Initial Diagnostic Audit - Unit F1: Formulae
Section F1.1 - Using Formulae
1. The perimeter of a square of side length a is given by P = 4a
What is the perimeter when a = 10 cm? P = cm
2. The surface area of a cuboid of side lengths a, b and c is given by the formula
SA = 2(ab + bc + ca)
What is the surface area of a cuboid with side lengths 4 cm, 5 cm and 5 cm? SA = cm2
3. The volume of a cuboid with side lengths a, b and c is given by V = abc
What is the volume of a cube with sides of length 5 cm? V = cm3
4. The final speed of a car is given by v = u + at where u is the initial speed, a the acceleration and t, the time.
(a) Find v when u = 50 mph, a = 100 mph2 and t = 15 minutes. v = mph

(b) Find v when u = 0 mph, a = 50 mph2 and t = 6 minutes. v = mph

Section F1.2 - Construct and Use Simple Formulae
5. (a) What is the formula for the perimeter, P, of this shape?

P = cm

(b) In the figure above, if a = c = 2 m, b = 10 m, f = d = 2 m and e = 7 m, what is the value of P?
P = cm

6. What is the formula for the area of this shape?

Area = a2

7. A central heating engineer's call-out fee is £40 plus £20 for each ¼ hour worked.

(a) What is the formula for his total charge if he works for x hours? C = £( + x)

(b) What will be the total charge if he works for 45 minutes? C = £

Section F1.3 - Revision of Negative Numbers
8. 7 – 10 =
9. -6 + 8 =
10. (-2) × (-3) =
11. (-16) ÷ 4 =
12. (-48) ÷ (-6) =
Section F1.4 - Substituting into Formulae
13. The formula for converting temperatures in degrees Celsius, C, to degrees Fahrenheit, F, is given by the formula

F =  
9C
  + 32
5

(a) What is F if C = 0?     F =

(b) What is F if C = 20?     F =

(c) What is F if C = -20?     F =

14. The formula for the distance s, travelled in t seconds is

s =  
1
(u + v)t
2

where u is the initial velocity and v is the final velocity.

(a) What is s if u = 2, v = 8 and t = 5?     s =

(b) What is s if u = -2, v = 10 and t = 12?     s =

Section F1.5 - More Complex Formulae

15.
If  
1
  =  
1
  +  
1
 , what is the value of f when
f
u
v

(a) u = 4 and v = 12?     f =

(b) u = -4 and v = 3?     f =


16.		 If z2 = x2 + y2, what are the values of z when x = 1.8 and y = 2.4?
z =  or      z =
17. Find the value of y when

1
  =  
x – 2
     and   x =  
1
y
x + 4
4

y =  
   
Section F1.6 - Changing the Subject

When completing this section, use fractions and conventional algebraic notation to avoid using × and ÷ symbols in your answers
18. Make x the subject in each of the following formulae.

(a)   y = 5x           

(b)   y = 
2 – x
3
       

(c)   y = ax + b           

19.
If F = 
9
5
 C + 32, express C in terms of F           

20.

If V = r2h, find an expression for r of the form r = 
      
Section F1.7 - More Change of Subject

When completing this section, use fractions and conventional algebraic notation to avoid using × and ÷ symbols in your answers

You may use a calculator for this section

21.
If a ball is dropped from a height, h, it hits the ground with speed v, given by v = 

(a)   Express h in terms of v and g           

(b)   Find the value of h if g = 10 and v = 12.    h =


22.
The volume of a cone is given by the formula V = 
1
 r2h
3

(a)   Rearrange the formula to express r in terms of V and h
      

(b)   What is the value of r when V = 750 and h = 22? Give your answer to 1 d.p.   r =

23. For an electric unit, the resistance, R, is given by the formula

1
  =  
1
   +  
1
  +  
1
R
X
Y
Z

What is the value of R when X = 10, Y = 20 and Z = 30?    R =  
   

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Produced by Russell Geach for CIMT - April 2013