National 5 Revision Booklet Expressions and Formula

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1 National 5 Revision Booklet Epessions and Fomula This evision coves the following topics.. Suds. Indices. Significant Figues. Suds This is a non calculato eecise.. Simplify: a. b. c. d. e. f. g. h. i.. Simplify as fa as possible: a. b. c. d. e. f.. Add o subtact these suds and simplify as fa as possible: a. b. c. - d. e. f. g. h.

2 . Epand and simplify: a. b. c. d. e. f. 5. Epand and simplify: a. b. c. d. e. f. 6. Rationalise the denominato in each faction and simplify as fa as possible: a. b. c. d. e. f. 7. Etensions Wok - Use the conjugate to ationalise each denominato: a. b. c. d. 8. A ectangle has sides measuing. Calculate the aea of the ectangle. 9. The eact aea of a ectangle is Given that the beadth of the ectangle is equal to cm. show that the length is End of Suds eview.

3 . Indices This is a non calculato eecise 0. Simplify the following epessions, epessing you answes with positive indices: a. y y y b. p p p p q c. a a b b a d. e. p p 7 f. a a g. y y h. a b a i. y y j. 8 k. d d l. a 0 6a a m. n. o. p. q... Simplify the following epessions, epessing you answes with positive indices: a. 5 b. - c. a 7 d. p - e. d -5 - f. 8 g. h. i. j. k. ab l. y m. n. y o. a b. Epess without oot signs: a a b p c 5 d 5 e a b. Epess without oot signs Wite with positive indices fist whee necessay a e p5 y 5 b w c d a

4 . Evaluate each of the following without the use of a calculato q p o n m l k j i h g f e d c b a 5. Simplify each of the following by: changing oot signs to factional powes moving s onto the numeatos epanding backets whee necessay l k j i h g f e d c b a End of Indices Review. Significant Figues- This is a non calculato eecise 6. Round each numbe to the amount of significant figues asked: a b. 88 c d Calculate the following, giving you answes to significant figues: a. b. 0.6 c. 6 d. 9 End of Significant Figues eview. END OF REVIEW

5 National 5 Revision Booklet Epessions and Fomula This evision coves the following topics.. Epanding Backets. Factoising. Completing the Squae. Simplifying Algebaic Factions.5 Algebaic Factions Opeations. Epanding backets This is a non calculato eecise. Multiply out the backets below: a h + b c n n³ - n² d 7 + n e 5 y + y. Multiply out the backets below: a y + y + 5 b t - t - c + - d y y² +y + e m + m² +m - f - ² Multiply out the backets below: a + 5 ² b c 5² c b c ² d a + ² e - p² f +² - +² End of Epanding backets eview

6 . Factoising This is a non calculato eecise. Factoise: a a + 8 b 6 8 c a² + a d 6z² - 8z e ab ac f 5w² - 6w 5. Factoise: a c² - d² b w² - 6 c 8 - e² d a² - 00 e 9 - n² f y² - 5 g 9y² - 6 h 8² - a² i w² - 9² j k² k 6u² - 9v² l a² - m a² - b² n c² - 7d² o 6y² - 6t² p a² - ay² q 7 m² 6. Factoise: a a² + a + b ² c m² + m - 5 d w² - 6w + 9 e w² + w + f y² - y + g ² h u² + 7u 6 7. Factoise: a ² - 8 b p² - 9 c 5² - 5 d ² - y² e ² - 5 f ² + 6 g a² + a + b² End of Factoising eview. Completing the Squae This is a non calculato eecise 8. In pats a f add a numbe to make a pefect squae: a ² + b y² + y c m² - 6m

7 d w² - 0w e ² In pats g j, wite in the fom +p + q: f v² - v g ² h y² - y + i z² + 8z 0 j m² + m 0. Wite in the fom p +q²: Etension Wok a + - ² b 5 - ² c ² d 6 - ². Wite in the fom a+p² + q: Etension Wok a b 5a² - 0a 8 c n² + n + d m² - m 6. Simplifying Algebaic Factions. Simplify these epessions: End of Completing the Squae eview a 5 5 b a b c d 6 pq q e i 6abc a c a a a f a b b g h. Factoise fist then simplify these epessions a 5 b 9 c End of Simplifying Algebaic Factions Review

8 .5 Applying the fou opeations to algebaic factions. Simplify: a a b b b a c a by k k d 6 e 5 a ab f g y y Simplify: a d g j g 5 b 5 7 g c m n e f 7 + d a a h i y k 6. Simplify: e f a ef b c d s t t e s y y y f 5 p p 8 h p p 5 i a b 7 j b a k l 5 m 5 End of Applying fou opeations to Algebaic factions eview END OF REVIEW

9 National 5 Revision Booklet Epessions and Fomula MIXED EXERCISE This homewok coves the following topics.. Calculating Gadient. Length of Ac/Aea of Secto. Volumes of Solids. Finding Gadient- This is a non calculato eecise. Calculate the gadient of the lines dawn on the following gid:. Calculate the gadient of a line passing though the points A-,- and B8, End of Gadient eview.

10 . Acs and Sectos - This is a calculato eecise. Calculate the length of the mino ac AB and the aea of secto AOB in each of the following whee O is the cente of the cicle: A B A O 5cm 6cm 0 o O O B 7 o A 7cm B. Calculate the angle maked in the diagam if the aea of the secto is 75cm². Give angle to neaest whole degee. O P o cm Q 5. The length of ac XY is 8.5cm. Calculate the cicumfeence of the cicle: O X 0 o Y 8.5cm

11 . Acs and Sectos - This is a calculato eecise 6. The aea of secto PQ is.cm. Calculate the adius of the cicle: O P 60 o.cm Q 7. Fom the diagam below a Calculate the peimete of the secto XOY. b Calculate the aea of the cicle. X 8cm O 50 o Y End of Acs and Sectos Review

12 . Volume - This is a calculato eecise Impotant Fomulae: Volume of a cuboid V = l b h Volume of a pism V = Aea of face length height Volume of a cylinde V = π h Volume of a sphee V = π Volume of a cone V = ⅓ π h Volume of a pyamid V = ⅓ aea of base height V = ⅓ A h 8. Calculate the volume of each cuboid below: cm 6cm cm cm 0cm 6cm 8mm 8mm 8mm 9. Calculate the volume of each pism below: 9cm a b 0m cm cm 8m 6cm 0cm m

13 . Volume - This is a calculato eecise 5cm c d cm 6cm 5cm m m cm m 0. Calculate the volume of each cylinde: cm cm 6cm 8cm mm m 0mm m

14 . Volume- This is a calculato eecise. A cylinde has a diamete of 0 cm and a height of 6cm. Calculate its volume.. A cylinde has a diamete of.6m and a height of 80cm. Calculate its volume to the neaest cubic mete.. Calculate the volume of each sphee below ounding you answes to decimal place: a Radius = 6cm b Radius = m c Radius = 9mm d Radius = cm

15 . Volume- This is a calculato eecise. A sphee has a diamete of 8cm. Calculate its volume giving you answes to significant figues. 5. Calculate the volume of each cone below ounding you answes to decimal place: h Height = 6cm Radius = cm h Height = mm Radius = 8mm h Height = 5cm Radius = cm h Height = 6m Radius = m

16 . Volume- This is a calculato eecise 6. A cone has a base diamete of 8cm and a height of 5cm. Calculate the volume of the cone. 7. A cone has a base diamete of 0cm and a slant height of cm. Calculate the volume of the cone: s 8. A cone has a base adius of 9cm and a slant height of 5cm. Calculate the volume of the cone. 9. A pyamid has a squae base of side cm and a vetical height of 7cm. Calculate the volume of the pyamid to significant figues. 0. A pyamid has a ectangula base measuing 6mm by mm and a vetical height of 0mm. Calculate its volume.. A Binnit waste bin is in the shape of a cylinde with a hemi-sphee on top. The diamete of the bin is 6cm and the total height is 70cm. Calculate the volume of the bin giving you answe to the neaest lite: 70cm 6cm End of Volume Review

9.5 Volume of Pyramids

9.5 Volume of Pyramids 9.5 Volume of Pyamids and Cones Goal Find the volumes of pyamids and cones. Key Wods pyamid p. 49 cone p. 49 volume p. 500 In the puzzle below, you can see that the squae pism can be made using thee conguent