AQA · Mathematics · 8300
GCSE Maths: Algebra: substitution
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Algebra: substitution (Corbettmaths Video 20), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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In algebra, ? means replacing a variable with its numerical value.
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substitution
What does 3a mean when a = 5?
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15. The expression 3a means 3 × a, so when a = 5, we have 3 × 5 = 15.
When substituting into a², what operation are you performing?
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Squaring the value of a (multiplying a by itself).
What is the value of fg when f = 5 and g = 6?
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30. The notation fg means f × g, so 5 × 6 = 30.
When substituting a negative value into an expression like 2c where c = −6, what is the result?
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−12. You multiply: 2 × (−6) = −12.
What does P = 2L + 2W represent geometrically?
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The perimeter of a rectangle, where L is length and W is width.
In the formula C = 15h + 30, what does the constant 30 likely represent?
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A fixed cost or base charge (independent of the value of h).
What is the formula to convert Celsius (C) to Fahrenheit (F)?
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F = 1.8C + 32
When substituting into 5(a + d), what operation must you perform first?
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Add a and d (the expression inside the parentheses), then multiply the result by 5.
If you know P = 2W + 2L and the values of P and L, how would you find W?
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Rearrange the formula: W = (P − 2L) / 2.
What is the value of (−3)² ?
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9. When you square a negative number, the result is positive: (−3) × (−3) = 9.
In the formula C = 40h + p + 0.5d, the variable ? represents the total cost of the plumbing job in pounds.
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C
In the formula C = 40h + p + 0.5d, the coefficient ? represents the cost per hour in pounds.
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40
In the formula C = 40h + p + 0.5d, the variable ? represents the distance travelled in miles.
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d
What is the formula for the kinematic equation relating velocity, initial velocity, acceleration, and time?
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v = u + at
If 2x − y = 17, what is the value of 6x − 3y?
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51. Because 6x − 3y = 3(2x − y) = 3(17) = 51.
If 2x − y = 17, what is the value of y − 2x?
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−17. Because y − 2x = −(2x − y) = −17.
In the formula y = 7x², what happens to the value of y when x doubles?
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y is multiplied by 4 (or quadruples). Because if x is replaced by 2x, then y = 7(2x)² = 7(4x²) = 4(7x²).
In the formula y = 800/x³, what happens to the value of y when x doubles?
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y is divided by 8 (or multiplied by 1/8). Because if x is replaced by 2x, then y = 800/(2x)³ = 800/(8x³) = (1/8)(800/x³).
What is the value of x^y − y^x when x = 3 and y = 6?
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513. Because 3⁶ = 729 and 6³ = 216, so 729 − 216 = 513.
If 80 = 2mn and both m and n are negative integers, give one possible pair of values for m and n.
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m = −5 and n = −8 (or m = −8 and n = −5, or m = −10 and n = −4, or m = −4 and n = −10, etc.). Since 2mn = 80, we have mn = 40, and both must be negative.
If y = (x − 5)(x + 1), what is y when x = −3?
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16. Because y = (−3 − 5)(−3 + 1) = (−8)(−2) = 16.
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