Sec 1 G1 Maths Algebra and sequences worksheet with answers

A free Sec 1 G1 Maths worksheet on algebra and sequences: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 G1 Maths worksheet: Algebra and sequences

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

(a)Write down an algebraic expression for

5

less than

x

Answer (a)[1]

(b)A taxi charges a flag-down fare of $

6

and $

2

for every kilometre travelled. Write down an expression, in terms of

x

, for the fare, in dollars, for a trip of

x

km.

Answer (b)[1]

(a)Write down the next term of the sequence

29, \ 32, \ 35, \ 38, \ \ldots

Answer (a)[1]

(b)Find the missing term in the sequence

21, \ 30, \ \_\_\_, \ 48, \ 57

Answer (b)[1]

(a)Simplify

6x + 8y - 2x + y

Answer (a)[1]

(b)Simplify

7x^{2} - 4x - 4x^{2} - 3x

Answer (b)[1]

Find the 15th term of the sequence

0, \ 7, \ 14, \ 21, \ \ldots

Answer[2]

(a)Write down the next term of the sequence

17, \ 11, \ 5, \ -1, \ \ldots

Answer (a)[1]

(b)Write down the next term of the sequence

24, \ 26, \ 28, \ 30, \ \ldots

Answer (b)[1]

(a)Given that

x = -4

and

y = -4

, find the value of

x(y + 4)

Answer (a)[2]

(b)Given that

x = -6

and

y = -6

, find the value of

2xy - 5

Answer (b)[2]

Section B

(a)(i)Find the 50th term of the sequence

11, \ 15, \ 19, \ 23, \ \ldots

Answer (a)(i)[2]

(a)(ii)Find the 25th term of the sequence

8, \ 10, \ 12, \ 14, \ \ldots

Answer (a)(ii)[2]

(b)(i)Given that

x = -1

and

y = 2

, find the value of

4x + 2y

Answer (b)(i)[2]

(b)(ii)Given that

x = -5

and

y = -2

, find the value of

5x^2 + 5y

Answer (b)(ii)[2]

(a)(i)Write down an algebraic expression for

n

decreased by

12

Answer (a)(i)[1]

(a)(ii)Write down an algebraic expression for

y

divided by

5

Answer (a)(ii)[1]

(b)(i)Simplify

4x - 8 - 2x + 7

Answer (b)(i)[1]

(b)(ii)Simplify

9x + 9y - 5x - 2y

Answer (b)(ii)[1]

(c)(i)Given that

x = 1

and

y = 4

, find the value of

5x^2 + 2y

Answer (c)(i)[2]

(c)(ii)Given that

x = 3

and

y = -5

, find the value of

5xy - 2

Answer (c)(ii)[2]

END OF PAPER

Answers and worked solutions

Question 1

(a)Answer:

x - 5

[1]

“5 less than x” means start with x and take away 5.

x - 5

(b)Answer:

2x + 6

[1]

2x

2x + 6

Question 2

(a)Answer:

\mathstrut 38 + 3 =

41

[1]

\mathstrut 32 - 29 =

3

\mathstrut 38 + 3 =

41

(b)Answer:

\mathstrut 30 + 9 =

39

[1]

\mathstrut 30 - 21 =

9

\mathstrut 30 + 9 =

39

Question 3

(a)Answer:

= 4x + 9y

[1]

= 6x - 2x + 8y + y

= 4x + 9y

(b)Answer:

= 3x^{2} - 7x

[1]

= 7x^{2} - 4x^{2} - 4x - 3x

= 3x^{2} - 7x

Question 4

Answer:

7 \times 15 - 7 = 98

[2]

\mathstrut 7 - 0 =

7

\mathstrut 0 - 7 =

-7

T_n = 7n - 7

7 \times 15 - 7 = 98

Question 5

(a)Answer:

\mathstrut -1 + (-6) =

-7

[1]

\mathstrut 11 - 17 =

-6

\mathstrut -1 + (-6) =

-7

(b)Answer:

\mathstrut 30 + 2 =

32

[1]

\mathstrut 26 - 24 =

2

\mathstrut 30 + 2 =

32

Question 6

(a)Answer:

= 0

[2]

x(y + 4) = \left(-4\right)(-4 + 4)

= \left(-4\right)(0)

= 0

(b)Answer:

= 67

[2]

2xy - 5 = 2\left(-6\right)\left(-6\right) - 5

= 72 - 5

= 67

Question 7

(a)(i)Answer:

4 \times 50 + 7 = 207

[2]

\mathstrut 15 - 11 =

4

\mathstrut 11 - 4 =

7

T_n = 4n + 7

4 \times 50 + 7 = 207

(a)(ii)Answer:

2 \times 25 + 6 = 56

[2]

\mathstrut 10 - 8 =

2

\mathstrut 8 - 2 =

6

T_n = 2n + 6

2 \times 25 + 6 = 56

(b)(i)Answer:

= 0

[2]

4x + 2y = 4\left(-1\right) + 2(2)

= -4 + 4

= 0

(b)(ii)Answer:

= 115

[2]

5x^2 + 5y = 5\left(-5\right)^2 + 5\left(-2\right)

= 125 - 10

= 115

Question 8

(a)(i)Answer:

n - 12

[1]

“Decreased by” means subtract.

n - 12

(a)(ii)Answer:

\dfrac{y}{5}

[1]

“y divided by 5”: y is on the top.

\dfrac{y}{5}

(b)(i)Answer:

= 2x - 1

[1]

= 4x - 2x - 8 + 7

= 2x - 1

(b)(ii)Answer:

= 4x + 7y

[1]

= 9x - 5x + 9y - 2y

= 4x + 7y

(c)(i)Answer:

= 13

[2]

5x^2 + 2y = 5(1)^2 + 2(4)

= 5 + 8

= 13

(c)(ii)Answer:

= -77

[2]

5xy - 2 = 5(3)\left(-5\right) - 2

= -75 - 2

= -77

Sec 1 G1 Maths Algebra and sequences worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)(i)Find the 50th term of the sequence

11, \ 15, \ 19, \ 23, \ \ldots

Answer (a)(i)[2]

(a)(ii)Find the 25th term of the sequence

8, \ 10, \ 12, \ 14, \ \ldots

Answer (a)(ii)[2]

(b)(i)Given that

x = -1

and

y = 2

, find the value of

4x + 2y

Answer (b)(i)[2]

(b)(ii)Given that

x = -5

and

y = -2

, find the value of

5x^2 + 5y

Answer (b)(ii)[2]

Answers and worked solutions

Question 1

(a)Answer:

x - 5

[1]

“5 less than x” means start with x and take away 5.

x - 5

(b)Answer:

2x + 6

[1]

2x

2x + 6

Question 2

(a)Answer:

\mathstrut 38 + 3 =

41

[1]

\mathstrut 32 - 29 =

3

\mathstrut 38 + 3 =

41

(b)Answer:

\mathstrut 30 + 9 =

39

[1]

\mathstrut 30 - 21 =

9

\mathstrut 30 + 9 =

39

Question 3

(a)Answer:

= 4x + 9y

[1]

= 6x - 2x + 8y + y

= 4x + 9y

(b)Answer:

= 3x^{2} - 7x

[1]

= 7x^{2} - 4x^{2} - 4x - 3x

= 3x^{2} - 7x

Question 4

Answer:

7 \times 15 - 7 = 98

[2]

\mathstrut 7 - 0 =

7

\mathstrut 0 - 7 =

-7

T_n = 7n - 7

7 \times 15 - 7 = 98

Question 5

(a)Answer:

\mathstrut -1 + (-6) =

-7

[1]

\mathstrut 11 - 17 =

-6

\mathstrut -1 + (-6) =

-7

(b)Answer:

\mathstrut 30 + 2 =

32

[1]

\mathstrut 26 - 24 =

2

\mathstrut 30 + 2 =

32

Question 6

(a)Answer:

= 0

[2]

x(y + 4) = \left(-4\right)(-4 + 4)

= \left(-4\right)(0)

= 0

(b)Answer:

= 67

[2]

2xy - 5 = 2\left(-6\right)\left(-6\right) - 5

= 72 - 5

= 67

Question 7

(a)(i)Answer:

4 \times 50 + 7 = 207

[2]

\mathstrut 15 - 11 =

4

\mathstrut 11 - 4 =

7

T_n = 4n + 7

4 \times 50 + 7 = 207

(a)(ii)Answer:

2 \times 25 + 6 = 56

[2]

\mathstrut 10 - 8 =

2

\mathstrut 8 - 2 =

6

T_n = 2n + 6

2 \times 25 + 6 = 56

(b)(i)Answer:

= 0

[2]

4x + 2y = 4\left(-1\right) + 2(2)

= -4 + 4

= 0

(b)(ii)Answer:

= 115

[2]

5x^2 + 5y = 5\left(-5\right)^2 + 5\left(-2\right)

= 125 - 10

= 115

Question 8

(a)(i)Answer:

n - 12

[1]

“Decreased by” means subtract.

n - 12

(a)(ii)Answer:

\dfrac{y}{5}

[1]

“y divided by 5”: y is on the top.

\dfrac{y}{5}

(b)(i)Answer:

= 2x - 1

[1]

= 4x - 2x - 8 + 7

= 2x - 1

(b)(ii)Answer:

= 4x + 7y

[1]

= 9x - 5x + 9y - 2y

= 4x + 7y

(c)(i)Answer:

= 13

[2]

5x^2 + 2y = 5(1)^2 + 2(4)

= 5 + 8

= 13

(c)(ii)Answer:

= -77

[2]

5xy - 2 = 5(3)\left(-5\right) - 2

= -75 - 2

= -77