Algebra: Formulae, Sequences and Equations - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 5)Algebra: Formulae, Sequences and Equations revision guide

This topic is chapter 13 of KS2 Maths: Fractions, Ratio and proportion, and Algebra Practice Book.

6.3 Algebra: Formulae, Sequences and Equations

Calculators not allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write the next number in this sequence: 7, 10, 13, 16, ...

(1)

A sequence starts 2, 5, 8, 11, ...
(a) What is the rule? (b) What is the 12th term?

(2)

Explain why the nth term 4n + 1 always gives an odd number. Give a short written explanation.

(3)

Fill in the missing number: n + 7 = 19. Find n.

(1)

The rule is: multiply by 2 then subtract 5. What is the output when the input is 9?

(2)

Solve this equation: 4 + 3x = 19. Find x.

(2)

A sequence is 5, 10, 20, 40. Explain whether this is an arithmetic sequence. Give a short explanation.

(2)

Find the nth term for the sequence 2, 5, 8, 11, ... Then find the 20th term.

(2)

Frank uses the formula A = l + w to find the area of a rectangle with length 6 m and width 4 m. Is Frank correct? Explain your answer.

(2)

Solve the equation n/4 + 3 = 10. Find n.

(2)

The rule for a sequence is "start at 4, then add 5 each time". Write the first five terms of this sequence.

(2)

Find the rule of the sequence and write the next term: 12, 9, 6, 3, ...

(2)

Complete the function machine. Input -> multiply by 3 -> add 4 -> output.
What is the output when the input is 5?

(2)

A formula gives the perimeter P of a rectangle: P = 2(l + w). Lila has a rectangle with length 7 cm and width 3 cm. Use the formula to find the perimeter.

(3)

The nth term of a sequence is 6n - 2. Find the 5th term.

(2)

Complete these equations. a + 8 = 21. Find a.
Then solve: 5b = 45. Find b.

(2)

Sofia writes a rule: Take a number, subtract 6, then double the result. For input 10 she gets output 8. Check whether Sofia is correct and explain your answer.

(2)

Write an equation for this word rule and then solve it: Three times a number minus 4 equals 11.

(2)

Mark scheme · 6.3 Algebra: Formulae, Sequences and Equations

Question 1

B1 19 cao
Answer: 19

Question 2

M1 rule add 3 each time or nth term 3n - 1 seen
A1 12th term 3 x 12 - 1 = 35 cao
Answer: Rule: add 3; 12th term = 35

Question 3

M1 states 4n is even (because 4 x n is multiple of 2) or equivalent
M1 adds 1 to even number gives odd (link made to 4n + 1)
A1 clear conclusion that 4n + 1 is odd for any integer n cao
Answer: Because 4n is always even (4n = 2 x 2n). Adding 1 to an even number gives an odd number, so 4n + 1 is always odd.

Question 4

B1 n = 12 cao
Answer: 12

Question 5

M1 method: 9 x 2 = 18 then 18 - 5
A1 13 cao
Answer: 13

Question 6

M1 shows 3x = 15 or equivalent
A1 x = 5 cao
Answer: x = 5

Question 7

B1 states it is not arithmetic (differences are not equal) or equivalent
B1 gives reason eg differences 5, 10, 20 are not constant; sequence is geometric with ×2
Answer: No. The differences are 5, 10 and 20 so they are not constant; it is a geometric sequence multiplying by 2.

Question 8

M1 nth term identified as 3n - 1 or equivalent
A1 20th term = 3 x 20 - 1 = 59 cao
Answer: nth term = 3n - 1; 20th term = 59

Question 9

M1 states formula is incorrect and gives correct formula A = l x w or equivalent
A1 brief explanation e.g. A = 6 x 4 = 24 m2 and not l + w cao
Answer: No. Area = l x w, so A = 6 x 4 = 24 m2; using l + w is incorrect.

Question 10

M1 shows n/4 = 7 or equivalent
A1 n = 28 cao
Answer: 28

Question 11

B1 first three terms correct oe
B1 all five terms correct cao
Answer: 4, 9, 14, 19, 24

Question 12

B1 rule subtract 3 each time or -3 oe
B1 next term 0 cao
Answer: 0

Question 13

M1 correct method shown 5 x 3 = 15 and 15 + 4 = 19
A1 19 cao
Answer: 19

Question 14

M1 substitution seen: l + w = 7 + 3 or equivalent
M1 2 x (10) = 20 or equivalent working
A1 20 cm cao
Answer: 20 cm

Question 15

M1 substitution n = 5 seen giving 6 x 5 - 2
A1 28 cao
Answer: 28

Question 16

B1 a = 13 cao
B1 b = 9 cao
Answer: a = 13; b = 9

Question 17

M1 correct method: (10 - 6) x 2 = 4 x 2 = 8 or equivalent
A1 Yes; output is 8 with brief explanation cao
Answer: Yes. (10 - 6) x 2 = 8

Question 18

M1 equation 3x - 4 = 11 or equivalent
A1 x = 5 cao
Answer: 3x - 4 = 11; x = 5

Algebra: Formulae, Sequences and Equations - Worksheets, Questions and Revision

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6.3 Algebra: Formulae, Sequences and Equations

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