Q1. Amina is making designs with two different shapes.

Transcription

1 Q1. Amina is making designs with two different shapes. She gives each shape a value. Total value is 147 Total value is 111 Calculate the value of each shape. Q2. n stands for a whole number. 2n is greater than 30 5n is less than 100 Write all the numbers that n stands for. Page 1 of 12

2 Q3. Here are three equations. a + b + c = 30 a + b = 24 b + c = 14 What are the values of a, b and c? Q4. The rule for this sequence of numbers is add 3 each time The sequence continues in the same way. Mary says, No matter how far you go there will never be a multiple of 3 in the sequence. Is she correct? Circle Yes or No. Yes / No Explain how you know. Page 2 of 12

3 Q5. Ann makes a pattern of L shapes with sticks. Ann says : "I find the number of sticks for a shape by first multiplying the shape number by 4, then adding 3". Work out the number of sticks for the shape that has shape-number 10 Ann uses 59 sticks to make another L shape in this pattern. What is its shape-number? Here is Ann s rule again: "I find the number of sticks for a shape by first multiplying the shape number by 4, then adding 3". Write a formula to work out the number of sticks for any L shape. Use S for the number of sticks and N for the shape-number. Page 3 of 12

4 Q6. Here is a sequence of patterns made from squares and circles. The sequence continues in the same way. Calculate how many squares there will be in the pattern which has 25 circles. Page 4 of 12

5 Q7. k, m and n each stand for a whole number. They add together to make 1500 k + m + n = 1500 m is three times as big as n. k is twice as big as n. Calculate the numbers k, m and n. Q8. Write the missing numbers so that 2a + 5b = 30 One is done for you. 2a + 5b = 30 when a = 0 and b = 6 2a + 5b = 30 when a = 5 and b = 2a + 5b = 30 when a = 15 and b = Q9. j and k stand for two numbers. Double j equals half of k. Write numbers to complete the sentence below. Page 5 of 12

6 When j is then k is Q10. Here is an equation. m 2n = 10 When n = 20 what is the value of m? m = When m = 20 what is the value of n? n = Q11. Here are Alfie and Emma with their parents. You can use the table below to predict how tall children will be when they are adults. There is one formula for boys and a different one for girls: Boy s predicted height Girl s predicted height 0.4(x + y) (x + y) + 29 x is the father s height in cm. y is the mother s height in cm. Page 6 of 12

7 (a) Calculate the predicted height of Alfie when he is an adult. (b) When Emma is an adult, she is predicted to be taller than her mother. How much taller? Q12. (a) There are n counters in Alfie s bag. Alfie puts 3 more counters in the bag. Write an expression for the number of counters that are in the bag now. (b) Megan has two boxes. There are m counters in each box. She puts all her counters together in a pile, then removes 5 of them. Write an expression for the number of counters that are in the pile now. Page 7 of 12

8 Q13. Here are an equilateral triangle and a regular pentagon. Not actual size Each side of the triangle is 10 cm Each side of the pentagon is d cm The perimeter of the pentagon is 4 centimetres more than the perimeter of the triangle. What number does d represent? Page 8 of 12

9 Q14. Here is a pattern of number pairs. a b Complete the rule for the number pattern. Q15. Alfie has some photographs printed. The cost is 2.50 for postage and 12 pence for each print. Alfie uses this formula for the total cost (C) in pence. C = n n stands for the number of photographs. The total cost for Alfie is 6.70 How many photographs does he have printed? Page 9 of 12

10 Q16. Here is an equation. (a) Find the value of k when n = 60 k = 100 4n (b) Find the value of n when k = 99 Q17. n = 22 What is 2n + 9? 2q + 4 = 100 Work out the value of q. Page 10 of 12

11 Q18. In this diagram, the shaded rectangles are all of equal width (w). Calculate the width (w) of one shaded rectangle. Page 11 of 12

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