Algebraic Expressions

13 Grade 8 Mathematics questions on Algebraic Expressions, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   1 mark

   Simplify: $5p-2q-3p+7q$

   A. 2p + 5q

   B. 8p + 5q

   C. 2p + 9q

   D. 2p - 5q

   (1 mark)

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2. Question 2

   3 marks

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

   (3 marks)

   Marking scheme

   Expand the first bracket: $3(2x+4)=6x+12$. (1)

   Expand the second, watching the minus sign in front: $-2(x-5)=-2x+10$. (1)

   Collect like terms: $6x-2x=4x$ and $12+10=22$. (1)

   Final answer: $4x+22$.

3. Question 3

   1 mark

   Simplify: $3x+5y-x+2y$

   A. 2x + 3y

   B. 4x + 7y

   C. 2x + 7y

   D. 3x + 7y

   (1 mark)

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4. Question 4

   1 mark

   Evaluate $2x^2-3y$ when x = 3 and y = 4.

   A. 30

   B. 24

   C. -6

   D. 6

   (1 mark)

   Marking scheme

   D. $6$ — square first, then multiply: $2(3{)}^2=2\times 9=18$ and $3(4)=12$, so $18-12=6$. B squares $2x$ instead of just $x$; C forgets the square altogether; A adds instead of subtracting.

5. Question 5

   1 mark

   Factorise completely: $8ab-12a$

   A. 2a(4b - 6)

   B. 4(2ab - 3a)

   C. 4a(2b - 3)

   D. 4a(2b + 3)

   (1 mark)

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6. Question 6

   1 mark

   Factorise: $6a+9$

   A. 3(2a + 3)

   B. 3(2a + 9)

   C. 2(3a + 3)

   D. 3(2a - 3)

   (1 mark)

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7. Question 7

   3 marks

   Evaluate $3a^2-2ab$ when a = 2 and b = -3.

   (3 marks)

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8. Question 8

   1 mark

   Expand: $3(2x-5)$

   A. 6x - 5

   B. 6x - 15

   C. 5x - 15

   D. 6x + 15

   (1 mark)

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9. Question 9

   3 marks

   Simplify: $5(x+2)-3(x-1)$

   (3 marks)

   Marking scheme

   Expand the first bracket: $5(x+2)=5x+10$. (1)

   Expand the second: $-3(x-1)=-3x+3$. The minus sign changes both terms. (1)

   Collect like terms: $5x-3x=2x$ and $10+3=13$. (1)

   Final answer: $2x+13$.

10. Question 10

    1 mark

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

    A. 6x - 22

    B. 6x - 2

    C. 6x + 2

    D. 10x - 2

    (1 mark)

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11. Question 11

    1 mark

    Evaluate $\frac{5x-2}{3}$ when x = 4.

    A. 6

    B. 18

    C. 7.3

    D. 2

    (1 mark)

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12. Question 12

    1 mark

    Simplify: $2a+3b+4a-b$

    A. 8ab

    B. 6a + 4b

    C. 2a + 2b

    D. 6a + 2b

    (1 mark)

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13. Question 13

    1 mark

    Simplify: $\frac{6x^2}{3x}$

    A. 2x²

    B. 3x

    C. 18x

    D. 2x

    (1 mark)

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