Write the next number in this sequence: 7, 10, 13, 16, ...
(1)
2
The rule for a sequence is "start at 4, then add 5 each time". Write the first five terms of this sequence.
(2)
3
Find the rule of the sequence and write the next term: 12, 9, 6, 3, ...
(2)
4
Complete the function machine. Input -> multiply by 3 -> add 4 -> output. What is the output when the input is 5?
(2)
5
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)
6
The nth term of a sequence is 6n - 2. Find the 5th term.
(2)
7
Complete these equations. a + 8 = 21. Find a. Then solve: 5b = 45. Find b.
(2)
8
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)
9
Write an equation for this word rule and then solve it: Three times a number minus 4 equals 11.
(2)
10
A sequence starts 2, 5, 8, 11, ... (a) What is the rule? (b) What is the 12th term?
(2)
11
Explain why the nth term 4n + 1 always gives an odd number. Give a short written explanation.
(3)
12
Fill in the missing number: n + 7 = 19. Find n.
(1)
13
The rule is: multiply by 2 then subtract 5. What is the output when the input is 9?
(2)
14
Solve this equation: 4 + 3x = 19. Find x.
(2)
15
A sequence is 5, 10, 20, 40. Explain whether this is an arithmetic sequence. Give a short explanation.
(2)
16
Find the nth term for the sequence 2, 5, 8, 11, ... Then find the 20th term.
(2)
17
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)
18
Solve the equation n/4 + 3 = 10. Find n.
(2)
Mark scheme · KS2.M-Y6N6 Algebra: Formulae, Sequences and Equations
Question 1
B1 19 cao
Answer: 19
Question 2
B1 first three terms correct oe
B1 all five terms correct cao
Answer: 4, 9, 14, 19, 24
Question 3
B1 rule subtract 3 each time or -3 oe
B1 next term 0 cao
Answer: 0
Question 4
M1 correct method shown 5 x 3 = 15 and 15 + 4 = 19
A1 19 cao
Answer: 19
Question 5
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 6
M1 substitution n = 5 seen giving 6 x 5 - 2
A1 28 cao
Answer: 28
Question 7
B1 a = 13 cao
B1 b = 9 cao
Answer: a = 13; b = 9
Question 8
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 9
M1 equation 3x - 4 = 11 or equivalent
A1 x = 5 cao
Answer: 3x - 4 = 11; x = 5
Question 10
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 11
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 12
B1 n = 12 cao
Answer: 12
Question 13
M1 method: 9 x 2 = 18 then 18 - 5
A1 13 cao
Answer: 13
Question 14
M1 shows 3x = 15 or equivalent
A1 x = 5 cao
Answer: x = 5
Question 15
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 16
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 17
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.