Algebraic Expressions

17 Grade 7 Mathematics questions on Algebraic Expressions, with worked marking schemes. 17 questions are available on this topic in full.

1. Question 1

   1 mark

   Evaluate 2a² − 3b when a = 4 and b = 2.

   A. 32

   B. 20

   C. 26

   D. 22

   (1 mark)

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2. Question 2

   2 marks

   Peter worked out a question on indices and got the answer as $p^2$. Which of the following is equivalent to $p^2$?

   A. p⁴ × p²

   B. (p⁴)²

   C. p⁴ − p²

   D. p⁴ ÷ p²

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3. Question 3

   1 mark

   Simplify: $\frac{12x^3}{4x}$

   A. 3x

   B. 8x²

   C. 3x³

   D. 3x²

   (1 mark)

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4. Question 4

   1 mark

   Factorise: 6xy + 9x

   A. 3(2xy + 3x)

   B. 3x(2y + 3)

   C. x(6y + 9)

   D. 6x(y + 9)

   (1 mark)

   Marking scheme

   B. $3x(2y+3)$ — take out the highest common factor of $6xy$ and $9x$, which is $3x$. A and C each take out only part of it, so they are correct in value but not fully factorised; D is simply wrong.

5. Question 5

   2 marks

   Simplify: $2(3x+4)-5x$.

   (2 marks)

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6. Question 6

   1 mark

   Simplify: $(2x{)}^3$

   A. 6x³

   B. 2x³

   C. 8x

   D. 8x³

   (1 mark)

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7. Question 7

   3 marks

   Simplify: $4(2x-3)-3(x-5)$

   (3 marks)

   Marking scheme

   Expand the first bracket: $4(2x-3)=8x-12$. (1)

   Expand the second, watching the minus sign in front: $-3(x-5)=-3x+15$. (1)

   Collect like terms: $8x-3x=5x$ and $-12+15=3$. (1)

   Final answer: $5x+3$.

8. Question 8

   3 marks

   Factorise completely: $8a^{2}b-12a{b}^2$

   (3 marks)

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9. Question 9

   1 mark

   Simplify: 3x + 5y − x + 2y

   A. 2x + 7y

   B. 4x + 7y

   C. 2x + 3y

   D. 4x + 3y

   (1 mark)

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10. Question 10

    1 mark

    Peter worked out a question on indices and got $p^2$. Which is equivalent?

    A. p⁴ × p²

    B. (p⁴)²

    C. p⁴ − p²

    D. p⁴ ÷ p²

    (1 mark)

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11. Question 11

    3 marks

    Expand: $(3x+2{)}^2$

    (3 marks)

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12. Question 12

    2 marks

    Peter worked out a question on indices and got the answer as $p^2$. Which of the following is equivalent to $p^2$?

    A. p⁴ × p²

    B. (p⁴)²

    C. p⁴ − p²

    D. p⁴ ÷ p²

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13. Question 13

    1 mark

    Expand: 2(3a − 4b)

    A. 5a − 6b

    B. 6a − 4b

    C. 6a − 8b

    D. 3a − 8b

    (1 mark)

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14. Question 14

    3 marks

    Simplify: $\frac{x^2-9}{x+3}$

    (3 marks)

    Marking scheme

    The numerator is a difference of two squares: $x^2-9=x^2-3^2$. (1)

    Factorise it: $x^2-9=(x+3)(x-3)$. (1)

    Cancel the common factor $(x+3)$, which is allowed provided $x\ne -3$. (1)

    Final answer: $x-3$.

15. Question 15

    3 marks

    If x = 3 and y = −2, evaluate $x^2-2xy+y^2$.

    (3 marks)

    Marking scheme

    Substitute $x=3$ and $y=-2$ into $x^2-2xy+y^2$. (1)

    $x^2=3^2=9$ and $y^2=(-2{)}^2=4$. For the middle term, $-2xy=-2(3)(-2)=+12$, because a negative multiplied by a negative gives a positive. (1)

    Add the three parts: $9+12+4=25$. (1)

    Final answer: $25$. Check: the expression is $(x-y{)}^2$, and $(3-(-2){)}^2=5^2=25$.

16. Question 16

    2 marks

    Simplify: $2(3x+4)-5x$.

    (2 marks)

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17. Question 17

    1 mark

    Expand and simplify: (x + 3)(x − 2)

    A. x² + 5x − 6

    B. x² − 6

    C. x² + x − 6

    D. x² − x − 6

    (1 mark)

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