12(d)

8.5 kg

✓✓

13

(4x + 7)(4x - 7)

E

(4x + 7)✓

(4x - 7)✓

15

x + (x + 10) + 3(x + 10) = 65

5x + 40 = 65

5x = 25

x = 5

Numbers are 5, 15 and 45

E

✓

✓

✓

✓

Achievement Criteria

Q

Evidence

Code

✓

Judgement

Sufficiency

Achievement

Find simple, unknown lengths of right-angled triangles from diagrams using trig ratios and Pythagoras.

1

7.2 cm

(7.211102551)

A

working ✓

answer ✓

3 A

2

1.43m

A

✓

3(a)

8.7 km

(8.693332437)

A

working ✓

answer ✓

3(b)

2.3 km

(2.329371406)

A

working ✓

answer ✓

Merit

Find unknowns of right-angled triangles from words and diagrams using trig ratios and Pythagoras.

4

29.7o

(29.7448813)

M

working ✓

answer ✓

Achievement

plus

2 M

5(a)

26.9 cm

(26.92582404)

M

working ✓

answer ✓

5(b)

21.8o

(21.80140949)

M

working ✓

answer ✓

Excellence

Model complex situations to find unknowns of a right-angled triangle using Pythagoras or trig ratios

6

45.2o

(45.2397299)

E

working ✓

22.6 ✓

doubling ✓

Merit

plus

2 E

7(a)

8.8 cm

(8.774964387)

E

working ✓

answer ✓

7(b)

27.1o

(27.11914277)

E

working ✓

answer ✓