PLC Papers Created For:

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1 PLC Papers Created For: year 9 revision booklet_half Term 1 Higher Algebra

2 Substitution 3 Grade 4 Objective: Substitute numerical values into formulae and expressions, including scientific formulae 1 Question 1 Complete this table of values. N 2n (Total 2 mark) Question 2 Calculate the value of y when x = 2 are You must show your working. = (Total 3 marks)

3 Question 3 a. Work out the value of v when u = 110, a = 15 and t = 12 b. Work out the value of v when u = 25, a = -12 and t = -15 = + (Total 2 mark) Question 4 Work out the value of T when (a) p = 5 and (b) p = -5 = 2 2 3

4 Question 5 This formula is used to work out the cost, C, of tiling a floor with n tiles. C = n 2 56 tiles are needed to tile a floor. Can the floor be tiled for less than 275? You must show your working. (Total 2 mark) TOTAL /10

5 Using Formulae 3 Grade 3 Objective: Understand and use mathematical formulae Question 1 The Great Pyramid at Giza has height of 262 m and a square base of side 434m. Work out the volume of the Great Pyramid. (Total 2 mark) Question 2 A spherical soap bubble has a radius of 4 cm. Work out the volume of the bubble. (Total 2 mark)

6 Question 3 A spherical ball is made from plastic. The external and internal radii of the ball are 50 cm and 49.5, respectively. Work ouf the volume of plastic used to make the ball. (Total 3 mark)

7 Question 4 A ring shaped flowerbed is to be created around a circular lawn of radius 2.55m. Roses costing 4.20 are to be planted approximately every 50 cm around this flowerbed. How much money will be needed for roses? (Total 3 mark) TOTAL /10

8 Collecting like terms 3 Grade 4 Objective: Simplify algebraic expressions by collecting like terms Question 1 Simplify 8x - 3y 3x + 9y (Total 2 marks) Question 2 Simplify 19f f + 6f (Total 1 marks) Question 3 Georgina, Samantha and Mason collect football stickers. Georgina has x stickers in her collection. Samantha has 9 stickers less than Georgina. Mason has 3 times as many stickers as Georgina. Write down an expression, in terms of x, for the total number of these stickers. Give you answer in its simplest form. (Total 4 marks)

9 Question 4 The diagram shows a triangle. Write down an expression in terms of x and y, for the perimeter of this triangle. Give your answer in its simplest form. 4x-2y 2x+5y 10y-x (Total 3 marks) TOTAL /10

10 Expressions 3 Grade 4 Objective: Use the correct algebraic notation in expressions and equations, including using brackets Question 1 x is shared equally between fifteen people. How much does each person receive? Question 2 Write an expression for the total cost of four apples at a pence each and fourteen pears at b pence each. Question 3 Write an expression for the number that is four times smaller than n Question 4 Nell buys c packets of sweets costing 55p per packet. He pays T pence altogether. Write a formula for the total cost of sweets Question 5 Write down an equation for three bananas at h pence each and two grapefruit at k pence each when the total cost is 1.36?

11 Question 6 Chloe is x years old. Her sister is four years older. Her brother is twice her age. The sum of their ages is 44 years. a. Write an expression, in terms of x, for her sister s age. b. Form an equation in x to work out Chloe s age. (Total 2 marks) Question 7 Two angles have a difference of 20 o. Together they form a straight line. The smaller angle is x o a. Write down an expression for the larger angle, in terms of x. b. Work out the value of x. TOTAL /10

12 Factorise single bracket 3 Grade 4 Objective: Take out common factors to factorise Question 1 Factorise 3y 2 + 9y Question 2 Factorise 10x 2 15x... Question 3 Factorise 9f Question 4 Factorise 4x 2 20 Question 5 Factorise 8a 2 32a Question 6 Factorise 8y 2 4y 3

13 Question 7 Factorise 6x+6 Question 8 Factorise 8s+4t Question 9 Factorise ac 2 -c 4 Question 10 Factorise 13x 2 +3x TOTAL /10

14 Multiplying single brackets 3 Grade 4 Objective: Multiply a single term over a bracket Question 1 Expand the following x(y+2) Question 2 Expand the following a(b 2 +c) Question 3 Expand the following -2(m 2-3) Question 4 Expand the following -4(x+2) Question 5 Expand the following -3(x-8) + 5x (Total 2 mark)

15 Question 6 Expand the following -3(d-2)-4(d-2) Question 7 (Total 2 mark) Expand the following -3(y-10)-2(y-5) (Total 2 mark) TOTAL /10

16 PLC Papers Created For: year 9 revision booklet_half Term 1 Higher Algebra

17 Substitution 3 Grade 4 Solutions Objective: Substitute numerical values into formulae and expressions, including scientific formulae 1 Question 1 Complete this table of values. N 2n Question 2 Calculate the value of y when x = 2 are You must show your working. = (Total 2 mark) 4 y = y = 6 6 y = 4 (Total 3 mark)

18 Question 3 a. Work out the value of v when u = 110, a = 15 and t = 12 b. Work out the value of v when u = 25, a = -12 and t = -15 = + v = v = v = 290 v = 25 + ( 12) ( 15) v = v = 205 (Total 2 mark) Question 4 Work out the value of T when (a) p = 5 and (b) p = -5 = T T T T T = 2(25) 15 = = 35 = 2(25) + 15 = 65

19 Question 5 This formula is used to work out the cost, C, of tiling a floor with n tiles. C = n 2 56 tiles are needed to tile a floor. Can the floor be tiled for less than 275? You must show your working. 9n C = C = C = C = 277 Not possible with 275, short 2. (Total 2 mark) TOTAL /10

20 Using Formulae 3 Grade 3 Solutions Objective: Understand and use mathematical formulae Question 1 The Great Pyramid at Giza has height of 262 m and a square base of side 434m. Work out the volume of the Great Pyramid. V V V lwh = = 3 = Volume = m 3 (Total 2 marks) Question 2 A spherical soap bubble has a radius of 4 cm. Work out the volume of the bubble. V V V 4 3 = πr 3 4 = π 4 3 = Volume = m 3 (Total 2 marks) Question 3 A spherical ball is made from plastic. The external and internal radii of the ball are 50 cm and 49.5, respectively. Work out the volume of plastic used to make the ball. V V V 4 3 = πr = π 50 3 =

21 V V V 4 3 = πr = π = Volume of plastic needed = = cm 3 (Total 3 marks) Question 4 A ring shaped flowerbed is to be created around a circular lawn of radius 2.55m. Roses costing 4.20 are to be planted approximately every 50 cm around this flowerbed. How much money will be needed for roses? C = πd C = C = Roses = = Cost = = Cost = = Cost of 33 Roses = or Cost of 32 Roses = (Total 3 marks) TOTAL /10

22 Collecting like terms 3 Grade 4 Solutions Objective: Simplify algebraic expressions by collecting like terms Question 1 Simplify 8x - 3y 3x + 9y 5x+6y Question 2 (Total 2 marks) Simplify 19f f + 6f 24f Question 3 (Total 1 marks) Georgina, Samantha and Mason collect football stickers. Georgina has x stickers in her collection. Samantha has 9 stickers less than Georgina. Mason has 3 times as many stickers as Georgina. Write down an expression, in terms of x, for the total number of these stickers. Give you answer in its simplest form. x + ( x 9) + 3x = 5x 9 (Total 4 marks)

23 Question 4 The diagram shows a triangle. Write down an expression in terms of x and y, for the perimeter of this triangle. Give your answer in its simplest form. 4x 2y + 2x + 5y + 10y x = 5x + 13y 4x-2y 2x+5y 10y-x (Total 3 marks) TOTAL /10

24 Expressions 3 Grade 4 Solutions Objective: Use the correct algebraic notation in expressions and equations, including using brackets Question 1 x is shared equally between fifteen people. How much does each person receive? 15 Question 2 Write an expression for the total cost of four apples at a pence each and fourteen pears at b pence each. 4a+14b Question 3 Write an expression for the number that is four times smaller than n 4 Question 4 Nell buys c packets of sweets costing 55p per packet. He pays T pence altogether. Write a formula for the total cost of sweets =55 Question 5 Write down an equation for three bananas at h pence each and two grapefruit at k pence each when the total cost is 1.36? 3h+2 =136

25 Question 6 Chloe is x years old. Her sister is four years older. Her brother is twice her age. The sum of their ages is 44 years. a. Write an expression, in terms of x, for her sister s age. +4 b. Form an equation in x to work out Chloe s age. +( +4)+2 = =44 =10 Question 7 (Total 2 marks) Two angles have a difference of 20 o. Together they form a straight line. The smaller angle is x o a. Write down an expression for the larger angle, in terms of x. +20 b. Work out the value of x = =180 =80 TOTAL /10

26 Factorise single bracket 3 Grade 4 Solutions Objective: Take out common factors to factorise Question 1 Factorise 3y(y+3) 3y 2 + 9y Question 2 Factorise 5x(2x-3) 10x 2 15x... Question 3 Factorise 9f + 9 9(f+1) Question 4 Factorise 4x (x 2-5) Question 5 Factorise 8a 2 32a 8a(a-4)...

27 Question 6 Factorise 8y 2 4y 3 4y 2 (2 y) Question 7... Factorise 6x+6 6(x+1) Question 8 Total 1 mark) Factorise 8s+4t 4(2s - t) Question 9... Factorise ac 2 -c 4 c 2 (a-c 2 ) Question Factorise 13x 2 +3x x(13x+3) TOTAL /10

28 Multiplying single brackets 3 Grade 4 Solutions Objective: Multiply a single term over a bracket Question 1 Expand the following x(y+2) xy+2x Question 2 Expand the following a(b 2 +c) ab 2 +ac Question 3 Expand the following -2(m 2-3) -2m 2 +6 Question 4 Expand the following -4(x+2) -4x-8 Question 5 Expand the following -3(x-8) + 5x 2x+24 (Total 2 mark)

29 Question 6 Expand the following -3(d-2)-4(d-2) -3d+6-4d+8 = -7d+14 Question 7 (Total 2 mark) Expand the following -3(y-10)-2(y-5) -3y+30-2y+10 = -5y+40 (Total 2 mark) TOTAL /10