N5 Practice Paper A National 5

Mathematics Paper 1 (Non-Calculator) Duration — 1 hour 15 minutes

Total marks — 50

You may NOT use a calculator.

Attempt ALL questions.

Use blue or black ink. Pencil may be used for graphs and diagrams only.

Write your working and answers in the booklet provided.

Full credit will be given only to solutions which contain appropriate working.

State the units for your answer where appropriate.

Before leaving the examination room you must give the answer booklet to the Invigilator.

If you do not, you may lose all the marks for this paper.

Do not take this paper out of the exam hall.

FORMULAE LIST

The roots of 𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0 are 𝑥 =−𝑏±√(𝑏²−4𝑎𝑐)

2𝑎

Sine rule: 𝑎

𝑠𝑖𝑛𝐴=

𝑏

𝑠𝑖𝑛𝐵=

𝑐

𝑠𝑖𝑛𝐶

Cosine rule: 𝑎² = 𝑏² + 𝑐² − 2𝑏𝑐 𝑐𝑜𝑠𝐴 or 𝑐𝑜𝑠𝐴 = 𝑏²+𝑐²−𝑎²

2𝑏𝑐

Area of a triangle: 𝐴 =1

2𝑎𝑏 𝑠𝑖𝑛𝐶

Volume of a sphere: 𝑉 =4

3𝜋𝑟³

Volume of a cone: 𝑉 =1

3𝜋𝑟²ℎ

Volume of a pyramid: 𝑉 =1

3𝐴ℎ

Standard deviation: 𝑠 = √∑(𝑥−�̅�)²

𝑛−1= √

∑ 𝑥²−(∑ 𝑥)²/𝑛

𝑛−1 , where 𝑛 is the sample size.

Attempt ALL questions

Total marks — 50

MARKS

1.

2

2. 2

3.

3

4.

2

5.

2

6.

2

7. (a)

3

(b) 2

8.

4

9. Find the coordinates of the point of intersection of the lines with

equations 𝑥 + 2𝑦 = −5 and 3𝑥 − 𝑦 = 13.

4

10.

3

11.

2

1

2

12.

3

13.

1

2

14. 1

2

15. Cleano washing powder is on special offer

Each box on special offer contains 20% more powder than the

standard box.

A box on special offer contains 900 grams of powder.

How many grams of powder does the standard box contain? 3

16.

2

1

N5

Practice Paper A National 5

Mathematics Paper 2 (Calculator) Date — February 2018

Duration — 1 hour 50 minutes

Total marks — 60

You may use a calculator.

Attempt ALL questions.

Use blue or black ink. Pencil may be used for graphs and diagrams only.

Write your working and answers in the booklet provided.

Full credit will be given only to solutions which contain appropriate working.

State the units for your answer where appropriate.

Before leaving the examination room you must give the answer booklet to the Invigilator.

If you do not, you may lose all the marks for this paper.

Do not take this paper out of the exam hall.

FORMULAE LIST

The roots of 𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0 are 𝑥 =−𝑏±√(𝑏²−4𝑎𝑐)

2𝑎

Sine rule: 𝑎

𝑠𝑖𝑛𝐴=

𝑏

𝑠𝑖𝑛𝐵=

𝑐

𝑠𝑖𝑛𝐶

Cosine rule: 𝑎² = 𝑏² + 𝑐² − 2𝑏𝑐 𝑐𝑜𝑠𝐴 or 𝑐𝑜𝑠𝐴 = 𝑏²+𝑐²−𝑎²

2𝑏𝑐

Area of a triangle: 𝐴 =1

2𝑎𝑏 𝑠𝑖𝑛𝐶

Volume of a sphere: 𝑉 =4

3𝜋𝑟³

Volume of a cone: 𝑉 =1

3𝜋𝑟²ℎ

Volume of a pyramid: 𝑉 =1

3𝐴ℎ

Standard deviation: 𝑠 = √∑(𝑥−�̅�)²

𝑛−1= √

∑ 𝑥²−(∑ 𝑥)²/𝑛

𝑛−1 , where 𝑛 is the sample size.

Attempt ALL questions

Total marks — 60

MARKS

1.

How many Chocpops will be eaten in 2016?

Give your answer in Scientific Notation. 3

2.

3

3.

3

4. The diagram below shows a stack of cubes with length one unit.

With the coordinate axes as shown, point A has coordinates (2, 4, 6)

Write down the coordinates of the points B, C and D shown. 3

5.

Find the equation of the straight line passing through (-3, 5)

and (7, -4) 3

6.

3

7.

4

8.

3

9.

3

10. 𝑚𝑥2 + 6𝑥 + 𝑚 = 0 has equal roots.

Find 𝑚.

5

11.

4

12.

5

13.

3

2

14.

2

15. (a) Find the resultant vector 2𝒂 + 𝒃 where 𝒂 = (−243

)

and 𝒃 = (0

−31

). 2

(b) Find |2𝒂 + 𝒃| the magnitude of 2𝒂 + 𝒃 . 2

16.

5

17.

2