Look at the function machines below. Each one shows an input, an operation and an output.
(a)Input: 8 -> add 5 -> Output: ?(1)
(b)Input: ? -> add 5 -> Output: 20(1)
2
Find the missing number in each equation.
(a)9 + ___ = 14(1)
(b)___ - 7 = 8(1)
(c)3 x ___ = 18(1)
3
Write an expression for each of the following. Use the letter given.
(a)A number, n, add 6(1)
(b)5 less than a number, y(1)
(c)Double a number, m, then add 3(1)
4
a = 4. Work out the value of each expression.
(a)a + 9(1)
(b)3a(1)
(c)2a - 5(2)
5
A function machine multiplies the input by 2, then adds 3.
Figure (to be drawn): input -> x2 -> +3 -> output
(a)Find the output when the input is 6.(1)
(b)Find the output when the input is 10.(1)
(c)The output is 25. Find the input.(2)
6
A sequence starts at 5 and increases by 4 each time.
(a)Write the first four terms of the sequence.(1)
(b)The nth term rule for this sequence is 4n + 1. Use the rule to find the 10th term.(2)
7
A square has side length s cm.
(a)Write a formula for the perimeter, P, of the square in terms of s.(1)
(b)Use your formula to find P when s = 7 cm.(1)
8
Solve each equation to find the value of the letter.
(a)n + 8 = 15(1)
(b)m - 6 = 9(1)
(c)5p = 35(1)
9
Solve each two-step equation to find the value of the letter. Show your working.
(a)3n + 2 = 17(2)
(b)2m - 5 = 11(2)
10
Priya has p pounds. Tom has 3 pounds more than Priya.
(a)Write an expression for the amount of money Tom has, in terms of p.(1)
(b)Priya has 12 pounds. Work out how much money Tom has.(1)
(c)The total amount of money they have together can be written as 2p + 3. Work out the value of 2p + 3 when p = 12, and use it to check your answer to part (b).(2)
11
The table shows the position and term of a number pattern. Position: 1, 2, 3, 4 Term: 4, 7, 10, 13
(a)Describe the term-to-term rule for this pattern.(1)
(b)Find the rule connecting the position number and the term. Write your rule using algebra, letting the position number be p.(2)
(c)Use your rule to find the 20th term.(1)
12
Solve the equation to find the value of n. Show your working. 2n + 3 = n + 9
(2)
13
The area of a rectangle can be found using the formula A = l x w, where l is the length and w is the width.
(a)A rectangle has length 9 cm and width 4 cm. Work out its area.(1)
(b)A different rectangle has an area of 48 cm2 and a width of 6 cm. Work out its length.(2)
14
a and b are two whole numbers. a + b = 20 and a is 6 more than b. Find the value of a and the value of b. Show your working.
(3)
15
Sam says: 'If you double a number and then add 3, the answer is always odd.' Is Sam correct? Explain your answer using at least one example.
(2)
16
A function machine subtracts 4, then multiplies by 3.
Simplify each expression by collecting like terms.
(a)3n + 2n(1)
(b)5m + 2 - 2m(2)
18
A rectangle has length (x + 3) cm and width 5 cm. The perimeter of the rectangle is 36 cm. Work out the value of x. Show your working.
(3)
19
A matchstick pattern is made so that position n uses 3n + 1 matchsticks.
(a)How many matchsticks are used in position 5?(1)
(b)A pattern in this sequence uses 40 matchsticks. Which position is it?(2)
20
Prove that the sum of any two consecutive whole numbers is always odd. Let the first whole number be n, so the next consecutive whole number is n + 1.
(3)
Mark scheme · KS2.M-ALG Introduction to Algebra
Question 1
(a) B1 13 cao
(a) Answer: 13
(b) B1 15 cao (accept use of the inverse operation)
(b) Answer: 15
Question 2
(a) B1 5 cao
(a) Answer: 5
(b) B1 15 cao
(b) Answer: 15
(c) B1 6 cao
(c) Answer: 6
Question 3
(a) B1 n + 6 oe
(a) Answer: n + 6
(b) B1 y - 5 oe (not 5 - y)
(b) Answer: y - 5
(c) B1 2m + 3 oe
(c) Answer: 2m + 3
Question 4
(a) B1 13 cao
(a) Answer: 13
(b) B1 12 cao
(b) Answer: 12
(c) M1 2 x 4 (= 8) seen or implied
(c) A1 3 cao
(c) Answer: 3
Question 5
(a) B1 15 cao
(a) Answer: 15
(b) B1 23 cao
(b) Answer: 23
(c) M1 25 - 3 (= 22) seen, using the inverse operations in reverse order
(c) A1 11 cao
(c) Answer: 11
Question 6
(a) B1 5, 9, 13, 17 all four correct cao
(a) Answer: 5, 9, 13, 17
(b) M1 4 x 10 (= 40) seen or implied
(b) A1 41 cao
(b) Answer: 41
Question 7
(a) B1 P = 4s oe (e.g. P = s + s + s + s)
(a) Answer: P = 4s
(b) B1 28 (cm) cao, ft their formula from part (a)
(b) Answer: 28 cm
Question 8
(a) B1 n = 7 cao
(a) Answer: n = 7
(b) B1 m = 15 cao
(b) Answer: m = 15
(c) B1 p = 7 cao
(c) Answer: p = 7
Question 9
(a) M1 3n = 15 oe (subtracts 2 from both sides)
(a) A1 n = 5 cao
(a) Answer: n = 5
(b) M1 2m = 16 oe (adds 5 to both sides)
(b) A1 m = 8 cao
(b) Answer: m = 8
Question 10
(a) B1 p + 3 oe
(a) Answer: p + 3
(b) B1 15 (pounds) cao, ft their expression from part (a)
(b) Answer: 15 pounds
(c) M1 2 x 12 + 3 (= 27) seen or implied
(c) A1 27 (pounds) stated, with a correct check that 12 + 15 = 27
(c) Answer: 27 pounds
Question 11
(a) B1 add 3 (each time) oe
(a) Answer: Add 3 each time
(b) M1 identifies 3 x p (or 3p) as part of the rule oe
(b) A1 term = 3p + 1 oe cao
(b) Answer: term = 3p + 1
(c) B1 61 cao, ft their rule from part (b)
(c) Answer: 61
Question 12
M1 subtracts n from both sides to get n + 3 = 9 oe
A1 n = 6 cao
Answer: n = 6
Question 13
(a) B1 36 (cm2) cao
(a) Answer: 36 cm2
(b) M1 48 / 6 seen or implied
(b) A1 8 (cm) cao
(b) Answer: 8 cm
Question 14
M1 forms b + (b + 6) = 20 oe, or an equivalent correct method (e.g. bar model or systematic trial and improvement with checking)
dM1 2b + 6 = 20 leading to 2b = 14, dependent on the previous method mark
A1 a = 13 and b = 7 both correct cao
Answer: a = 13, b = 7
Question 15
B1 states Sam is correct
B1 correct explanation with a valid example and reasoning, e.g. doubling any whole number always gives an even number, and an even number plus 3 (an odd number) always gives an odd number; example: double 5 = 10, 10 + 3 = 13, which is odd
Answer: Yes, Sam is correct
Question 16
(a) B1 18 cao
(a) Answer: 18
(b) B1 6 cao
(b) Answer: 6
(c) M1 30 / 3 (= 10) seen, using the inverse operations in reverse order
(c) A1 14 cao
(c) Answer: 14
Question 17
(a) B1 5n cao
(a) Answer: 5n
(b) M1 5m - 2m (= 3m) seen or implied
(b) A1 3m + 2 cao
(b) Answer: 3m + 2
Question 18
M1 forms 2(x + 3) + 2(5) = 36 oe, or an equivalent correct method
dM1 2x + 16 = 36 leading to 2x = 20, dependent on the previous method mark
A1 x = 10 cao
Answer: x = 10
Question 19
(a) B1 16 cao
(a) Answer: 16
(b) M1 3n = 39 oe (subtracts 1, then sets up the equation)
(b) A1 position 13 (n = 13) cao
(b) Answer: position 13
Question 20
M1 n + (n + 1) written oe
A1 simplifies to 2n + 1
B1 correct reasoning that 2n is always even (a multiple of 2), so 2n + 1 is one more than an even number, which is always odd