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Substituting Complex Formulas Worksheet
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Substituting Complex Formulas Worksheet
Replace each variable with its given value. Use brackets for negative values, then follow the order of operations. Show your working where space is provided.
Worked examples
Study the substitution and calculation in each example.
1.For P = 2a² + 5b − 4, find P when a = 3 and b = 6. Substitution: P = 2(3)² + 5(6) − 4 = 18 + 30 − 4 = 44.
2.For Q = 3x(y + 2) − 2y², find Q when x = −2 and y = 4. Substitution: Q = 3(−2)(4 + 2) − 2(4)² = −36 − 32 = −68.
3.For R = (m − n)² + 2mn, find R when m = 5 and n = −3. Substitution: R = (5 − (−3))² + 2(5)(−3) = 64 − 30 = 34.
Practise substituting
Calculate each value. Keep track of negative numbers and powers.
4.If A = 3x² + 2y, find A when x = −4 and y = 7.
5.If B = 5p − 3q², find B when p = 8 and q = −2.
6.If C = 4m(n − 3), find C when m = −3 and n = 8.
7.If D = (r + s)² − 2rs, find D when r = 6 and s = 2.
8.If E = 2a² − b² + 3c, find E when a = −3, b = 4 and c = 5.
9.If F = 2x(y + 1) − 4y², find F when x = 3 and y = −2.
Use formulas in context
Substitute the given values into each formula, then calculate.
10.A rectangular display has length (3x + 2) cm and width (x − 1) cm. Its area is A = length × width. Find A when x = 4.
11.A cylinder's volume is V = πr²h. Find its volume when r = 2 cm and h = 7 cm, using π = 3.14. Give your answer to 2 decimal places.
12.For T = 2(a + b)² − (a − b)², find T when a = 5 and b = 1.
13.A bicycle hire charge is C = 4.50 + 0.80h pounds, where h is the number of hours. Find the cost for 6 hours.
14.If G = 3u² − 2v, find G when u = −2 and v = 5. Choose the correct value.
- 2
- −2
- 22
- −22
15.Match each formula and substitution to its calculated value.
- H = 2x + y, for x = 3 and y = 4
- J = a² − 3b, for a = 5 and b = 2
- K = 4p(q − 1), for p = 2 and q = 3
- L = (m + n)², for m = −1 and n = 6
- 25
- 10
- 19
- 16
3 printable pages
Page 1
Page 2
Page 3
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