A1 Further Worksheet 1

Transcription

1 Cambridge Essentials Mathematics Extension 7 A1 Further Worksheet 1 A1 Further Worksheet 1 1 Here is a puzzle. Each symbol stands for a number. The column on the right shows the total of each row. For example, + + = What number does each symbol stand for? 2 A chocolate bar costs g pence. William buys 1 bar and pays for it with a 1 coin. Which of these expressions shows his change in pence? a g 1 b g 100 c 1 g d 100 g John takes q minutes to walk to school each day. He takes three times as long to walk home. a How long does it take for John to walk home? b How long does John spend walking to and from school in a week? 4 p = 4 and y = 11. Find the value of each expression. a p + y 6 b p y 2 c y p d y p + p 5 Each letter stands for a number. Find its value. a g + g + 4 = 10 b y = 21 c x 4 = 2 9 d r + r r = 19

2 Cambridge Essentials Mathematics Extension 7 A1 Further Worksheet 1 6 Is each of these a sequence? If it is, write the pattern and say whether you can predict how the sequence will continue. a The time that the sun rose each morning for the last two weeks. b Kerry runs 1 kilometre this week. Next week she runs 2 kilometres. She increases the distance she runs by 1 kilometre each week. c The house numbers on one side of a street. d Your pulse rate taken every 5 minutes after jumping up and down rapidly 0 times. 7 a The nth term of a sequence is 5n 6. What is the 20th term? n + b The nth term of a different sequence is. 4n Write down the first three terms of this sequence. 8 This is the start of sequence: 2, 4,... What could the rest of the sequence be? Continue it in three different ways. Write the next three terms each time and write the term-to-term rule for each sequence. 9 Sharif is making houses with arrows. 1 house uses 6 arrows. 2 houses use 11 arrows. houses use 16 arrows. a Find the nth term for the number of arrows. b How many arrows will be needed for 10 houses? Original Material Cambridge University Press

3 Cambridge Essentials Mathematics Extension 7 A1 Further Worksheet 2 A1 Further Worksheet 2 1 Copy and complete these function machines. a 1 9 b c 1 5 d Find two different ways to complete each function machine. a 1 8 b Copy and complete these function machines. a b In a board game, players land on different numbers. The numbers are different colours. The players use rules to work out their scores. For example, when a player lands on a blue number: score = blue number then 2. The other players can check that the score is correct by working backwards: blue number = score + 2 then What will players do to check these results? a score = yellow number + 1 then 4 b score = red number 7 then + 5 c score = green number 2 then

4 Cambridge Essentials Mathematics Extension 7 A2 Further Worksheet A2 Further Worksheet 1 a The perimeter of this shape is 2g + 6h. Write an expression for the length of the unmarked side. b The perimeter of this shape is 4x + 9y. The two unmarked sides are the same length. Write an expression for the length of one of the unmarked sides. 2 The number in each brick is the sum the two blocks below it. Copy and complete the diagrams. Simplify your answers as much as possible. a b If p = 5 work out of the value of each expression. a i p + p + p + p ii p + 2p + p iii 2p + 2p iv 4p b What do you notice about all the answers? c Which is the simplest way of writing all the expressions in part a? 4 Explain why the expressions in each pair are different. a 5x and 5(x ) b x and x c x x + + and 4 4 d x 10 and 10 x

5 Cambridge Essentials Mathematics Extension 7 A2 Further Worksheet 5 Sophie uses the formula ( u+ v) t s = 2 What is s for these values of u, v and t? a u = 4, v = 6, t = 5 b u = 0, v = 0, t = 7 c u = 1.5, v = 10.5, t = 4 6 Use the formula p = q 2 to find a p when q = 4 b p when q = 10 c p when q = 1 d q when p = 25 e q when p = 144 f q when p = 49 7 Grace thinks of some numbers. Remember, the opposite of squaring is finding the square root. Let n represent the number each time. i ii Make an equation for each number. Solve the equation. Use function machines. iii Solve the equation. Use algebra. a She multiplies it by and adds 4. She gets 19. b She adds 4 and multiplies by. She gets 15. c She divides it by 4 and adds. She gets 10. d She divides it by 5 and subtracts 2. She gets 0. e She squares it and adds 7. She gets 16. Original Material Cambridge University Press

6 Cambridge Essentials Mathematics Extension 7 A Further Worksheet A Further Worksheet 1 x =. Match each algebraic expression with a value. 5x 17 2(x 2) 11 4x + 5 6x 5 x x x x x 2 Solve these equations. a 4p 7 = p + 11 b m 2 = 2m + 1 c 4x + = 18 2x Expand the brackets. Simplify each expression. a 7 + (7m 2) b 8a + 2(4 a) 7 c 2(8 4k) + (2k + 5) + 4(k ) 4 The expression in each rectangle is the sum of the expressions in the circles on either side of it. Copy and complete the diagram. Simplify each expression. 5 Solve these equations. Expand the brackets first. a (4x ) = 40 b 5(2a 9) = (a + 2) 6 This function machine maps x onto y. x add? divide by? y a Using the function machine 4, 7 6 and 1 9. Copy and complete the function machine. b Write the rule for this function machine in the form y =. c What is the value of y when x = 25? d Copy and complete the mapping for this function.

7 Cambridge Essentials Mathematics Extension 7 A4 Further Worksheet A4 Further Worksheet 1 Find the equation of each line. a The line parallel to x = 4 and passing through the point (, 7). b The line parallel to y = 2.7 and passing through the point ( 9, 4.5). c The line parallel to y = x and passing through the point (, 7). d The line parallel to y = 2x 7 and passing through the point (1, ). 2 a Copy the axes and draw the line y = 5 x. b Copy and complete the table for the equation y = 2x 2.5 x y c Plot the values from your table as coordinates on your copy of the axes. d Draw and label the line y = 2x 2.5 e Use your diagram to solve the equation 2x 2.5 = 5 x. a Draw the line y = 6.5 x on the axes used in question 2. b Write down the x-coordinate of the point where this line intersects the line y = 2x 2.5 c The x-coordinate of the intersection of the two lines in part b represents the solution of an equation. i What is this equation? ii Show that your answer to part b is the solution.

8 Cambridge Essentials Mathematics Extension 7 A5 Further Worksheet A5 Further Worksheet 1 Find an expression for the area of this shape. 2 Chris is joining dots to make as many straight lines as possible. None of the lines are allowed to cross. dots can be joined with straight lines. 6 dots can be joined with 9 straight lines. Investigate for other numbers of dots. Find an expression for the number of lines possible for n dots. Maisie s father was 27 years old when Maisie was born. Maisie is n years old now and her father is four times an old as she is. Write an equation and solve it to find n. 4 Solve this equation. Show your working. 5(2y 7) = y 5 For each equation, when x increases by 4, what happen to y? a y = x b y = 2x c y = x The distance from Upton to Dorchester is 20 miles. The graph shows the distance time graph of a cyclist travelling from Upton to Dorchester. At 0940 a motorist leaves Dorchester to travel to Upton along the same road as the cyclist. The motorist travels at an average speed of 40 mph. Copy the diagram, draw on the distance time graph of the motorist and find the time at which the motorist met the cyclist.