GCSE MATHEMATICS topic sheet. SUBSTITUTION into formulas

GCSE MATHEMATICS topic sheet.
SUBSTITUTION into formulas
1. A formula is given as V = 4h + p 2
Find the value of V when h = 0.5 and p = 8
2. Given that s = ut + ½ at 2
Find the value of s when u = 20, t = 3 and a = –10.
3. Find the exact value of
1 1 +
a b
when a = 2
1 and b = 3
1
b
4. Find the value of ab
2 + when a = 4 a 5
and b = –3.
5. The formula F = 9 / 5 C + 32
is used to change temperatures in degrees Centigrade (C) to temperatures in degrees
Fahrenheit (F).
A thermometer reads a temperature of 15 °C.
What is the equivalent temperature in degrees Fahrenheit?
6. Calculate the value of
b
2
3 1
4ac
when a = , b = 2 and c = –2.
4 2
7. S = 1 + 1 .
x y
Calculate the value of S when x = 0.5 and y = –2.
8. Using the formula v = 3u + 5t
calculate the value of v when u = 5.1 and t = 27.3
9. Using p = 18.8, q = 37.2, r = 0.4, work out
(a)
p + r
q
(b)
p + q
r
10. Given that m = 1 , p = 3 2 4
, t = –2 calculate
( m + p)
(a) mp + t (b)
t
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SOLUTIONS / ANSWERS.
1. V = 4 × 0.5 + 8 2 = 66.
2. s = 20 × 3 + 1 2 × (10) × 32 Always a good idea to place negative
numbers in brackets!
= 15.
3. Best to use the divide button: 1 ÷ 1 2 + 1 ÷ 1 3 = 5.
4.
4
5
×
(3)2 + (3) ÷ 4
5
= 3 9 20
or 3.45.
If in doubt, use brackets!
5. F = 9 5
× 15 + 32 = 59.
( )
2
6. 2.5 4 0.75 ( 2)
× × The first set of brackets are a must!
= 3.5. NOTE also the use of decimals. This can
make life easier!
7. S = 1 ÷ 0.5 + 1 ÷ (2) = 1.5.
8. v = 3 × 5.1 + 5 × 27.3 = 151.8.
9. (a) 18.8 + 37.2 ÷ 0.4 = 111.8.
(b) (18.8 + 37.2) ÷ 0.4 The brackets are essential.
= 140.
10. (a) 0.5 × 0.75 + (2) = 1.625,
1 3
or ( 2) × ( 4)
+ (2) = 1 5 . 8
(b) (0.5 + 0.75) ÷ (2) = 0.625,
1
+
3
÷ (2) = 5 . 8
or ( )
2 4
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