GCSE Substitution Practice Questions

Free GCSE Substitution practice questions with full step-by-step worked solutions. Covers substitution, multiplication, addition, order of operations. Practise exam-style problems and check your method.

substitutionmultiplicationadditionorder of operationssubtractiondivision
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Work out the value of 3x3x when x=4x = 4.
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Worked solution

  1. Write down the expression

    3x3x

    You need the value of 3x, which means 3 multiplied by x.

  2. Substitute x=4x = 4

    3×43 \times 4

    Replace the letter x with the number 4.

  3. Work out the answer

    3×4=123 \times 4 = 12

    Three lots of four is twelve.

Answer
1212
Question 2
2 markseasy
The perimeter of a square is given by P=4sP = 4s. Work out PP when s=7s = 7 cm.
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Worked solution

  1. Write down the formula

    P=4sP = 4s

    The perimeter is four times the side length.

  2. Substitute s=7s = 7

    P=4×7P = 4 \times 7

    Replace s with 7.

  3. Work out the answer

    P=28P = 28

    Four times seven is 2828, so the perimeter is 2828 cm.

Answer
28 cm28\text{ cm}
Question 3
2 marksintermediate
The area of a triangle is A=12bhA = \frac{1}{2}bh. Work out AA when b=8b = 8 and h=5h = 5.
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Worked solution

  1. Write down the formula

    A=12bhA = \frac{1}{2}bh

    Area of a triangle is half base times height.

  2. Substitute b=8b = 8 and h=5h = 5

    A=12×8×5A = \frac{1}{2} \times 8 \times 5

    Replace b and h.

  3. Multiply the base and height

    8×5=408 \times 5 = 40

    Work left to right.

  4. Rewrite

    12×40\frac{1}{2} \times 40

    Now take half.

  5. Halve

    12×40=20\frac{1}{2} \times 40 = 20

    Half of 4040 is 2020.

  6. State the answer

    A=20A = 20

    The area is 2020 square units.

Answer
2020
Question 4
3 markshard
The perimeter of a rectangle is P=2(l+w)P = 2(l + w). Work out PP when l=6.5l = 6.5 and w=3.5w = 3.5.
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Worked solution

  1. Write down the formula

    P=2(l+w)P = 2(l + w)

    Perimeter of a rectangle.

  2. Write down the values

    l=6.5, w=3.5l = 6.5,\ w = 3.5

    Substitute both.

  3. Substitute

    P=2(6.5+3.5)P = 2(6.5 + 3.5)

    Replace l and w.

  4. Work out the bracket

    6.5+3.5=106.5 + 3.5 = 10

    The decimals add to a whole number.

  5. Rewrite

    P=2×10P = 2 \times 10

    Now double.

  6. Multiply

    2×10=202 \times 10 = 20

    Twenty.

  7. Add units

    20 cm20 \text{ cm}

    Perimeter is a length.

  8. Check

    2×6.5+2×3.5=13+7=202 \times 6.5 + 2 \times 3.5 = 13 + 7 = 20

    Expanding gives the same total.

  9. Interpret

    distance around=20\text{distance around} = 20

    That is once around the edge.

  10. State the answer

    2020

    The perimeter is 2020.

Answer
2020
Question 5
6 markschallenging
Work out the value of 2a2−bc+d\frac{2a^2 - b}{c + d} when a=3a = 3, b=4b = 4, c=5c = 5 and d=2d = 2.
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Worked solution

  1. Write down the expression

    2a2−bc+d\frac{2a^2 - b}{c + d}

    Top and bottom each act as a bracket.

  2. Write down the values

    a=3, b=4, c=5, d=2a = 3,\ b = 4,\ c = 5,\ d = 2

    Substitute all four.

  3. Substitute

    2×32−45+2\frac{2 \times 3^2 - 4}{5 + 2}

    Replace every letter.

  4. Square a

    32=93^2 = 9

    Index on the top first.

  5. Multiply by 22

    2×9=182 \times 9 = 18

    The first part of the numerator.

  6. Finish the top

    18−4=1418 - 4 = 14

    Numerator is 1414.

  7. Work out the bottom

    5+2=75 + 2 = 7

    Denominator is 77.

  8. Rewrite

    147\frac{14}{7}

    Now divide.

  9. Divide

    147=2\frac{14}{7} = 2

    Fourteen over seven is 22.

  10. Check

    2×7=142 \times 7 = 14

    Multiply back to confirm.

  11. Interpret

    the value is a whole number\text{the value is a whole number}

    The division is exact.

  12. Common mistake

    2×32≠622 \times 3^2 \neq 6^2

    Square before multiplying by 22.

  13. Order note

    top and bottom separately, then divide\text{top and bottom separately, then divide}

    The bar groups each part.

  14. Estimate

    147=2\frac{14}{7} = 2

    Exactly 22.

  15. State the answer

    22

    The value is 22.

Answer
22

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