Tutorial 1 - revision

Maths 1

100

Calculate 2 - 6 x 4 + 22

0

200

Calculate 6 - 4 + 6 /2 + 3 x 0

5

300

Calculate [ (-2 + 5) x 3 + 3 ] / 4 

3

400

Simplify [ y² y⁴ ] / y^-3 y²

y⁷

500

Simplify [ (a^-2 a⁵) / a² ] ^-3

a^-3 or 1/a³

Maths 2

100

Round 123.456 to 2 decimal places

123.46

200

Round 5.678 to 2 significant figures

5.7

300

Simplify u^3/2 / u^1/2

u

400

Calculate  (64/12) / (25/3). Express as a fraction in lowest terms.

16/25

500

Simplify (a^2/3 a^-4/5)^-2/3

a^4/45

Maths 3

100

Calculate (2/3) x (6/5)

4/5

200

Write the following expression as a single algebraic fraction:

(x+3)/(x+2) + 5x

(6x + 13) / (x+2)

300

A power station emits 5000 tonnes of CO2 per day.

After a carbon capture and storage system is installed there is a 75% reduction in CO2 emissions.

How much CO2 is emitted per day after installation of the system?

1250 tonnes

400

Carbon, Capture and Storage (CCS) technology has been installed at a power station, resulting in a 10% overall increase in the cost of electricity.

Prior to installation of the CCS technology the electricity cost was £70 per MWh. How much is the cost of electricity after installation?  

£77

500

A quantity of concrete has to be mixed using a ratio of 2:3:6 cement:sand:gravel.

What quantity of cement will be needed (in m³) if the total amount of concrete required is 22m³?

4m³

Maths 4

100

A right angle triangle has sides of length 6cm and 8cm. What is the length of the third side?

10cm

200

If x = 2 and y = -3 what is 3x + 2y³ -4?

a. 56

b. -52

c. -214

b. -52

300

If a = 4 and b= -2 what is 

3a - 2b² / 3b - 2a² as a fraction?

-2/19

400

What is the sine rule for a triangle ABC with sides of length a,b,c and angles A,B,C?

a/sinA = b/SinB = c/sinC

500

What is the cosine rule to calculate the side of length a in a triangle ABC with sides of length a, b and c and angles A,B and C?

a² = b² + c² -2bc cosA

Maths 5

100

Simplify the following:

2x (3y + 1)

6xy +2x

200

Simplify the following:

-3x (-2y +8)

6xy -24x

300

Express x as the subject:

3x + 6 = 3(y - x)

x = y/2 -1

400

What is the value of x⁰ + y⁰ + 1?

a. 1

b. 2

c. 3

c. 3

500

Multiply out the following:

-5z (4 + 6z) + 5z (4-6z)

-30z²