Substitution High School Math Topics Substitution into Expressions

Substitution High School Math Topics Substitution into Expressions Substitution into Mathematical Formulae Substitution into Scientific Formulae Algebra

Substitution into Expressions This is where we replace the letters in an expression with numbers, and then work out the value of the numerical expression. Here is a mathematical expression. 3 e + 4 f An expression consists of a collection of letters and/or numbers. Here, if we are given the values of e and f, we can replace the letters in the expression with these values to work out the value of the expression. High School Math Topics - Algebra

Substitution into Expressions Find the value of the expression: Example 1 3 e + 4 f if e = 7 and f = 9. Replace each letter in the formula with the given value 3× 7 + 4× 9 Multiply each pair of values 21 + 36 Add to find the answer 57 High School Math Topics - Algebra

Substitution into Expressions Find the value of the expression: Example 2 3 e + 4 f if e = 81 and f = 27. Replace each letter in the formula with the given value 3 × 81 + 4 × 27 Multiply each pair of values 243 + 108 Add to find the answer 351 High School Math Topics - Algebra

Substitution into Expressions Find the value of the expression: Example 3 3 e + 4 f if e = 9. 4 and f = 17. 6 Replace each letter in the formula with the given value 3 × 9. 4 + 4 × 17. 6 Multiply each pair of values 28. 2 + 70. 4 Add to find the answer 98. 6 High School Math Topics - Algebra

Substitution into Expressions Find the value of the expression: Example 4 5 g² − 2 h if g = 3 and h = 11. Replace each letter in the formula with the given value 5 × 3² − 2 × 11 Square the 3 5 × 9 − 2 × 11 Multiply each pair of values 45 − 22 Subtract to find the answer 23 High School Math Topics - Algebra

Substitution into Expressions Find the value of the expression: Example 5 5 g² − 2 h if g = 2. 5 and h = 1. 4 Replace each letter in the formula with the given value 5 × 2. 5² − 2 × 1. 4 Square the 2. 5 5 × 6. 25 − 2 × 1. 4 Multiply each pair of values 31. 25 − 2. 8 Subtract to find the answer 28. 45 High School Math Topics - Algebra

Substitution into Expressions Find the value of the expression: Example 6 5 g² − 2 h if g = 1. 4 and h = 8. 4 Replace each letter in the formula with the given value 5 × 1. 4² − 2 × 8. 4 Square the 1. 4 5 × 1. 96 − 2 × 8. 4 Multiply each pair of values 9. 8 − 16. 8 Subtract to find the answer − 7 High School Math Topics - Algebra

Substitution into Mathematical Formulae This is where we replace the letters in a formula for numbers, and then work out the value of the numerical expression. Here is the formula for calculating the perimeter, P, of a rectangle if we know the base, b and height, h. P = 2 b + 2 h h b If we are given the values of b and h, we can replace the letters in the formula with these values to work out the perimeter, P. High School Math Topics - Algebra

Substitution into Mathematical Formulae Using the formula for calculating the perimeter of a rectangle, find the value of P if: b = 13 cm and h = 7 cm. Example 1 h P = 2 b + 2 h Replace each letter in the formula with the given value P = 2 × 13 + 2 × 7 Multiply each pair of expressions P = 26 + 14 Add to find the answer, and give the correct units P = 40 b High School Math Topics - Algebra cm

Substitution into Mathematical Formulae Using the formula for calculating the perimeter of a rectangle, find the value of P if: b = 9. 8 m and h = 5. 2 m. Example 2 h P = Replace each letter in the formula with the given value P = 2 × 9. 8 + 2 × 5. 2 Multiply each pair of expressions P = Add to find the answer, and give the correct units P = 2 b + 2 h b 19. 6 + 10. 4 30 High School Math Topics - Algebra m

Substitution into Mathematical Formulae Using the formula for calculating the perimeter of a rectangle, find the value of P if: b = 142 mm and h = 49 mm. Example 3 h P = Replace each letter in the formula with the given value P = 2 × 142 + 2 × 49 Multiply each pair of expressions P = 284 + 98 Add to find the answer, and give the correct units P = 382 2 b + 2 h b High School Math Topics - Algebra mm

Substitution into Mathematical Formulae Here is the formula for calculating the area, A, of the trapezium shown. a A = a + b 2 × h h b If we are given the values of a, b and h, we can replace the letters in the formula with these values to work out the area, A. High School Math Topics - Algebra

Substitution into Mathematical Formulae Using the formula for calculating the area of a trapezium, find the value of A if: a = 5 cm, b = 9 cm and h = 4 cm. Example 1 a A = a + b 2 × h Replace each letter in the formula with the given value A = 5 + 9 2 × 4 Work out the value on top of the fraction A = 14 2 × 4 Carry out the division A = 7 × 4 Find the answer, and give the correct units A = 28 h b High School Math Topics - Algebra cm²

Substitution into Mathematical Formulae Using the formula for calculating the area of a trapezium, find the value of A if: a = 8. 4 m, b = 12. 2 m and h = 6. 7 m. Example 2 a A = a + b 2 × h Replace each letter in the formula with the given value A = 8. 4 + 12. 2 2 × 6. 7 Work out the value on top of the fraction A = 20. 6 2 × 6. 7 Carry out the division A = 10. 3 × 6. 7 Find the answer, and give the correct units A = 19. 01 h b High School Math Topics - Algebra m²

Substitution into Mathematical Formulae Using the formula for calculating the area of a trapezium, find the value of A if: a = 88 mm, b = 152 mm and h = 64 mm. Example 3 a A = a + b 2 × h Replace each letter in the formula with the given value A = 88 + 152 2 × 64 Work out the value on top of the fraction A = 240 2 × 64 Carry out the division A = 120 × 64 Find the answer, and give the correct units A = 7680 h b High School Math Topics - Algebra mm²

Substitution into Scientific Formulae This formula is used in science to calculate the Force acting upon an object if we know the mass and acceleration. F = m × a So in this formula, we just multiply the values of m and a to get F. Example 1 Use the formula F = m × a to find the value of F, in Newtons if: m = 9 kg and a = 5 m/s². Replace each letter in the formula with the given value Multiply to give the answer, together with the correct units F F = m × a F = 9 × 5 = 45 High School Math Topics - Algebra N

Substitution into Scientific Formulae This formula is used in science to calculate the Force acting upon an object if we know the mass and acceleration. F = m × a So in this formula, we just multiply the values of m and a to get F. Example 2 Use the formula F = m × a to find the value of F, in Newtons if: m = 245 kg and a = 3. 2 m/s². Replace each letter in the formula with the given value Multiply to give the answer, together with the correct units F F = 245 × 3. 2 = m × a 784 High School Math Topics - Algebra N

Substitution into Scientific Formulae This formula is used in science to calculate the Force acting upon an object if we know the mass and acceleration. F = m × a So in this formula, we just multiply the values of m and a to get F. Example 3 Use the formula F = m × a to find the value of F, in Newtons if: m = 0. 75 kg and a = 9. 8 m/s². Replace each letter in the formula with the given value Multiply to give the answer, together with the correct units F F = 0. 75 × 9. 8 = m × a 7. 35 High School Math Topics - Algebra N

Substitution into Scientific Formulae This formula is used to calculate the velocity, v of an object after a given time, t and acceleration a, with an initial velocity, u. v = u + at Use the formula v = u + at to find the value of v if: u = 5 m/s, a = 3 m/s² and t = 12 s. Example 1 v = u + at Replace each letter in the formula with the given value v = 5 + 3 × 12 Multiply the last pair of terms v = 5 + 36 Add to give the answer, together with the correct units v = 41 High School Math Topics - Algebra m/s²

Substitution into Scientific Formulae This formula is used to calculate the velocity, v of an object after a given time, t and acceleration a, with an initial velocity, u. v = u + at Use the formula v = u + at to find the value of v if: u = 12 m/s, a = 1. 5 m/s² and t = 28 s. Example 2 v = Replace each letter in the formula with the given value v = 12 + 1. 5 × 28 Multiply the last pair of terms v = Add to give the answer, together with the correct units v = u + at 12 + 42 54 High School Math Topics - Algebra m/s²

Substitution into Scientific Formulae This formula is used to calculate the velocity, v of an object after a given time, t and acceleration a, with an initial velocity, u. v = u + at Use the formula v = u + at to find the value of v if: u = 9. 5 m/s, a = 2. 2 m/s² and t = 16 s. Example 3 v = Replace each letter in the formula with the given value v = 9. 5 + 2. 2 × 16 Multiply the last pair of terms v = Add to give the answer, together with the correct units v = u + at 9. 5 + 35. 2 44. 7 High School Math Topics - Algebra m/s²